Ságodi, Á., & Park, I. M. (2026). Universal Approximation Theorems for Dynamical Systems with Infinite-Time Horizon Guarantees. In Advances in Neural Information Processing Systems (NeurIPS). https://openreview.net/forum?id=JFUIDA4w6C

@inproceedings{Sagodi2026b,
  author = {S\'agodi, \'Abel and Park, Il Memming},
  title = {Universal Approximation Theorems for Dynamical Systems with Infinite-Time Horizon Guarantees},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2026,
  month = dec,
  url = {https://openreview.net/forum?id=JFUIDA4w6C},
  url2 = {https://neurips.cc/virtual/2026/loc/sydney/poster/153723},
  eprint = {2602.08640},
  archiveprefix = {arXiv},
  primaryclass = {math.DS},
  abstract = {Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving multistability and limit cycles unaddressed. We prove that Neural ODEs achieve $\varepsilon$-$\delta$ closeness -- trajectories within error $\varepsilon$ except for initial conditions of measure $< \delta$ -- over the infinite time horizon $[0,\infty)$ for three target classes: (1) Morse-Smale systems (a structurally stable class) with hyperbolic fixed points, (2) Morse-Smale systems with hyperbolic limit cycles via exact period matching, and (3) systems with normally hyperbolic continuous attractors via discretization. We further establish a temporal generalization bound: $\varepsilon$-$\delta$ closeness implies Lp error $\leq \varepsilon^p + \delta \cdot D^p$ for all $t \geq 0$, bridging topological guarantees to training metrics. These results provide the first universal approximation framework for multistable infinite-horizon dynamics.},
}

Jeon, H., & Park, I. M. (2026). Beyond the attractor: closed-loop stimulation design for learning multistable neural dynamics. https://doi.org/10.64898/2026.10.05.756678

@unpublished{Jeon2026a,
  author = {Hyungju Jeon and Il Memming Park},
  title = {Beyond the attractor: closed-loop stimulation design for learning multistable neural dynamics},
  journal = {bioRxiv},
  year = 2026,
  month = oct,
  doi = {10.64898/2026.10.05.756678},
  url = {https://www.biorxiv.org/content/10.64898/2026.10.05.756678v1},
  abstract = {Online identification of nonlinear dynamical systems faces two challenges. Noisy, partial observations make the latent state difficult to estimate. Local attractors can also keep passive trajectories in regions that reveal little about the unknown dynamics. Both challenges commonly arise in closed-loop neural experiments where stimulation must be chosen from noisy spike counts, while neural activity may remain near a stable state unless stimulation drives it elsewhere. We address this problem by actively selecting inputs to collect informative observations during the experiment. We introduce PALDI (Planning-based Active Latent Dynamics Identification), which combines extended-Kalman state prediction, single-step Laplace state updates, blockwise Gaussian parameter updates, and finite-horizon planning. Its parameter expected-information-gain surrogate combines dynamics sensitivity with state Fisher information and discounts apparent parameter information when latent states are uncertain. We compare PALDI with nonadaptive inputs, a myopic policy, and two active baselines: the one-step D-optimal method FLEX and receding-horizon curiosity with uncertainty sampling. On a bistable Wilson-Cowan model of excitatory and inhibitory populations, PALDI approaches the true-model reference and remains strongest as the observation signal-to-noise ratio decreases or the readout geometry becomes biased. We then test identification in a spiking decision network where we use a reduced dynamics and observation model to approximate the data-generating process. PALDI reaches a median held-out prediction $R^2$ of 0.90, close to a fitted reference, and its model gives the highest change-of-mind success among identification policies. Information-guided finite-horizon planning is a practical strategy for identifying neural circuit dynamics with closed-loop stimulation.},
  keywords = {active learning, system identification, closed-loop stimulation, PALDI},
}

Ságodi, Á., & Park, I. M. (2026, July). Universal Approximation Theorems for Dynamical Systems with Infinite-Time Horizon Guarantees [Poster presentation]. Poster presented at XLVI Dynamics Days Europe, Lisbon, Portugal.

@misc{Sagodi2026c,
  author = {S\'agodi, \'Abel and Park, Il Memming},
  title = {Universal Approximation Theorems for Dynamical Systems with Infinite-Time Horizon Guarantees},
  howpublished = {Poster presented at {XLVI Dynamics Days Europe}, Lisbon, Portugal},
  year = 2026,
  month = {July},
  note = {Poster presentation},
}

Dowling, M., Jeon, H., Savin, C., & Park, I. M. (2026). Memory by Design: Probabilistic Sequence Layers. arXiv. https://doi.org/10.48550/arXiv.2605.31163

@unpublished{Dowling2026a,
  author = {Matthew Dowling and Hyungju Jeon and Cristina Savin and Il Memming Park},
  title = {Memory by Design: Probabilistic Sequence Layers},
  year = 2026,
  url = {http://arxiv.org/abs/2605.31163},
  eprint = {2605.31163},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {We introduce the design-model framework: a way to derive efficient recurrent sequence maps from explicit assumptions about memory. A design model writes evidence into memory by exact Bayesian filtering; a query-dependent readout produces a predictive distribution whose mean is the layer output. In our linear-Gaussian instantiation, the Bayesian Layer propagates both a mean and a covariance: the covariance tracks uncertainty over stored associations, steering writes toward uncertain directions, attenuating gains as evidence accumulates, and preserving confident memories. The same framework unifies several sub-quadratic recurrences. Linear attention, GLA, and Mamba-2/SSD are exact filters under one design model, whereas DeltaNet and related Delta-rule models arise as covariance-reset reductions under another. Restoring the covariance yields closed-form predictions for retrieval dynamics, verified empirically, and improves robustness beyond the training regime across controlled collision studies, learned associative recall, and the Zoology MQAR benchmark; distilling Bayesian Layers into a pretrained 340M Gated DeltaNet improves RULER long-context retrieval at matched compute.},
  keywords = {state-space models, sequence models, Bayesian filtering, associative memory},
}

Kautz, J., Vermani, A., & Park, I. M. (2026). Tracking Changes in Neural Dynamics over the Course of Learning [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Kautz2026a,
  author = {Justus Kautz and Ayesha Vermani and Il Memming Park},
  title = {Tracking Changes in Neural Dynamics over the Course of Learning},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2026,
}

Liang, A., Ságodi, A., Sokół, P., & Park, I. M. (2026). Symmetry-Regularized Learning of Continuous Attractor Dynamics [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Liang2026a,
  author = {Arthur Liang and \'Abel S\'agodi and Piotr Sok\'o\l{} and Il Memming Park},
  title = {Symmetry-Regularized Learning of Continuous Attractor Dynamics},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2026,
  poster_no = {3-213},
}

Park, I. M., & Pillow, J. W. (in press). Bayesian Efficient Coding. PLOS Computational Biology. https://www.biorxiv.org/content/10.1101/178418

@article{Park2017a,
  author = {Park, Il Memming and Pillow, Jonathan W.},
  title = {{B}ayesian Efficient Coding},
  journal = {{PLOS} Computational Biology},
  year = 2026,
  note = {In press},
  url = {https://www.biorxiv.org/content/10.1101/178418},
  eprint = {178418},
  archiveprefix = {bioRxiv},
  abstract = {The efficient coding hypothesis, which proposes that neurons are optimized to maximize information about the environment, has provided a guiding theoretical framework for sensory and systems neuroscience. More recently, a theory known as the Bayesian Brain hypothesis has focused on the brain's ability to integrate sensory and prior sources of information in order to perform Bayesian inference. Although pieces of a connection between these two hypotheses have appeared in prior work, a general formulation that treats the optimality criterion as an arbitrary functional of the posterior distribution -- and thereby admits both information-theoretic and non-information-theoretic objectives within a single formalism -- has remained largely implicit. Here we make this formulation explicit, developing a Bayesian theory of efficient coding that defines Bayesian efficient codes in terms of four basic ingredients: (1) a stimulus prior distribution; (2) an encoding model; (3) a capacity constraint, specifying a neural resource limit; and (4) a loss functional, quantifying the desirability or undesirability of various posterior distributions. Classic efficient codes arise as the special case in which the loss functional is the posterior entropy, leading to a code that maximizes mutual information, but alternate loss functionals give solutions that differ dramatically from information-maximizing codes. Within this framework we introduce {\it covtropy}, a novel family of posterior-functional losses parameterized by a single exponent, and use it to show that decorrelation of sensory inputs -- optimal under classic efficient codes in low-noise settings -- can be disadvantageous for objectives that penalize large errors. We then reanalyze Laughlin's seminal data on contrast coding in the blowfly large monopolar cell, and find that the measured response nonlinearity is better explained by minimizing $L_p$ reconstruction error with $p = 1/2$ than by infomax, overturning a forty-year-old interpretation. Bayesian efficient coding thus enlarges the family of normatively optimal codes and provides a more general framework for understanding the design principles of sensory systems.},
  data = {https://doi.org/10.5281/zenodo.3970842},
  keywords = {bayesian-efficient-coding, preprint, tuning-curve},
}

Park, I. M., Vermani, A., de Polavieja, G. G., Gallego, J. Á., Esfahany, K., Saxena, S., Orger, M., Ijspeert, A., Dowling, M., McNamee, D., Turaga, S. C., Mainen, Z., Paton, J. J., & Renart, A. (2026). Integrative Neurocybernetic Modeling in the Era of Large-Scale Neuroscience. arXiv. https://doi.org/10.48550/arXiv.2604.23903

@unpublished{Park2026a,
  author = {I. Memming Park and Ayesha Vermani and Gonzalo G. de Polavieja and Juan \'Alvaro Gallego and Kathleen Esfahany and Shreya Saxena and Michael Orger and Auke Ijspeert and Matthew Dowling and Daniel McNamee and Srinivas C. Turaga and Zachary Mainen and Joseph J. Paton and Alfonso Renart},
  title = {Integrative Neurocybernetic Modeling in the Era of Large-Scale Neuroscience},
  year = 2026,
  url = {http://arxiv.org/abs/2604.23903},
  eprint = {2604.23903},
  archiveprefix = {arXiv},
  abstract = {Large-scale neuroscience is generating rich datasets across animals, brain areas and behavioral contexts, yet our modeling efforts remains fragmented across isolated experiments. We argue that understanding behavior requires integrative neurocybernetic models: understandable dynamical models that capture the closed-loop coupling of brain, body and environment, treat the brain as a controller pursuing latent objectives, represent structured variation across scales, and scale to heterogeneous datasets. Such models shift the goal from predicting neural recordings in isolation to inferring the organizing principles that govern neural and behavioral dynamics. We outline a practical route toward this goal by combining nonlinear state-space models and meta-dynamical extensions with scalable inference, knowledge distillation, mixed open- and closed-loop training, and connectomics-informed architectures. By pooling complementary constraints from recordings, behavior, perturbations and anatomy, integrative neurocybernetic models can provide statistical amplification, few-shot generalization, and mechanistic insight into shared dynamical structure, individual variation, and the control objectives that govern behavior. This agenda offers a model-centric path from fragmented data to a mechanistic science of how brains produce behavior.},
  keywords = {neurocybernetics, cybernetics, perspective},
}

Ságodi, Á., & Park, I. M. (2026). Dynamical archetype analysis: Autonomous computation [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Sagodi2026a,
  author = {S\'agodi, \'Abel and Park, Il Memming},
  title = {Dynamical archetype analysis: Autonomous computation},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2026,
  abstract = {The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to organize and incrementally build intuition. We argue that systems with the same effective behavior should be abstracted by their ideal representative, i.e., archetype, defined by its asymptotic dynamical structure. We propose a library of archetypical computations and a new measure of dissimilarity that allows us to group systems based on their effective behavior by explicitly considering both deformations that break topological conjugacy as well as diffeomorphisms that preserve it. The proposed dissimilarity can be estimated from observed trajectories. Numerical experiments demonstrate our method's ability to overcome previously reported fragility of existing (dis)similarity measures for approximate continuous attractors and high-dimensional recurrent neural networks. Although our experiments focus on working memory systems, our theoretical approach naturally extends to general mechanistic interpretation of recurrent dynamics in both biological and artificial neural systems. We argue that abstract dynamical archetypes, rather than detailed dynamical systems, offer a more useful vocabulary for describing neural computation.},
}

Schaffer, E., Saxena, S., Keller, R., Lazzari, J., McGill, M., Nayebi, A., Olivos-Castillo, I., Park, I. M., Perich, M. G., Pitkow, X., & Turaga, S. C. (in press). Embodied Computation: How does embodiment impact sensorimotor and cognitive processing? The Journal of Neuroscience.

@article{Schaffer2026a,
  author = {Evan Schaffer and Shreya Saxena and Reece Keller and John Lazzari and Mason McGill and Aran Nayebi and Itzel Olivos-Castillo and Il Memming Park and Matthew G. Perich and Xaq Pitkow and Srinivas C. Turaga},
  title = {Embodied Computation: How does embodiment impact sensorimotor and cognitive processing?},
  journal = {The Journal of Neuroscience},
  year = 2026,
  note = {In press},
  keywords = {embodiment, sensorimotor, cognition, review, symposium},
}

Ságodi, Á., & Park, I. M. (2025). Dynamical archetype analysis: Autonomous computation. arXiv. https://doi.org/10.48550/arXiv.2507.05505

@unpublished{Sagodi2025b,
  author = {S\'agodi, \'Abel and Park, Il Memming},
  title = {Dynamical archetype analysis: Autonomous computation},
  year = 2025,
  month = jul,
  url = {http://arxiv.org/abs/2507.05505},
  eprint = {2507.05505},
  archiveprefix = {arXiv},
  primaryclass = {math.DS},
  abstract = {The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to organize and incrementally build intuition. We argue that systems with the same effective behavior should be abstracted by their ideal representative, i.e., archetype, defined by its asymptotic dynamical structure. We propose a library of archetypical computations and a new measure of dissimilarity that allows us to group systems based on their effective behavior by explicitly considering both deformations that break topological conjugacy as well as diffeomorphisms that preserve it. The proposed dissimilarity can be estimated from observed trajectories. Numerical experiments demonstrate our method's ability to overcome previously reported fragility of existing (dis)similarity measures for approximate continuous attractors and high-dimensional recurrent neural networks. Although our experiments focus on working memory systems, our theoretical approach naturally extends to general mechanistic interpretation of recurrent dynamics in both biological and artificial neural systems. We argue that abstract dynamical archetypes, rather than detailed dynamical systems, offer a more useful vocabulary for describing neural computation.},
}

Nassar, J., Zhao, Y., Jordan, I., & Park, I. M. (2025). System and method of model-based machine learning for non-episodic state space exploration (U.S. Patent Application Publication No. 20250209344 A1). United States Patent and Trademark Office. https://patentimages.storage.googleapis.com/27/07/f1/3ce01937875384/US20250209344A1.pdf

@misc{Nassar2025patent,
  author = {Nassar, Josue and Zhao, Yuan and Jordan, Ian and Park, Il Memming},
  title = {System and method of model-based machine learning for non-episodic state space exploration},
  journal = {United States Patent and Trademark Office},
  year = 2025,
  month = jun,
  number = {20250209344:A1},
  url = {https://patentimages.storage.googleapis.com/27/07/f1/3ce01937875384/US20250209344A1.pdf},
  abstract = {A system and method of conducting non-episodic state space exploration of a world, the world being a real-world system having one or more dimensions, including: receiving a current state of an agent observed in relation to its interaction with the world; updating one or more parameters of a dynamic model that approximates the world based on the current state of the agent, wherein the parameters as updated improve approximation of the world; generating an intrinsic reward associated with the exploration by the agent based on a closest distance of the current state of the agent in relation to a previous state of one or more previous states of the agent in its exploration of the world; and generating a control from a sequence of actions based on the dynamic model to maximize the intrinsic reward, wherein execution of the control perturbs the current state of the agent in its exploration of the world.},
}

Vermani, A., Nassar, J., Jeon, H., Dowling, M., & Park, I. M. (2025). Meta-dynamical state space models for integrative neural data analysis. In International Conference on Learning Representations (ICLR). https://openreview.net/forum?id=SRpq5OBpED

@inproceedings{Vermani2024b,
  author = {Vermani, Ayesha and Nassar, Josue and Jeon, Hyungju and Dowling, Matthew and Park, Il Memming},
  title = {Meta-dynamical state space models for integrative neural data analysis},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = 2025,
  month = apr,
  url = {https://openreview.net/forum?id=SRpq5OBpED},
  eprint = {2410.05454},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel settings. However, there has been limited work exploiting the shared structure in neural activity during similar tasks for learning latent dynamics from neural recordings. Existing approaches are designed to infer dynamics from a single dataset and cannot be readily adapted to account for statistical heterogeneities across recordings. In this work, we hypothesize that similar tasks admit a corresponding family of related solutions and propose a novel approach for meta-learning this solution space from task-related neural activity of trained animals. Specifically, we capture the variabilities across recordings on a low-dimensional manifold which concisely parametrizes this family of dynamics, thereby facilitating rapid learning of latent dynamics given new recordings. We demonstrate the efficacy of our approach on few-shot reconstruction and forecasting of synthetic dynamical systems, and neural recordings from the motor cortex during different arm reaching tasks.},
}

Filipe, C., Elmakki, M., Costa-Ferreira, G., & Park, I. M. (2025). Conditional diffusion framework for analyzing neural dynamics across multiple contexts [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Filipe2025a,
  author = {Carolina Filipe and Mahmoud Elmakki and Guilherme Costa-Ferreira and Il Memming Park},
  title = {Conditional diffusion framework for analyzing neural dynamics across multiple contexts},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2025,
}

Filipe, A. C., Bernaerts, Y., Ságodi, A., Elmakki, M., & Park, I. M. (2025). One Model to Train Them All: A Unified Diffusion Framework for Multi-Context Neural Population Forecasting. https://openreview.net/forum?id=R9feGbYRG7

@unpublished{Filipe2025b,
  author = {A. Carolina Filipe and Yves Bernaerts and \'Abel S\'agodi and Mahmoud Elmakki and I. Memming Park},
  title = {One Model to Train Them All: A Unified Diffusion Framework for Multi-Context Neural Population Forecasting},
  year = 2025,
  url = {https://openreview.net/forum?id=R9feGbYRG7},
}

Liang, A., Ságodi, A., Sokół, P., & Park, I. M. (2025). Symmetry-Regularized Learning of Continuous Attractor Dynamics [Conference abstract]. NeurIPS 2025 Workshop on Symmetry and Geometry in Neural Representations (NeurReps 2025). https://openreview.net/forum?id=W8Gf7CYCo8

@inproceedings{Liang2025a,
  author = {Arthur Liang and \'Abel S\'agodi and Piotr Sok\'o\l{} and Il Memming Park},
  title = {Symmetry-Regularized Learning of Continuous Attractor Dynamics},
  booktitle = {NeurIPS 2025 Workshop on Symmetry and Geometry in Neural Representations (NeurReps 2025)},
  year = 2025,
  note = {(4p extended abstract)},
  url = {https://openreview.net/forum?id=W8Gf7CYCo8},
  abstract = {Neural population dynamics exhibit rich geometric structure, yet prevailing computational models often overlook this by primarily accounting for variability in the data. We show that incorporating prior knowledge about dynamical symmetries yields efficient and interpretable models. Focusing on ring attractor dynamics---canonical circuits that are approximately equivariant under planar rotations---we introduce a symmetry-regularized variational state space model. Our method augments the standard variational objective with a symmetry penalty, encouraging the learned dynamical system to respect rotational invariance. We demonstrate that this regularization preserves predictive performance while yielding parsimonious models with interpretable latent dynamics. This framework establishes a principled approach for embedding symmetry priors into neural dynamical system learning, highlighting how exploiting geometric structure can improve both scientific insight and model generalization.},
}

Ságodi, Á., Martín-Sánchez, G., Sokół, P., & Park, I. M. (2025). Approximate continuous attractor theory [Conference abstract]. Computational and Systems Neuroscience (COSYNE). https://www.world-wide.org/cosyne-25/approximate-continuous-attractor-25422ef2/

@inproceedings{Sagodi2025a,
  author = {S\'agodi, \'Abel and Mart\'in-S\'anchez, Guillermo and Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {Approximate continuous attractor theory},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2025,
  url = {https://www.world-wide.org/cosyne-25/approximate-continuous-attractor-25422ef2/},
  poster_no = {3-113},
}

Vermani, A., Nassar, J., Jeon, H., Dowling, M., & Park, I. M. (2025). Meta-dynamical state space models for integrative neural data analysis [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Vermani2025a,
  author = {Ayesha Vermani and Josue Nassar and Hyungju Jeon and Matthew Dowling and Il Memming Park},
  title = {Meta-dynamical state space models for integrative neural data analysis},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2025,
  abstract = {Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel settings. However, there has been limited work exploiting the shared structure in neural activity during similar tasks for learning latent dynamics from neural recordings. Existing approaches are designed to infer dynamics from a single dataset and cannot be readily adapted to account for statistical heterogeneities across recordings. In this work, we hypothesize that similar tasks admit a corresponding family of related solutions and propose a novel approach for meta-learning this solution space from task-related neural activity of trained animals. Specifically, we capture the variabilities across recordings on a low-dimensional manifold which concisely parametrizes this family of dynamics, thereby facilitating rapid learning of latent dynamics given new recordings. We demonstrate the efficacy of our approach on few-shot reconstruction and forecasting of synthetic dynamical systems, and neural recordings from the motor cortex during different arm reaching tasks.},
}

Vermani, A. (2025). Identifying Invariant Representations underlying Neural Computation [Doctoral dissertation]. NOVA Repository. http://hdl.handle.net/10362/190610

@phdthesis{Vermani2025b,
  author = {Vermani, Ayesha},
  title = {Identifying Invariant Representations underlying Neural Computation},
  publisher = {NOVA Repository},
  year = 2025,
  url = {http://hdl.handle.net/10362/190610},
}

Dowling, M., Zhao, Y., & Park, I. M. (2024). eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling. In Advances in Neural Information Processing Systems (NeurIPS). https://doi.org/10.52202/079017-0430

@inproceedings{Dowling2024b,
  author = {Dowling, Matthew and Zhao, Yuan and Park, Il Memming},
  title = {{eXponential} {FAmily} Dynamical Systems ({XFADS}): Large-scale nonlinear Gaussian state-space modeling},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2024,
  month = dec,
  doi = {10.52202/079017-0430},
  url = {https://openreview.net/forum?id=Ln8ogihZ2S},
  eprint = {2403.01371},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {State-space graphical models and the variational autoencoder framework provide a principled apparatus for learning dynamical systems from data. State-of-the-art probabilistic approaches are often able to scale to large problems at the cost of flexibility of the variational posterior or expressivity of the dynamics model. However, those consolidations can be detrimental if the ultimate goal is to learn a generative model capable of explaining the spatiotemporal structure of the data and making accurate forecasts. We introduce a low-rank structured variational autoencoding framework for nonlinear Gaussian state-space graphical models capable of capturing dense covariance structures that are important for learning dynamical systems with predictive capabilities. Our inference algorithm exploits the covariance structures that arise naturally from sample based approximate Gaussian message passing and low-rank amortized posterior updates -- effectively performing approximate variational smoothing with time complexity scaling linearly in the state dimensionality. In comparisons with other deep state-space model architectures our approach consistently demonstrates the ability to learn a more predictive generative model. Furthermore, when applied to neural physiological recordings, our approach is able to learn a dynamical system capable of forecasting population spiking and behavioral correlates from a small portion of single trials.},
  arxivid = {2403.01371},
  code = {https://github.com/catniplab/xfads},
}

Ságodi, Á., Martín-Sánchez, G., Sokół, P., & Park, I. M. (2024). Back to the continuous attractor. In Advances in Neural Information Processing Systems (NeurIPS). https://doi.org/10.52202/079017-2136

@inproceedings{Sagodi2024a,
  author = {S\'agodi, \'Abel and Mart\'in-S\'anchez, Guillermo and Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {Back to the continuous attractor},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2024,
  month = dec,
  doi = {10.52202/079017-2136},
  url = {https://openreview.net/forum?id=fvG6ZHrH0B},
  url2 = {https://papers.neurips.cc/paper_files/paper/2024/hash/7b78a2a7360d5a9ad750834dc5a33bfb-Abstract-Conference.html},
  eprint = {2408.00109},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general--they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurally stable forms. Although their asymptotic behaviors to maintain memory are categorically distinct, their finite-time behaviors are similar. We build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the persistent manifold that survives the seemingly destructive bifurcation. Moreover, recurrent neural networks trained on analog memory tasks display approximate continuous attractors with predicted slow manifold structures. Therefore, continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory.},
  arxivid = {2408.00109},
}

Jeon, H., & Park, I. M. (2024). Quantifying signal-to-noise ratio in neural latent trajectories via Fisher information. In European Signal Processing Conference.

@inproceedings{Jeon2024b,
  author = {Hyungju Jeon and Il Memming Park},
  title = {Quantifying signal-to-noise ratio in neural latent trajectories via {F}isher information},
  booktitle = {European Signal Processing Conference},
  year = 2024,
  month = aug,
  eprint = {2408.08752},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are useful for building brain machine interfaces and understanding the neural computation underlying meaningful behavior. We derive a practical upper bound to the signal-to-noise ratio (SNR) of inferred neural latent trajectories using Fisher information. We show that the SNR bound is proportional to the overdispersion factor and the Fisher information per neuron. Further numerical experiments show that inference methods that exploit the temporal regularities can achieve higher SNRs that are proportional to the bound. Our results provide insights for fitting models to data, simulating neural responses, and design of experiments.},
  code = {https://github.com/catniplab/neurofisherSNR},
}

Vermani, A., Park, I. M., & Nassar, J. (2024). Leveraging generative models for unsupervised alignment of neural time series data. In International Conference on Learning Representations (ICLR). https://openreview.net/forum?id=9zhHVyLY4K

@inproceedings{Vermani2023b,
  author = {Ayesha Vermani and Il Memming Park and Josue Nassar},
  title = {Leveraging generative models for unsupervised alignment of neural time series data},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = 2024,
  month = may,
  url = {https://openreview.net/forum?id=9zhHVyLY4K},
  abstract = {Large scale inference models are widely used in neuroscience to extract latent representations from high-dimensional neural recordings. Due to the statistical heterogeneities between sessions and animals, a new model is trained from scratch to infer the underlying dynamics for each new dataset. This is computationally expensive and does not fully leverage all the available data. Moreover, as these models get more complex, they can be challenging to train. In parallel, it is becoming common to use pre-trained models in the machine learning community for few shot and transfer learning. One major hurdle that prevents the re-use of generative models in neuroscience is the complex spatio-temporal structure of neural dynamics within and across animals. Interestingly, the underlying dynamics identified from different datasets on the same task are qualitatively similar. In this work, we exploit this observation and propose a source-free and unsupervised alignment approach that utilizes the learnt dynamics and enables the re-use of trained generative models. We validate our approach on simulations and show the efficacy of the alignment on neural recordings from the motor cortex obtained during a reaching task.},
}

Dowling, M., Zhao, Y., & Park, I. M. (2024). XFADS: Predicting single-trial cued behavior solely from preparatory activity [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Dowling2024a,
  author = {Matthew Dowling and Yuan Zhao and Il Memming Park},
  title = {{XFADS}: Predicting single-trial cued behavior solely from preparatory activity},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2024,
  abstract = {Consider a classic neuroscience dataset --- comprising recordings from monkey's motor cortex during a center-out reaching task. A prevailing hypothesis elucidating the coordinated neural population dynamics in this task suggests that the initial condition of a dynamical system, steering muscle movement, is set during the preparatory phase of the trial. The motor cortex, released from the initial condition and governed by the dynamical system, controls the muscles orchestrating the monkey's movement. However, existing cutting-edge tools often rely on extraneous-input-driven dynamical systems, which tend to learn control inputs anti-causally or lack a dynamic systems model entirely. This led us to explore the feasibility of learning the hypothesized autonomous dynamical system, exclusively from neural data, that is capable of causally predicting, initiated before movement onset, monkey's reaching. Consequently, we developed a novel Bayesian inference framework, eXponential FAmily Dynamical System (XFADS), aimed at learning highly expressive dynamical systems from neural data. Remarkably, we confirm the long standing autonomous nature of motor cortex activity associated with the planned reach behavior through single-trial causal forecasting. Specifically, our inferred stochastic dynamics revealed that the causally-inferred latent states, derived without any prior knowledge of the target or future behavior, were nearly as effective in predicting the monkey's arm velocity as the latent states utilizing the entire trial data.},
}

Filipe, A. C., & Park, I. M. (2024). NeuroTask: A benchmark dataset for multi-task neural analysis [Conference abstract]. Bernstein Conference. https://doi.org/10.12751/nncn.bc2024.020

@inproceedings{Filipe2024a,
  author = {Filipe, A. Carolina and Park, Il Memming},
  title = {{NeuroTask}: A benchmark dataset for multi-task neural analysis},
  booktitle = {Bernstein Conference},
  year = 2024,
  doi = {10.12751/nncn.bc2024.020},
  url = {https://abstracts.g-node.org/conference/BC24/abstracts#/uuid/ccb5dd62-403b-4da0-a839-2652ab70ac28},
  code = {https://github.com/catniplab/NeuroTask/tree/nwb},
  poster_no = {I 1},
}

Jeon, H., Dowling, M., & Park, I. M. (2024). Closed-loop active sensing for nonlinear system identification in attractor dynamics disorders [Conference abstract]. European Conference on Brain Stimulation.

@conference{Jeon2024a,
  author = {Hyungju Jeon and Matthew Dowling and Il Memming Park},
  title = {Closed-loop active sensing for nonlinear system identification in attractor dynamics disorders},
  booktitle = {European Conference on Brain Stimulation},
  year = 2024,
  note = {(oral presentation)},
  abstract = {Neurological disorders pose multifaceted challenges for intervention due to their diverse root causes, ranging from cellular, pathogenic, or metabolic dysfunctions to more recently discovered disruptions in complex neuronal dynamics. While conventional treatment methods have demonstrated efficacy in conditions with known cellular or metabolic dysfunctions, they fall short in disorders arising from system-level dynamics disruptions, such as movement disorders, and psychiatric conditions like schizophrenia. However, identifying the underlying mechanisms of such disturbances in system-level dynamics is often hindered by modern data-driven challenges, particularly regarding the size of datasets. The sheer volume of neural recordings measuring the synchronous activity of thousands of neurons simultaneously can impede timely and efficient identification of underlying mechanisms. To address these challenges, we propose a real-time closed-loop active sensing for nonlinear system identification. Our approach aims to expedite the throughput of current experimental design paradigms and bridge the gap between traditional treatments and the complexities of brain-system dynamics. In particular, we employ Bayesian experimental design to accelerate inference of underlying neural dynamics and their changes by introducing structured perturbation to the system. We consider a synthetic test-bed mimicking neurological disorders characterized by the emergence of disease state attractors; then, we show how statistically informed interventions in the form of carefully chosen perturbations can be used to identify the dynamics of the attractor and restore regularity of the population level neural dynamics by driving the neural state away from disease state attractors.},
}

Park, I. M. (2024). Persistent activity bump on a ring without a continuous ring attractor [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2024a,
  author = {Il Memming Park},
  title = {Persistent activity bump on a ring without a continuous ring attractor},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2024,
  abstract = {We propose a robust recurrent memory mechanism for integrating and maintaining head direction without a ring attractor. The ring attractor is a popular theoretical mechanism for maintaining a continuous internal representation of a periodic variable. For instance, they are used to describe the neural dynamics underlying head direction cells, grid cells, and visual working memory. At the same time, it is well-known that mathematically, continuous attractors are prone to fine tuning, where small changes in the connectivity or biophysical parameters lead to the destruction of the mechanism. We describe an alternative, robust mechanism for working memory of a periodic variable using the theory of stable limit cycles. In particular, we detail a biophysical implementation that can explain the bump of activity observed over the ellipsoid body of insects. The content of working memory is stored in the relative phase difference between two independent oscillators, whose periods are constrained by conduction delay. A phase independent readout is achieved through a delay line and nonlinear coincidence detectors that can be mapped onto the readout system, i.e., the ellipsoid body. Our theory makes several strong predictions: the bump of activity on the ellipsoid body is tightly periodic on a short time scale, is robust to partial lesions, and exhibits small, consistent systematic drifts due to misadjustments within each animal. Furthermore, we investigate the impact of diffusion in information encoding and memory due to various noise sources.},
}

Ságodi, Á., Martín-Sánchez, G., Sokół, P., & Park, I. M. (2024). Slow manifold dynamics for working memory are near continuous attractors [Conference abstract]. Bernstein Conference. https://doi.org/10.12751/nncn.bc2024.076

@inproceedings{Sagodi2024b,
  author = {S\'agodi, \'Abel and Mart\'in-S\'anchez, Guillermo and Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {Slow manifold dynamics for working memory are near continuous attractors},
  booktitle = {Bernstein Conference},
  year = 2024,
  doi = {10.12751/nncn.bc2024.076},
  url = {https://abstracts.g-node.org/conference/BC24/abstracts#/uuid/5964bd61-91e8-4d1a-a9ca-e6d137f456b4},
  poster_no = {I 59},
}

Vermani, A., Dowling, M., Jeon, H., Jordan, I., Nassar, J., Bernaerts, Y., Zhao, Y., Van Vaerenbergh, S., & Park, I. M. (2024). Real-time machine learning strategies for a new kind of neuroscience experiments. In European Signal Processing Conference.

@inproceedings{Vermani2024a,
  author = {Ayesha Vermani and Matthew Dowling and Hyungju Jeon and Ian Jordan and Josue Nassar and Yves Bernaerts and Yuan Zhao and Van Vaerenbergh, Steven and Il Memming Park},
  title = {Real-time machine learning strategies for a new kind of neuroscience experiments},
  booktitle = {European Signal Processing Conference},
  year = 2024,
  eprint = {2409.01280},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
}

Park, I. M., Ságodi, Á., & Sokół, P. A. (2023). Persistent learning signals and working memory without continuous attractors. arXiv. https://doi.org/10.48550/arXiv.2308.12585

@unpublished{Park2023a,
  author = {Park, Il Memming and S{\'a}godi, {\'A}bel and Sok{\'o}{\l}, Piotr Aleksander},
  title = {Persistent learning signals and working memory without continuous attractors},
  year = 2023,
  month = aug,
  eprint = {2308.12585},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support useful learning signals necessary to adapt to changes in the temporal structure of the environment. We show that in addition to the continuous attractors that are widely implicated, periodic and quasi-periodic attractors can also support learning arbitrarily long temporal relationships. Unlike the continuous attractors that suffer from the fine-tuning problem, the less explored quasi-periodic attractors are uniquely qualified for learning to produce temporally structured behavior. Our theory has broad implications for the design of artificial learning systems and makes predictions about observable signatures of biological neural dynamics that can support temporal dependence learning and working memory. Based on our theory, we developed a new initialization scheme for artificial recurrent neural networks that outperforms standard methods for tasks that require learning temporal dynamics. Moreover, we propose a robust recurrent memory mechanism for integrating and maintaining head direction without a ring attractor.},
  arxivid = {2308.12585},
}

Dowling, M., Zhao, Y., & Park, I. M. (2023). Linear time GPs for inferring latent trajectories from neural spike trains. In International Conference on Machine Learning (ICML). https://openreview.net/forum?id=1hWB5XEUMa

@inproceedings{Dowling2023c,
  author = {Matthew Dowling and Yuan Zhao and Il Memming Park},
  title = {Linear time {GP}s for inferring latent trajectories from neural spike trains},
  booktitle = {International Conference on Machine Learning (ICML)},
  year = 2023,
  month = Jul,
  url = {https://openreview.net/forum?id=1hWB5XEUMa},
  eprint = {2306.01802},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.},
  arxivid = {2306.01802},
}

Kepple, D. R., Lee, D. W., Isler, I. V., Rajan, K., Park, I. M., & Lee, D. D. (2023). Jointly learning visual motion and confidence from local patches in event cameras (U.S. Patent No. 11,694,304). United States Patent and Trademark Office. https://patents.google.com/patent/US11694304B2/en

@misc{Kepple2023a,
  author = {Kepple, Daniel Robert and Lee, Dae Won and Isler, Ibrahim Volkan and Rajan, Kanaka and Park, Il Memming and Lee, Daniel Dongyuel},
  title = {Jointly learning visual motion and confidence from local patches in event cameras},
  journal = {United States Patent and Trademark Office},
  year = 2023,
  month = jul,
  number = {11,694,304},
  note = {Assignee: Samsung Electronics},
  url = {https://patents.google.com/patent/US11694304B2/en},
  abstract = {A method may include obtaining a set of events, of a set of pixels of a dynamic vision sensor, associated with an object; determining a set of voltages of the set of pixels, based on the set of events; generating a set of images, based on the set of voltages of the set of pixels; inputting the set of images into a first neural network configured to output a visual motion estimation of the object; inputting the set of images into a second neural network configured to output a confidence score of the visual motion estimation output by the first neural network; obtaining the visual motion estimation of the object and the confidence score of the visual motion estimation of the object, based on inputting the set of images into the first neural network and the second neural network; and providing the visual motion estimation of the object and the confidence score.},
}

Stone, I. R., Sagiv, Y., Park, I. M., & Pillow, J. W. (2023). Spectral learning of Bernoulli linear dynamical systems models for decision-making. Transactions on Machine Learning Research. https://openreview.net/forum?id=giw2vcAhiH

@article{Stone2023b,
  author = {Stone, Iris R and Sagiv, Yotam and Park, Il Memming and Pillow, Jonathan W},
  title = {Spectral learning of {B}ernoulli linear dynamical systems models for decision-making},
  journal = {Transactions on Machine Learning Research},
  year = 2023,
  month = Jul,
  url = {https://openreview.net/forum?id=giw2vcAhiH},
  eprint = {2303.02060},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making and discrete stochastic processes such as binned neural spike trains. Here, we develop a spectral learning method for fast, efficient fitting of Bernoulli latent linear dynamical system (LDS) models. Our approach extends traditional subspace identification methods to the Bernoulli setting via a transformation of the first and second sample moments. This results in a robust, fixed-cost estimator that avoids the hazards of local optima and the long computation time of iterative fitting procedures like the expectation-maximization (EM) algorithm. In regimes where data is limited or assumptions about the statistical structure of the data are not met, we demonstrate that the spectral estimate provides a good initialization for Laplace-EM fitting. Finally, we show that the estimator provides substantial benefits to real world settings by analyzing data from mice performing a sensory decision-making task.},
  arxivid = {2303.02060},
  code = {https://github.com/irisstone/bestLDS},
  issn = {2835-8856},
}

Arora, T. (2023). Exploring the expressive power of latent variable models [Unpublished master's thesis]. Stony Brook University.

@mastersthesis{Arora2023a,
  author = {Tushar Arora},
  title = {Exploring the expressive power of latent variable models},
  school = {Stony Brook University},
  year = 2023,
  month = may,
  abstract = {Advancements in neural recording technologies has allowed us to collect high dimensional observations by recording thousands of neurons at the same time. However, experimental evidence has shown that high dimensional neural activity may be confined to a manifold of much lower dimension. This phenomenon has been observed for example in context dependent decision making tasks, and delay modulated tasks. Latent variable models (LVMs) are powerful models used to recover the low dimensional dynamics. Some popular variants of LVMs are factor analysis, state space models (SSM), principal component analysis (static SSM), etc. We will be concentrating on non-linear SSMs which are expressive enough to capture complex dynamics while remaining interpretable. Inferring dynamics from temporal data is integral to many applications in machine learning and neuroscience, but the complexity and expressive power of the dynamics model can vary. In Machine Learning applications, sequence models for language and video use large recurrent networks where the complexity of the dynamics model is tied to the dimensionality of the states and the number of the recurrent units. In these models increasing the state space and number of units helps increase the expressive power. Meanwhile for neuroscience applications, increasing the dimensionality of state space and recurrent units is not desired as the end goal is to understand the dynamics and the topological properties. Given the postulate that computations underlying high dimensional observations live on a low dimensional manifold, it is detrimental to have a large state space dimension. When using these methods, ideally we should be able to keep the dimensionality of the latent variables/hidden variables/factors low. In this work we show that (1) prediction measures for goodness of learned dynamics model is more informative quantification and should be the standard measure for testing generative models; (2) using dynamics model that decouple expressive power from state space dimensionality makes model selection easier, produce better long term predictions, and we claim it makes the model more interpretable.},
}

Sokół, P. (2023). Geometry of learning and representation in neural networks [Unpublished doctoral dissertation]. Stony Brook University.

@phdthesis{Sokol2023b,
  author = {Piotr Sok{\'o}{\l}},
  title = {Geometry of learning and representation in neural networks},
  school = {Stony Brook University},
  year = 2023,
  month = may,
  abstract = {Advances in artificial neural networks and computational neuroscience highlight pertinent properties of latent representations, such as their dimensionality and topology, and how the two relate to overall performance on behavioral tasks, learning, and generalization. We develop mathematical approaches that focus on learnability and robustness to adversarial perturbations as essential properties of latent representations. In Chapters 1 and 2, we propose a theory that specifies the conditions that allow neural models to learn through backpropagation. Dually, it has significant implications that shed light on representations in the brain. Interestingly, by requiring that backpropagating gradients neither explode nor vanish, we can recover equivalent conditions under which neural representations can faithfully represent continuous variables. In Chapter 3 we analyze the relationship between the dimensionality of neural representations and their robustness to adversarial perturbations. This highlights an interesting tradeoff between efficacy, dimensionality, and robustness. This tradeoff is equally salient for models of biological computation and artificial neural networks.},
}

Levi, A. J., Zhao, Y., Park, I. M., & Huk, A. C. (2023). Sensory and choice responses in MT distinct from motion encoding. Journal of Neuroscience, 43(12), 2090–2103. https://doi.org/10.1523/JNEUROSCI.0267-22.2023

@article{Levi2021a,
  author = {Levi, Aaron J and Zhao, Yuan and Park, Il Memming and Huk, Alexander C},
  title = {Sensory and choice responses in {MT} distinct from motion encoding},
  journal = {Journal of Neuroscience},
  year = 2023,
  month = mar,
  volume = {43},
  number = {12},
  pages = {2090--2103},
  note = {(Levi and Zhao are co-first authors)},
  doi = {10.1523/JNEUROSCI.0267-22.2023},
  url = {https://www.jneurosci.org/content/43/12/2090},
  abstract = {Macaque area MT is well known for its visual motion selectivity and relevance to motion perception, but the possibility of it also reflecting non-sensory functions has largely been ignored. Manipulating subjects' temporal evidence weighting revealed multiple components of MT responses that were, surprisingly, not interpretable as behaviorally-relevant modulations of motion encoding, nor as consequences of readout of motion direction. MT's time-varying motion-driven responses were starkly changed by our strategic manipulation, but with timecourses opposite the subjects' temporal weighting strategies. Furthermore, large choice-correlated signals were represented in population activity distinctly from motion responses (even after the stimulus) with multiple phases that both lagged psychophysical readout and preceded motor responses. These results reveal multiple cognitive contributions to MT responses that are task-related but not functionally relevant to encoding or decoding of motion for psychophysical direction discrimination, calling into question its nature as a simple sensory area. \#\#\# Competing Interest Statement The authors have declared no competing interest.},
  pmcid = {10042117},
  pmid = {36781221},
}

Dowling, M., Zhao, Y., & Park, I. M. (2023). Real-time variational method for learning neural trajectory and its dynamics. In International Conference on Learning Representations (ICLR). https://openreview.net/forum?id=M_MvkWgQSt

@inproceedings{Dowling2023a,
  author = {Matthew Dowling and Yuan Zhao and Il Memming Park},
  title = {Real-time variational method for learning neural trajectory and its dynamics},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = 2023,
  month = feb,
  note = {(top 25\%)},
  url = {https://openreview.net/forum?id=M_MvkWgQSt},
  eprint = {2305.11278},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural recordings. However, despite the potential of real-time alternatives to give immediate feedback to experimentalists, and enhance experimental design, they have received markedly less attention. In this work, we introduce the exponential family variational Kalman filter (eVKF), an online recursive Bayesian method aimed at inferring latent trajectories while simultaneously learning the dynamical system generating them. eVKF works for arbitrary likelihoods and utilizes the constant base measure exponential family to model the latent state stochasticity. We derive a closed-form variational analog to the predict step of the Kalman filter which leads to a provably tighter bound on the ELBO compared to another online variational method. We validate our method on synthetic and real-world data, and, notably, show that it achieves competitive performance.},
  arxivid = {2305.11278},
  youtube = {https://iclr.cc/virtual/2023/poster/10849},
}

Dowling, M., Zhao, Y., & Park, I. M. (2023). The Exponential Family Variational Kalman Filter for Real-time Neural Dynamics [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Dowling2023b,
  author = {Matthew Dowling and Yuan Zhao and Il Memming Park},
  title = {The Exponential Family Variational Kalman Filter for Real-time Neural Dynamics},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2023,
}

Park, I. M., Ságodi, Á., & Sokół, P. A. (2023). Persistent learning signals without continuous attractors [Conference abstract]. Bernstein Conference. https://doi.org/10.12751/nncn.bc2023.348

@inproceedings{Park2023b,
  author = {Park, Il Memming and S{\'a}godi, {\'A}bel and Sok{\'o}{\l}, Piotr Aleksander},
  title = {Persistent learning signals without continuous attractors},
  booktitle = {Bernstein Conference},
  year = 2023,
  doi = {10.12751/nncn.bc2023.348},
  url = {https://abstracts.g-node.org/conference/BC23/abstracts#/uuid/ecbf6440-d119-4cbc-8324-665e7cefe8d6},
  poster_no = {IV 302},
}

Sokół, P., & Park, I. M. (2023). Only two types of attractors support representation of continuous variables, and learning over long time-spans [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Sokol2023a,
  author = {Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {Only two types of attractors support representation of continuous variables, and learning over long time-spans},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2023,
}

Stone, I., Sagiv, Y., Park, I. M., & Pillow, J. W. (2023). Spectral learning of Bernoulli latent dynamical system models for decision-making [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Stone2023a,
  author = {Iris Stone and Yotam Sagiv and Il Memming Park and Jonathan W. Pillow},
  title = {Spectral learning of {B}ernoulli latent dynamical system models for decision-making},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2023,
}

Stone, I., Sagiv, Y., Park, I. M., & Pillow, J. (2023). Spectral learning of Bernoulli linear dynamical systems models [Conference abstract]. Bernstein Conference. https://doi.org/10.12751/nncn.bc2023.288

@inproceedings{Stone2023c,
  author = {Stone, Iris and Sagiv, Yotam and Park, Il Memming and Pillow, Jonathan},
  title = {Spectral learning of {B}ernoulli linear dynamical systems models},
  booktitle = {Bernstein Conference},
  year = 2023,
  doi = {10.12751/nncn.bc2023.288},
  url = {https://abstracts.g-node.org/conference/BC23/abstracts#/uuid/9067fd8a-f2c4-4535-a686-8fe99c653492},
  abstract = {Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making and discrete stochastic processes (e.g., binned neural spike trains). Here we develop a spectral learning method for fast, efficient fitting of probit-Bernoulli latent linear dynamical system (LDS) models. Our approach extends traditional subspace identification methods to the Bernoulli setting via a transformation of the first and second sample moments. This results in a robust, fixed-cost estimator that avoids the hazards of local optima and the long computation time of iterative fitting procedures like the expectation-maximization (EM) algorithm. In regimes where data is limited or assumptions about the statistical structure of the data are not met, we demonstrate that the spectral estimate provides a good initialization for Laplace-EM fitting. Finally, we show that the estimator provides substantial benefits to real world settings by analyzing data from mice performing a sensory decision-making task.},
  poster_no = {IV 108},
}

Vermani, A., Nassar, J., & Park, I. M. (2023). Aligning high-dimensional neural recordings for data efficient inference of dynamics and prediction [Conference abstract]. Bernstein Conference. https://doi.org/10.12751/nncn.bc2023.291

@inproceedings{Vermani2023a,
  author = {Vermani, Ayesha and Nassar, Josue and Park, Il Memming},
  title = {Aligning high-dimensional neural recordings for data efficient inference of dynamics and prediction},
  booktitle = {Bernstein Conference},
  year = 2023,
  doi = {10.12751/nncn.bc2023.291},
  url = {https://abstracts.g-node.org/conference/BC23/abstracts#/uuid/9c78d90e-d9e2-4ac6-9c41-e00328c57426},
  poster_no = {IV 111},
}

Neophytou, D., Arribas, D., Levy, R., Arora, T., Park, I. M., & Oviedo, H. V. (2022). Differences in temporal processing speeds between the right and left auditory cortex reflect the strength of recurrent synaptic connectivity. PLoS Biology, 20(10), Article e3001803. https://doi.org/10.1371/journal.pbio.3001803

@article{Neophytou2021b,
  author = {Neophytou, Demetrios and Arribas, Diego and Levy, Robert and Arora, Tushar and Park, Il Memming and Oviedo, Hysell V},
  title = {Differences in temporal processing speeds between the right and left auditory cortex reflect the strength of recurrent synaptic connectivity},
  journal = {PLoS Biology},
  year = 2022,
  month = oct,
  volume = {20},
  number = {10},
  pages = {e3001803},
  doi = {10.1371/journal.pbio.3001803},
  url = {https://www.biorxiv.org/content/10.1101/2021.04.14.439872},
  eprint = {2021.04.14.439872},
  archiveprefix = {bioRxiv},
  abstract = {Brain asymmetry in the sensitivity to spectrotemporal modulation is an established functional feature that underlies the perception of speech and music. The left Auditory Cortex (ACx) is believed to specialize in processing fast temporal components of speech sounds, and the right ACx slower components. However, the circuit features and neural computations behind these lateralized spectrotemporal processes are poorly understood. To answer these mechanistic questions we use mice, an animal model that captures some relevant features of human communication systems. In this study, we screened for circuit features that could subserve temporal integration differences between the left and right ACx. We mapped excitatory input to principal neurons in all cortical layers and found significantly stronger recurrent connections in the superficial layers of the right ACx compared to the left. We hypothesized that the underlying recurrent neural dynamics would exhibit differential characteristic timescales corresponding to their hemispheric specialization. To investigate, we recorded spike trains from awake mice and estimated the network time constants using a statistical method to combine evidence from multiple weak signal-to-noise ratio neurons. We found longer temporal integration windows in the superficial layers of the right ACx compared to the left as predicted by stronger recurrent excitation. Our study shows substantial evidence linking stronger recurrent synaptic connections to longer network timescales. These findings support speech processing theories that purport asymmetry in temporal integration is a crucial feature of lateralization in auditory processing.},
  doi_biorxiv = {10.1101/2021.04.14.439872},
  language = {en},
  pmcid = {9629599},
  pmid = {36269764},
}

Brinkman, B. A. W., Yan, H., Maffei, A., Park, I. M., Fontanini, A., Wang, J., & La Camera, G. (2022). Metastable dynamics of neural circuits and networks. Applied Physics Reviews, 9(1), Article 011313. https://doi.org/10.1063/5.0062603

@article{Brinkman2021a,
  author = {Brinkman, Braden A W and Yan, Han and Maffei, Arianna and Park, Il Memming and Fontanini, Alfredo and Wang, Jin and La Camera, Giancarlo},
  title = {Metastable dynamics of neural circuits and networks},
  journal = {Applied Physics Reviews},
  publisher = {American Institute of Physics},
  year = 2022,
  month = mar,
  volume = {9},
  number = {1},
  pages = {011313},
  doi = {10.1063/5.0062603},
  eprint = {2110.03025},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Cortical neurons emit seemingly erratic trains of action potentials, or ``spikes'', and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of patterns which emerge spontaneously or in response to incoming activity produced by sensory inputs. In this review, we focus on neural dynamics that is best understood as a sequence of repeated activations of a number of discrete hidden states. These transiently occupied states are termed ``metastable'' and have been linked to important sensory and cognitive functions. In the rodent gustatory cortex, for instance, metastable dynamics have been associated with stimulus coding, with states of expectation, and with decision making. In frontal, parietal and motor areas of macaques, metastable activity has been related to behavioral performance, choice behavior, task difficulty, and attention. In this article, we review the experimental evidence for neural metastable dynamics together with theoretical approaches to the study of metastable activity in neural circuits. These approaches include: (i) a theoretical framework based on non-equilibrium statistical physics for network dynamics; (ii) statistical approaches to extract information about metastable states from a variety of neural signals, and (iii) recent neural network approaches, informed by experimental results, to model the emergence of metastable dynamics. By discussing these topics, we aim to provide a cohesive view of how transitions between different states of activity may provide the neural underpinnings for essential functions such as perception, memory, expectation or decision making, and more generally, how the study of metastable neural activity may advance our understanding of neural circuit function in health and disease.},
  arxivid = {2110.03025},
  pmcid = {8900181},
  pmid = {35284030},
}

Zhao, Y., Nassar, J., Jordan, I., Bugallo, M., & Park, I. M. (2022). Streaming variational Monte Carlo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(1), 1150–1161. https://doi.org/10.1109/TPAMI.2022.3153225

@article{Zhao2019a,
  author = {Zhao, Yuan and Nassar, Josue and Jordan, Ian and Bugallo, M{\'o}nica and Park, Il Memming},
  title = {Streaming variational {M}onte {C}arlo},
  journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year = 2022,
  month = feb,
  volume = {45},
  number = {1},
  pages = {1150--1161},
  doi = {10.1109/TPAMI.2022.3153225},
  url = {http://dx.doi.org/10.1109/TPAMI.2022.3153225},
  eprint = {1906.01549},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneously inferring the state and their nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides a filtering posterior arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently infer a posterior over the dynamics using sparse Gaussian processes. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications.},
  arxivid = {1906.01549},
  code = {https://github.com/catniplab/svmc},
  issn = {0162-8828},
  pmcid = {10082974},
  pmid = {35201981},
}

Dowling, M., Sokół, P., & Park, I. M. (2022). Hida-Matérn Gaussian Processes [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Dowling2022a,
  author = {Dowling, Matthew and Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {{H}ida-{M}at{\'e}rn Gaussian Processes},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2022,
}

Jordan, I. D. (2022). Metastable Dynamics Underlying Neural Computation [Unpublished doctoral dissertation]. Stony Brook University.

@phdthesis{Jordan2022a,
  author = {Ian D. Jordan},
  title = {Metastable Dynamics Underlying Neural Computation},
  school = {Stony Brook University},
  year = 2022,
}

Nassar, J. (2022). Bayesian Machine Learning for Analyzing and Controlling Neural Populations [Unpublished doctoral dissertation]. Stony Brook University.

@phdthesis{Nassar2022a,
  author = {Josue Nassar},
  title = {Bayesian Machine Learning for Analyzing and Controlling Neural Populations},
  school = {Stony Brook University},
  year = 2022,
}

Vermani, A., Chen, K., Kogan, J., Fontanini, A., & Park, I. M. (2022). Can time dependent and invariant decoders co-exist? [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Vermani2022a,
  author = {Ayesha Vermani and Ke Chen and Joshua Kogan and Alfredo Fontanini and Il Memming Park},
  title = {Can time dependent and invariant decoders co-exist?},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2022,
}

Pei, F., Ye, J., Zoltowski, D., Wu, A., Chowdhury, R. H., Sohn, H., O'Doherty, J. E., Shenoy, K. V., Kaufman, M. T., Churchland, M., Jazayeri, M., Miller, L. E., Pillow, J., Park, I. M., Dyer, E. L., & Pandarinath, C. (2021). Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity. In Advances in Neural Information Processing Systems (NeurIPS). https://openreview.net/forum?id=KVMS3fl4Rsv

@inproceedings{Pei2021b,
  author = {Pei, Felix and Ye, Joel and Zoltowski, David and Wu, Anqi and Chowdhury, Raeed H and Sohn, Hansem and O'Doherty, Joseph E and Shenoy, Krishna V and Kaufman, Matthew T and Churchland, Mark and Jazayeri, Mehrdad and Miller, Lee E and Pillow, Jonathan and Park, Il Memming and Dyer, Eva L and Pandarinath, Chethan},
  title = {Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2021,
  month = sep,
  note = {(PF and YU are co-first authors)},
  url = {https://openreview.net/forum?id=KVMS3fl4Rsv},
  eprint = {2109.04463},
  archiveprefix = {arXiv},
  primaryclass = {cs.LG},
  abstract = {Advances in neural recording present increasing opportunities to study neural activity in unprecedented detail. Latent variable models (LVMs) are promising tools for analyzing this rich activity across diverse neural systems and behaviors, as LVMs do not depend on known relationships between the activity and external experimental variables. However, progress in latent variable modeling is currently impeded by a lack of standardization, resulting in methods being developed and compared in an ad hoc manner. To coordinate these modeling efforts, we introduce a benchmark suite for latent variable modeling of neural population activity. We curate four datasets of neural spiking activity from cognitive, sensory, and motor areas to promote models that apply to the wide variety of activity seen across these areas. We identify unsupervised evaluation as a common framework for evaluating models across datasets, and apply several baselines that demonstrate benchmark diversity. We release this benchmark through EvalAI. http://neurallatents.github.io},
  arxivid = {2109.04463},
}

Dowling, M., Sokół, P., & Park, I. M. (2021). Hida-Matérn Kernel. arXiv. https://doi.org/10.48550/arXiv.2107.07098

@unpublished{Dowling2021b,
  author = {Dowling, Matthew and Sok{\'o}{\l}, Piotr and Park, Il Memming},
  title = {{H}ida-{M}at{\'e}rn Kernel},
  year = 2021,
  month = jul,
  url = {http://arxiv.org/abs/2107.07098},
  eprint = {2107.07098},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {We present the class of Hida-Mat{\'e}rn kernels, which is the canonical family of covariance functions over the entire space of stationary Gauss-Markov Processes. It extends upon Mat{\'e}rn kernels, by allowing for flexible construction of priors over processes with oscillatory components. Any stationary kernel, including the widely used squared-exponential and spectral mixture kernels, are either directly within this class or are appropriate asymptotic limits, demonstrating the generality of this class. Taking advantage of its Markovian nature we show how to represent such processes as state space models using only the kernel and its derivatives. In turn this allows us to perform Gaussian Process inference more efficiently and side step the usual computational burdens. We also show how exploiting special properties of the state space representation enables improved numerical stability in addition to further reductions of computational complexity.},
  arxivid = {2107.07098},
}

Arribas, D., Zhao, Y., & Park, M. (2021). Framework to generate more realistic GLM spike trains [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Arribas2021a,
  author = {Diego Arribas and Yuan Zhao and Memming Park},
  title = {Framework to generate more realistic GLM spike trains},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2021,
}

Dowling, M., Zhao, Y., & Park, M. (2021). NP-GLM: Nonparametric GLM [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Dowling2021a,
  author = {Matthew Dowling and Yuan Zhao and Memming Park},
  title = {{NP-GLM}: Nonparametric {GLM}},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2021,
}

Jordan, I. D., Sokol, P. A., & Park, I. M. (2021). Gated recurrent units viewed through the lens of continuous time dynamical systems. Frontiers in Computational Neuroscience. https://doi.org/10.3389/fncom.2021.678158

@article{Jordan2019a,
  author = {Jordan, Ian D and Sokol, Piotr Aleksander and Park, Il Memming},
  title = {Gated recurrent units viewed through the lens of continuous time dynamical systems},
  journal = {Frontiers in Computational Neuroscience},
  year = 2021,
  doi = {10.3389/fncom.2021.678158},
  eprint = {1906.01005},
  archiveprefix = {arXiv},
  primaryclass = {cs.LG},
  abstract = {Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.},
  pmcid = {8339926},
  pmid = {34366817},
}

Jordan, I., Sokol, P., & Park, I. M. (2021). Mechanisms Underlying Sequence-to-Sequence Working Memory [Conference abstract]. DeepMath. https://www.deepmath-conference.com

@conference{Jordan2021a,
  author = {Ian Jordan and Piotr Sokol and Il Memming Park},
  title = {Mechanisms Underlying Sequence-to-Sequence Working Memory},
  booktitle = {DeepMath},
  year = 2021,
  url = {https://www.deepmath-conference.com},
}

Neophytou, D., Arribas, D., Oviedo, H., & Park, I. M. (2021). Quasi-Bayesian estimation of time constants supports lateralized auditory computation [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Neophytou2021a,
  author = {Demetrios Neophytou and Diego Arribas and Hysell Oviedo and Il Memming Park},
  title = {{Quasi-Bayesian} estimation of time constants supports lateralized auditory computation},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2021,
}

Pei, F., Ye, J., Sedler, A. R., Zoltowski, D., Wu, A., Chowdhury, R. H., Sohn, H., O'Doherty, J. E., Shenoy, K. V., Kaufman, M. T., Churchland, M., Jazayeri, M., Miller, L. E., Park, I. M., Dyer, E., Pillow, J., & Pandarinath, C. (2021). Advancing the investigation of neural population structure with the Neural Latents Benchmark [Conference abstract]. Society for Neuroscience.

@inproceedings{Pei2021a,
  author = {Felix Pei and Joel Ye and Andrew R. Sedler and David Zoltowski and Anqi Wu and Raeed H. Chowdhury and Hansem Sohn and Joseph E. O'Doherty and Krishna V. Shenoy and Matthew T. Kaufman and Mark Churchland and Mehrdad Jazayeri and Lee E. Miller and Il Memming Park and Eva Dyer and Jonathan Pillow and Chethan Pandarinath},
  title = {Advancing the investigation of neural population structure with the Neural Latents Benchmark},
  booktitle = {Society for Neuroscience},
  year = 2021,
}

Arribas, D. M., Zhao, Y., & Park, I. M. (2020). Rescuing neural spike train models from bad MLE. In Advances in Neural Information Processing Systems (NeurIPS). https://papers.nips.cc/paper/2020/hash/186b690e29892f137b4c34cfa40a3a4d-Abstract.html

@inproceedings{Arribas2020a,
  author = {Diego M. Arribas and Yuan Zhao and Il Memming Park},
  title = {Rescuing neural spike train models from bad {MLE}},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2020,
  month = oct,
  url = {https://papers.nips.cc/paper/2020/hash/186b690e29892f137b4c34cfa40a3a4d-Abstract.html},
  eprint = {2010.12362},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {The standard approach to fitting an autoregressive spike train model is to maximize the likelihood for one-step prediction. This maximum likelihood estimation (MLE) often leads to models that perform poorly when generating samples recursively for more than one time step. Moreover, the generated spike trains can fail to capture important features of the data and even show diverging firing rates. To alleviate this, we propose to directly minimize the divergence between neural recorded and model generated spike trains using spike train kernels. We develop a method that stochastically optimizes the maximum mean discrepancy induced by the kernel. Experiments performed on both real and synthetic neural data validate the proposed approach, showing that it leads to well-behaving models. Using different combinations of spike train kernels, we show that we can control the trade-off between different features which is critical for dealing with model-mismatch.},
  arxivid = {2010.12362},
  code = {https://github.com/catniplab/mmd-glm},
}

Nassar, J., Sokol, P., Chang, S., Harris, K., & Park, I. M. (2020). On 1/n neural representation and robustness. In Advances in Neural Information Processing Systems (NeurIPS). https://papers.nips.cc/paper/2020/hash/44bf89b63173d40fb39f9842e308b3f9-Abstract.html

@inproceedings{Nassar2020c,
  author = {Josue Nassar and Piotr Sokol and SueYeon Chang and Kenneth Harris and Il Memming Park},
  title = {On $1/n$ neural representation and robustness},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year = 2020,
  month = oct,
  note = {(JN and PS are co-first authors)},
  url = {https://papers.nips.cc/paper/2020/hash/44bf89b63173d40fb39f9842e308b3f9-Abstract.html},
  eprint = {2012.04729},
  archiveprefix = {arXiv},
  primaryclass = {cs.LG},
  abstract = {Understanding the nature of representation in neural networks is a goal shared by neuroscience and machine learning. It is therefore exciting that both fields converge not only on shared questions but also on similar approaches. A pressing question in these areas is understanding how the structure of the representation used by neural networks affects both their generalization, and robustness to perturbations. In this work, we investigate the latter by juxtaposing experimental results regarding the covariance spectrum of neural representations in the mouse V1 (Stringer et al) with artificial neural networks. We use adversarial robustness to probe Stringer et al's theory regarding the causal role of a 1/n covariance spectrum. We empirically investigate the benefits such a neural code confers in neural networks, and illuminate its role in multi-layer architectures. Our results show that imposing the experimentally observed structure on artificial neural networks makes them more robust to adversarial attacks. Moreover, our findings complement the existing theory relating wide neural networks to kernel methods, by showing the role of intermediate representations.},
  arxivid = {2012.04729},
}

Zhao, Y., & Park, I. M. (2020). Variational online learning of neural dynamics. Frontiers in Computational Neuroscience. https://doi.org/10.3389/fncom.2020.00071

@article{Zhao2017c,
  author = {Zhao, Yuan and Park, Il Memming},
  title = {Variational online learning of neural dynamics},
  journal = {Frontiers in Computational Neuroscience},
  year = 2020,
  month = oct,
  doi = {10.3389/fncom.2020.00071},
  eprint = {1707.09049},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {State space models provide an interpretable framework for complex time series by combining an intuitive dynamical system model with a probabilistic observation model. We developed a flexible online learning framework for latent nonlinear state dynamics and filtered latent states. Our method utilizes the stochastic gradient variational Bayes method to jointly optimize the parameters of the nonlinear dynamics, observation model, and the black-box recognition model. Unlike previous approaches, our framework can incorporate non-trivial observation noise models and has potential of inferring in real-time. We test our method on point process and Gaussian observations driven by continuous attractor dynamics and nonstationary systems, demonstrating its ability to recover the phase portrait, filtered trajectory, and produce long-term predictions for online machine learning.},
  code = {https://github.com/catniplab/vjf.git},
  pmcid = {7591751},
  pmid = {33154718},
}

Dowling, M., Zhao, Y., & Park, I. M. (2020). Non-parametric generalized linear model. arXiv. https://doi.org/10.48550/arXiv.2009.01362

@unpublished{Dowling2020a,
  author = {Dowling, Matthew and Zhao, Yuan and Park, Il Memming},
  title = {Non-parametric generalized linear model},
  year = 2020,
  month = sep,
  eprint = {2009.01362},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {A fundamental problem in statistical neuroscience is to model how neurons encode information by analyzing electrophysiological recordings. A popular and widely-used approach is to fit the spike trains with an autoregressive point process model. These models are characterized by a set of convolutional temporal filters, whose subsequent analysis can help reveal how neurons encode stimuli, interact with each other, and process information. In practice a sufficiently rich but small ensemble of temporal basis functions needs to be chosen to parameterize the filters. However, obtaining a satisfactory fit often requires burdensome model selection and fine tuning the form of the basis functions and their temporal span. In this paper we propose a nonparametric approach for jointly inferring the filters and hyperparameters using the Gaussian process framework. Our method is computationally efficient taking advantage of the sparse variational approximation while being flexible and rich enough to characterize arbitrary filters in continuous time lag. Moreover, our method automatically learns the temporal span of the filter. For the particular application in neuroscience, we designed priors for stimulus and history filters useful for the spike trains. We compare and validate our method on simulated and real neural spike train data.},
  arxivid = {2009.01362},
}

Jordan, I. D., & Park, I. M. (2020). Birhythmic analog circuit maze: A nonlinear neurostimulation testbed. Entropy, 22(5), Article 537. https://doi.org/10.3390/e22050537

@article{Jordan2019b,
  author = {Jordan, Ian D. and Park, Il Memming},
  title = {Birhythmic analog circuit maze: A nonlinear neurostimulation testbed},
  journal = {Entropy},
  publisher = {Multidisciplinary Digital Publishing Institute},
  year = 2020,
  month = may,
  volume = {22},
  number = {5},
  pages = {537},
  doi = {10.3390/e22050537},
  url = {https://www.mdpi.com/1099-4300/22/5/537},
  eprint = {2004.10658},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.NC},
  abstract = {Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesize that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation.},
  arxivid = {2004.10658},
  language = {en},
  pmcid = {7517031},
  pmid = {33286310},
}

Michaelis, B., Leathers, K., Ache, B., Bobkov, Y., Principe, J., Baharloo, R., Park, I. M., & Reidenbach, M. (2020). Odor tracking in marine organisms: the importance of temporal and spatial intermittency of the odor signal. Scientific Reports, 10, Article 7961. https://doi.org/10.1038/s41598-020-64766-y

@article{Michaelis2020a,
  author = {Brenden Michaelis and Kyle Leathers and Barry Ache and Yuriy Bobkov and Jose Principe and Raheleh Baharloo and Il Memming Park and Matthew Reidenbach},
  title = {Odor tracking in marine organisms: the importance of temporal and spatial intermittency of the odor signal},
  journal = {Scientific Reports},
  year = 2020,
  month = may,
  volume = {10},
  pages = {7961},
  doi = {10.1038/s41598-020-64766-y},
  abstract = {In aquatic and terrestrial environments, odorants are dispersed by currents that create concentration distributions that are spatially and temporally complex. Animals navigating in a plume must therefore rely upon intermittent, and time-varying information to find the source. Navigation has typically been studied as a spatial information problem, with the aim of movement towards higher mean concentrations. However, this spatial information alone, without information of the temporal dynamics of the plume, is insufficient to explain the accuracy and speed of many animals tracking odors. Recent studies have identified a subpopulation of olfactory receptor neurons (ORNs) that consist of intrinsically rhythmically active `bursting' ORNs (bORNs) in the lobster, Panulirus argus. As a population, bORNs provide a neural mechanism dedicated to encoding the time between odor encounters. Using a numerical simulation of a large-scale plume, the lobster is used as a framework to construct a computer model to examine the utility of intermittency for orienting within a plume. Results show that plume intermittency is reliably detectable when sampling simulated odorants on the order of seconds, and provides the most information when animals search along the plume edge. Both the temporal and spatial variation in intermittency is predictably structured on scales relevant for a searching animal that encodes olfactory information utilizing bORNs, and therefore is suitable and useful as a navigational cue.},
  issn = {2045-2322},
  pmcid = {7224200},
  pmid = {32409665},
}

Zhao, Y., Yates, J. L., Levi, A., Huk, A., & Park, I. M. (2020). Stimulus-choice (mis)alignment in primate area MT. PLOS Computational Biology. https://doi.org/10.1371/journal.pcbi.1007614

@article{Zhao2019b,
  author = {Yuan Zhao and Jacob L. Yates and Aaron Levi and Alex Huk and Il Memming Park},
  title = {Stimulus-choice (mis)alignment in primate area {MT}},
  journal = {{PLOS} Computational Biology},
  year = 2020,
  month = may,
  doi = {10.1371/journal.pcbi.1007614},
  url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007614},
  abstract = {For stimuli near perceptual threshold, the trial-by-trial activity of single neurons in many sensory areas is correlated with the animal's perceptual report. This phenomenon has often been attributed to feedforward readout of the neural activity by the downstream decision-making circuits. The interpretation of choice-correlated activity is quite ambiguous, but its meaning can be better understood in the light of population-wide correlations among sensory neurons. Using a statistical nonlinear dimensionality reduction technique on single-trial ensemble recordings from the middle temporal area during perceptual-decision-making, we extracted low-dimensional neural trajectories that captured the population-wide fluctuations. We dissected the particular contributions of sensory-driven versus choice-correlated activity in the low-dimensional population code. We found that the neural trajectories strongly encoded the direction of the stimulus in single dimension with a temporal signature similar to that of single MT neurons. If the downstream circuit were optimally utilizing this information, choice-correlated signals should be aligned with this stimulus encoding dimension. Surprisingly, we found that a large component of the choice information resides in the subspace orthogonal to the stimulus representation inconsistent with the optimal readout view. This misaligned choice information allows the feedforward sensory information to coexist with the decision-making process. The time course of these signals suggest that this misaligned contribution likely is feedback from the downstream areas. We hypothesize that this non-corrupting choice-correlated feedback might be related to learning or reinforcing sensory-motor relations in the sensory population.},
  data = {https://doi.org/10.6084/m9.figshare.11413182.v1},
  pmcid = {7259805},
  pmid = {32421716},
  youtube = {https://youtu.be/qMDYBgxIxdU},
}

Dikecligil, G. N., Graham, D., Park, I. M., & Fontanini, A. (2020). Layer and cell type specific response properties of gustatory cortex neurons in awake mice. Journal of Neuroscience. https://doi.org/10.1523/JNEUROSCI.1579-19.2020

@article{Dikecligil2019a,
  author = {Gulce Nazli Dikecligil and Dustin Graham and Il Memming Park and Alfredo Fontanini},
  title = {Layer and cell type specific response properties of gustatory cortex neurons in awake mice},
  journal = {Journal of Neuroscience},
  year = 2020,
  doi = {10.1523/JNEUROSCI.1579-19.2020},
  abstract = {Studies in visual, auditory, and somatosensory cortices have revealed that different cell types as well as neurons located in different laminae display distinct stimulus response profiles. The extent to which these layer and cell type-specific distinctions generalize to gustatory cortex (GC) remains unknown. In this study, we performed extracellular recordings in adult female mice to monitor the activity of putative pyramidal and inhibitory neurons located in deep and superficial layers of GC. Awake, head-restrained mice were trained to lick different tastants (sucrose, salt, citric acid, quinine, and water) from a lick spout. We found that deep layer neurons show higher baseline firing rates (FRs) in GC with deep-layer inhibitory neurons displaying highest FRs at baseline and following the stimulus. GC's activity shows robust modulations before animals' contact with tastants, and this phenomenon is most prevalent in deep-layer inhibitory neurons. Furthermore, we show that licking activity strongly shapes the spiking pattern of GC pyramidal neurons, eliciting phase-locked spiking across trials and tastants. We demonstrate that there is a greater percentage of taste-coding neurons in deep versus superficial layers with chemosensitive neurons across all categories showing similar breadth of tuning, but different decoding performance. Lastly, we provide evidence for functional convergence in GC, with neurons that can show prestimulus activity, licking-related rhythmicity and taste responses. Overall, our results demonstrate that baseline and stimulus-evoked firing profiles of GC neurons and their processing schemes change as a function of cortical layer and cell type in awake mice.SIGNIFICANCE STATEMENT Sensory cortical areas show a laminar structure, with each layer composed of distinct cell types embedded in different circuits. While studies in other primary sensory areas have elucidated that pyramidal and inhibitory neurons belonging to distinct layers show distinct response properties, whether and how response properties of gustatory cortex (GC) neurons change as a function of their laminar position and cell type remains uninvestigated. Here, we show that there are several notable differences in baseline, prestimulus, and stimulus-evoked response profiles of pyramidal and inhibitory neurons belonging to deep and superficial layers of GC.},
}

Kepple, D. R., Lee, D., Prepscius, C., Isler, V., Park, I. M., & Lee, D. L. (2020). Jointly learning visual motion and confidence from local patches in event cameras. In 16th European conference on computer vision (ECCV2020). https://doi.org/10.1007/978-3-030-58539-6_30

@inproceedings{Kepple2020a,
  author = {Daniel R. Kepple and Daewon Lee and Colin Prepscius and Volkan Isler and Il Memming Park and Daniel L. Lee},
  title = {Jointly learning visual motion and confidence from local patches in event cameras},
  booktitle = {16th {E}uropean conference on computer vision ({ECCV}2020)},
  year = 2020,
  note = {spotlight},
  doi = {10.1007/978-3-030-58539-6_30},
}

Nassar, J., Sokol, P., Chung, S., Harris, K., & Park, I. M. (2020). Spectral regularization in biological and artificial neural networks [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Nassar2020a,
  author = {Josue Nassar and Piotr Sokol and SueYeon Chung and Kenneth Harris and Il Memming Park},
  title = {Spectral regularization in biological and artificial neural networks},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2020,
}

Nassar, J., Sokol, P., Chung, S. Y., Harris, K., & Park, I. M. (2020). On 1/n neural representation and robustness [Conference abstract]. DeepMath. https://www.deepmath-conference.com

@conference{Nassar2020d,
  author = {Josue Nassar and Piotr Sokol and Sue Yeon Chung and Kenneth Harris and Il Memming Park},
  title = {On ${1/n}$ neural representation and robustness},
  booktitle = {DeepMath},
  year = 2020,
  url = {https://www.deepmath-conference.com},
  abstract = {Understanding the nature of representation in neural networks is a goal shared by neuroscience and machine learning. It is therefore exciting that both fields converge not only on shared questions but also on similar approaches. A pressing question in these areas is understanding how the structure of the representation used by neural networks affects both their generalization, and robustness to perturbations. In this work, we investigate the latter by juxtaposing experimental results regarding the covariance spectrum of neural representations in the mouse V1 (Stringer et al) with artificial neural networks. We use adversarial robustness to probe Stringer et al's theory regarding the causal role of a 1/n covariance spectrum. We empirically investigate the benefits such a neural code confers in neural networks, and illuminate its role in multi-layer architectures. Our results show that imposing the experimentally observed structure on artificial neural networks makes them more robust to adversarial attacks. Moreover, our findings complement the existing theory relating wide neural networks to kernel methods, by showing the role of intermediate representations.},
}

Sokol, P., & Park, I. M. (2020). Information geometry of orthogonal initializations and training. In International Conference on Learning Representations (ICLR). https://openreview.net/forum?id=rkg1ngrFPr

@inproceedings{Sokol2018a,
  author = {Piotr Sokol and Il Memming Park},
  title = {Information geometry of orthogonal initializations and training},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = 2020,
  url = {https://openreview.net/forum?id=rkg1ngrFPr},
  eprint = {1810.03785},
  archiveprefix = {arXiv},
  abstract = {Recently mean field theory has been successfully used to analyze properties of wide, random neural networks. It gave rise to a prescriptive theory for initializing feed-forward neural networks with orthogonal weights, which ensures that both the forward propagated activations and the backpropagated gradients are near `2 isometries and as a consequence training is orders of magnitude faster. Despite strong empirical performance, the mechanisms by which critical initializations confer an advantage in the optimization of deep neural networks are poorly understood. Here we show a novel connection between the maximum curvature of the optimization landscape (gradient smoothness) as measured by the Fisher information matrix (FIM) and the spectral radius of the input-output Jacobian, which partially explains why more isometric networks can train much faster. Furthermore, given that orthogonal weights are necessary to ensure that gradient norms are approximately preserved at initialization, we experimentally investigate the benefits of maintaining orthogonality throughout training, and we conclude that manifold optimization of weights performs well regardless of the smoothness of the gradients. Moreover, we observe a surprising yet robust behavior of highly isometric initializations- even though such networks have a lower FIM condition number at initialization, and therefore by analogy to convex functions should be easier to optimize, experimentally they prove to be much harder to train with stochastic gradient descent. We propose an explanation for this phenomenon by exploting connections between Fisher geometry and the recently introduced Neural Tangent Kernel.},
  day = {9},
  keywords = {deep-learning, machine-learning, mean-field},
}

Sokol, P. A., Jordan, I., Kadile, E., & Park, I. M. (2020). Unexpected benefits of learning with neural oscillation: stable backpropagation with limit cycles [Conference abstract]. From Neuroscience to Artificially Intelligent Systems (NAISys).

@conference{Sokol2020d,
  author = {Piotr A. Sokol and Ian Jordan and Eben Kadile and Il Memming Park},
  title = {Unexpected benefits of learning with neural oscillation: stable backpropagation with limit cycles},
  booktitle = {From Neuroscience to Artificially Intelligent Systems (NAISys)},
  year = 2020,
  poster_no = {168},
}

Zhao, Y., Nassar, J., & Park, I. M. (2020). Real-time discovery of effective dynamics from streaming noisy neural observations [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Zhao2020a,
  author = {Yuan Zhao and Josue Nassar and Il Memming Park},
  title = {Real-time discovery of effective dynamics from streaming noisy neural observations},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2020,
}

Nassar, J., Linderman, S. W., Bugallo, M., & Park, I. M. (2019). Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling. In International Conference on Learning Representations (ICLR). https://openreview.net/forum?id=HkzRQhR9YX

@inproceedings{Nassar2018b,
  author = {Josue Nassar and Scott W. Linderman and Monica Bugallo and Il Memming Park},
  title = {Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = 2019,
  month = nov,
  url = {https://openreview.net/forum?id=HkzRQhR9YX},
  eprint = {1811.12386},
  archiveprefix = {arXiv},
  abstract = {Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability.},
  code = {https://github.com/catniplab/tree_structured_rslds},
  day = {30},
  keywords = {neural-dynamics, statistical-neuroscience},
}

Hocker, D., & Park, I. M. (2019). Myopic control of neural dynamics. PLOS Computational Biology. https://doi.org/10.1371/journal.pcbi.1006854

@article{Hocker2019a,
  author = {David Hocker and Il Memming Park},
  title = {Myopic control of neural dynamics},
  journal = {{PLOS} Computational Biology},
  year = 2019,
  month = mar,
  doi = {10.1371/journal.pcbi.1006854},
  url = {https://www.biorxiv.org/content/early/2017/12/30/241299},
  abstract = {Manipulating the dynamics of neural systems through targeted stimulation is a frontier of research and clinical neuroscience; however, the control schemes considered for neural systems are mismatched for the unique needs of manipulating neural dynamics. An appropriate control method should respect the variability in neural systems, incorporating moment to moment ``input'' to the neural dynamics and behaving based on the current neural state, irrespective of the past trajectory. We propose such a controller under a nonlinear state-space feedback framework that steers one dynamical system to function as through it were another dynamical system entirely. This ``myopic'' controller is formulated through a novel variant of a model reference control cost that manipulates dynamics in a step-wise manner, omitting the need to pre-calculate a rigid and computationally costly neural feedback control solution. To demonstrate the breadth of this control's utility, two examples with distinctly different applications in neuroscience are studied. First an unhealthy motor-like system containing an unwanted beta-oscillation spiral attractor is controlled to function as a healthy motor system, a relevant clinical example for neurological disorders. Second, we show the myopic control's utility to probe the causal dynamics of cognitive processes by transforming a winner-take-all decision-making system to operate as a robust neural integrator of evidence.},
  pmcid = {6428347},
  pmid = {30856171},
}

Bobkov, Y., Park, I., Michaelis, B. T., Matthews, T., Reidenbach, M. A., Príncipe, J. C., & Ache, B. (2019). Coding spatiotemporal characteristics of odor signals [Conference abstract]. Association for Chemoreception (AChemS) Annual Meeting.

@inproceedings{Bobkov2019a,
  author = {Yuriy Bobkov and Il Park and Brenden T. Michaelis and Tom Matthews and Matthew A. Reidenbach and Jos\'e C. Pr\'incipe and Barry Ache},
  title = {Coding spatiotemporal characteristics of odor signals},
  booktitle = {Association for Chemoreception (AChemS) Annual Meeting},
  year = 2019,
  abstract = {Odor signals are generally assumed to be processed based on input from canonical tonically active primary olfactory receptor neurons (ORNs). Recent evidence suggests, however, that a subpopulation of ORNs consists of intrinsically rhythmically active, `bursting' ORNs (bORNS) with unique functional properties. (1) They encode olfactory information by having their rhythmicity entrained by the odor stimulus; they don't discharge phaso-tonically as do canonical ORNs. (2) As a population they can accurately and instantaneously encode the interval since the last odor encounter up to 10s of seconds using information inherent in the olfactory modality. (3) Particularly interesting is that they can do this without the need to implicate a memory mechanism. Given the structure inherent in turbulent odor plumes, the ability of bORNs to encode the time between `whiffs' would provide a novel way of navigating turbulent plumes. Indeed, recent computational modeling shows an `animat' can navigate odor plumes with considerable more efficiency using odor time than odor concentration. To further support and expand this computational model, we are now using combined physiological and morphological analysis to characterize the molecular receptive range of bORNs, map their central projection, and begin to identify the strategy for synaptic processing of bORN-derived information at the first olfactory relay. While more work clearly needs to be done, and hopefully our work will encourage others to do that, our findings suggest encoding odor time is a fundamental feature of olfaction that potentially can be used to navigate odor plumes in animals as diverse as crustaceans and mammals.},
}

Mofakham, S., Fry, A., Adachi, J., Ashcroft, B., Winans, N., Liang, J., Sharma, H., Fiore, S., Park, I. M., & Mikell, C. (2019). Recovery of consciousness after traumatic brain injury: Biomarkers and a mechanistic model [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Mofakham2019a,
  author = {Sima Mofakham and Adam Fry and Joseph Adachi and Bradley Ashcroft and Nathan Winans and Justine Liang and Himanshu Sharma and Susan Fiore and Il Memming Park and Charles Mikell},
  title = {Recovery of consciousness after traumatic brain injury: Biomarkers and a mechanistic model},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2019,
}

Mofakham, S., Fry, A., Adachi, J., Winans, N., Liang, J., Ashcroft, B., Sharma, H., Fiore, S., Park, I. M., & Mikell, C. (2019). Electrophysiological prognostication of functional cortical integrity after traumatic brain injury [Conference abstract]. American Association of Neurological Surgeons (AANS).

@inproceedings{Mofakham2019b,
  author = {Sima Mofakham and Adam Fry and Joseph Adachi and Nathan Winans and Justine Liang and Bradley Ashcroft and Himanshu Sharma and Susan Fiore and Il Memming Park and Charles Mikell},
  title = {Electrophysiological prognostication of functional cortical integrity after traumatic brain injury},
  booktitle = {American Association of Neurological Surgeons ({AANS})},
  year = 2019,
  abstract = {Whether and how consciousness returns after severe traumatic brain injury (TBI) is not clear, mainly due to our lack of understanding of how consciousness arises. Previous studies revealed that correlated activity across a distributed network of cortical cells, the frontoparietal network (FPN), is required for return of consciousness. But data on the transition from coma to wakefulness are sparse. To address this gap, we performed depth electrode recordings of the anterior cingulate gyrus (ACC) and dorsolateral prefrontal cortex (DLPFC) along with simultaneous scalp EEG recording in patients recovering from coma after TBI. We sought to extract predictive electrophysiological biomarkers of regaining consciousness after traumatic brain injury. Methods: In this study one healthy control (epilepsy) and five comatose traumatic brain injury patients with GCS < 8 and with no major brain structural abnormalities were enrolled. Upon obtaining informed consent by a legally authorized representative, we implanted a seizure monitoring stereotactic (10-contact) depth electrode spanning from DLPFC to ACC. To probe the functional integrity of cortical webs we administered repetitive single-pulse stimulation to ACC and DLPFC (100 $\mu$S, 1 Hz stimulation, 100 reps). Cortico-cortical evoked potentials (CCEPs) were recorded both via the implanted depth electrode and scalp contacts. Results: We found that recovery of consciousness is associated with increasing amplitude and complexity of CCEPs in DLFPC. While all patients had increased amplitude over time, patients who recovered developed polyphasic, complex waveforms, as measured by zero crossing and permutation entropy (n = 5). The patients who did not recover (n = 2) had large-amplitude, but simple-waveform CCEP responses. Conclusion: The characteristics of the evoked responses to electrical stimulation may be a useful surrogate measurement of the integrity of cortical networks required for consciousness. CCEPs potentially be used as an indicator of integrity of cortex to predict outcome after TBI.},
}

Nassar, J., Linderman, S., Park, I. M., & Bugallo, M. (2019). Tree-structured locally linear dynamics model to uproot Bayesian neural data analysis [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Nassar2019a,
  author = {Josue Nassar and Scott Linderman and Il Memming Park and Monica Bugallo},
  title = {Tree-structured locally linear dynamics model to uproot {B}ayesian neural data analysis},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2019,
}

Sokol, P., Jordan, I., Kadile, E., & Park, I. M. (2019). Adjoint dynamics of stable limit cycle neural networks. In 53rd Asilomar Conference on Signals, Systems and Computers. https://doi.org/10.1109/IEEECONF44664.2019.9049080

@inproceedings{Sokol2019a,
  author = {Piotr Sokol and Ian Jordan and Eben Kadile and Il Memming Park},
  title = {Adjoint dynamics of stable limit cycle neural networks},
  booktitle = {53rd Asilomar Conference on Signals, Systems and Computers},
  year = 2019,
  doi = {10.1109/IEEECONF44664.2019.9049080},
  abstract = {Exploding and vanishing gradient are both major problems often faced when an artificial neural network is trained with gradient descent. Inspired by the ubiquity and robustness of nonlinear oscillations in biological neural systems, we investigate the properties of their artificial counterpart, the stable limit cycle neural networks. Using a continuous time dynamical system interpretation of neural networks and backpropagation, we show that stable limit cycle neural networks have non-exploding gradients, and at least one effective non-vanishing gradient dimension. We conjecture that limit cycles can support the learning of long temporal dependence in both biological and artificial neural networks.},
  keywords = {limit cycle; backpropagation},
  pdf = {Sokol2019a.pdf},
}

Sokol, P., & Park, I. M. (2019). Limit Cycle Neural Networks Have Infinite Memory [Conference abstract]. DeepMath. https://www.deepmath-conference.com

@conference{Sokol2019b,
  author = {Piotr Sokol and Il Memming Park},
  title = {Limit Cycle Neural Networks Have Infinite Memory},
  booktitle = {DeepMath},
  year = 2019,
  url = {https://www.deepmath-conference.com},
}

Sokol, P., Jordan, I., & Park, I. M. (2019). Information geometry at initialization and beyond [Conference abstract]. DeepMath. https://www.deepmath-conference.com

@conference{Sokol2019c,
  author = {Piotr Sokol and Ian Jordan and Il Memming Park},
  title = {Information geometry at initialization and beyond},
  booktitle = {DeepMath},
  year = 2019,
  url = {https://www.deepmath-conference.com},
}

Bobkov, Y., Park, I. M., Michaelis, B. T., Matthews, T., Reidenbach, M. A., Príncipe, J. C., & Ache, B. (2018, September). Rhythmically discharging olfactory receptor neurons can encode the spatiotemporal characteristics of odor signals within complexfluid environments [Conference abstract]. European Chemoreception Research Organization (ECRO), Würzburg, Germany. https://coms.events/ECRO2018/data/abstracts/en/abstract_0089.html

@inproceedings{Bobkov2018a,
  author = {Yuriy Bobkov and Il Memming Park and Brenden T. Michaelis and Tom Matthews and Matthew A. Reidenbach and Jos\'e C. Pr\'incipe and Barry Ache},
  title = {Rhythmically discharging olfactory receptor neurons can encode the spatiotemporal characteristics of odor signals within complexfluid environments},
  booktitle = {European Chemoreception Research Organization (ECRO)},
  year = 2018,
  month = sep,
  url = {https://coms.events/ECRO2018/data/abstracts/en/abstract_0089.html},
  abstract = {Sensory signals, including olfactory signals, are typically encoded by tonic receptor neurons. A significant portion of the olfactory receptor neurons in some species is intrinsically rhythmically active or `bursting' (bORNS). Rather than phaso-tonically discharging to the odor onset as characteristic of tonic olfactory receptor neurons, in bORNs the frequency of their inherent burst is entrained by the intermittency inherent in turbulent odor plumes. Each bORN responds to a relatively narrow range of stimulus frequencies (intermittency) based on their inherent rate of bursting discharge and the phase dependency of their response to odor stimulation. Using computational and analytical approaches we have shown that heterogeneous populations of such uncoupled oscillatory neurons have the capacity to reliably encode the temporal properties of intermittent odor signals as long as seconds to many tens of seconds that characterize natural odor plumes. In the present study, we expand our current understanding bORN-based encoding by characterizing the molecular receptive range of bORNs, mapping their central projection, and beginning to identify the strategy for the synaptic processing of bORN-derived information at the first olfactory relay.},
  address = {W\"urzburg, Germany},
  comment = {Poster session: Theme II - Vertebrate taste and olfaction: periphery (Th-P-054)},
}

Esfahany, K., Siergiej, I., Zhao, Y., & Park, I. M. (2018). Organization of neural population code in mouse visual system. eNeuro, 0414–17. https://doi.org/10.1523/ENEURO.0414-17.2018

@article{Esfahany2018b,
  author = {Esfahany, Kathleen and Siergiej, Isabel and Zhao, Yuan and Park, Il Memming},
  title = {Organization of neural population code in mouse visual system},
  journal = {eNeuro},
  publisher = {Society for Neuroscience},
  year = 2018,
  month = jul,
  pages = {0414--17},
  doi = {10.1523/ENEURO.0414-17.2018},
  url = {https://www.biorxiv.org/content/early/2018/03/25/220558},
  eprint = {220558},
  archiveprefix = {bioRxiv},
  abstract = {The mammalian visual system consists of several anatomically distinct areas, layers, and cell types. To understand the role of these subpopulations in visual information processing, we analyzed neural signals recorded from excitatory neurons from various anatomical and functional structures. For each of 186 mice, one of six genetically tagged cell-types and one of six visual areas were targeted while the mouse was passively viewing various visual stimuli. We trained linear classifiers to decode one of six visual stimulus categories with distinct spatiotemporal structures from the population neural activity. We found that neurons in both the primary visual cortex and secondary visual areas show varying degrees of stimulus-specific decodability, and neurons in superficial layers tend to be more informative about the stimulus categories. Additional decoding analyses of directional motion were consistent with these findings. We observed synergy in the population code of direction in several visual areas suggesting area-specific organization of information representation across neurons. These differences in decoding capacities shed light on the specialized organization of neural information processing across anatomically distinct subpopulations, and further establish the mouse as a model for understanding visual perception.},
  day = {6},
}

Kirschen, G. W., Ge, S., & Park, I. M. (2018). Probability of viral labeling of neural stem cells in vivo. Neuroscience Letters. https://doi.org/10.1016/j.neulet.2018.05.016

@article{Kirschen2018a,
  author = {Kirschen, Gregory W. and Ge, Shaoyu and Park, Il Memming},
  title = {Probability of viral labeling of neural stem cells {\it in vivo}},
  journal = {Neuroscience Letters},
  year = 2018,
  month = may,
  doi = {10.1016/j.neulet.2018.05.016},
  abstract = {In the neuroscience field over the past several decades, viral vectors have become powerful gene delivery systems to study neural populations of interest. For neural stem cell (NSC) biology, such viruses are often used to birth-date and track NSCs over developmental time in lineage tracing experiments. Yet, the probability of successful infection of a given stem cell in vivo remains unknown. This information would be helpful to inform investigators interested in titrating their viruses to selectively target sparsely-populated clusters of cells in the nervous system. Here, we describe a novel approach to calculate the probability of successful viral infection of NSCs using experimentally-derived cell cluster data from our newly-developed method to sparsely label adult NSCs, and a simple statistical derivation. Others interested in precisely defining their viral infection efficiency can use this method for a variety of basic and translational studies.},
  keywords = {neural-stem-cells, probability-estimation},
}

Esfahany, K., Siergiej, I., Zhao, Y., & Park, I. M. (2018). Organization of neural population code in mouse visual system [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Esfahany2018a,
  author = {Kathleen Esfahany and Isabel Siergiej and Yuan Zhao and Il Memming Park},
  title = {Organization of neural population code in mouse visual system},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2018,
  abstract = {The mammalian visual system consists of several anatomically distinct areas, layers, and cell types. To understand the role of these subpopulations in visual information processing, we analyzed neural signals recorded from excitatory neurons from various anatomical and functional structures. For each of 186 mice, one of six genetically tagged cell-types and one of six visual areas were targeted while the mouse was passively viewing various visual stimuli. We trained linear classifiers to decode one of six visual stimulus categories with distinct spatiotemporal structures from the population neural activity. We found that neurons in both the primary visual cortex and secondary visual areas show varying degrees of stimulus-specific decodability, and neurons in superficial layers tend to be more informative about the stimulus categories. Additional decoding analyses of directional motion were consistent with these findings. We observed synergy in the population code of direction in several visual areas suggesting area-specific organization of information representation across neurons. These differences in decoding capacities shed light on the specialized organization of neural information processing across anatomically distinct subpopulations, and further establish the mouse as a model for understanding visual perception.},
}

Hocker, D., & Park, I. M. (2018). Myopic Control: A New Control Objective for Neural Population Dynamics [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Hocker2018a,
  author = {David Hocker and Il Memming Park},
  title = {Myopic Control: A New Control Objective for Neural Population Dynamics},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2018,
}

Nassar, J., Linderman, S., Zhao, Y., Bugallo, M., & Park, I. M. (2018). Learning structured neural dynamics from single trial population recording. In 52nd Asilomar Conference on Signals, Systems and Computers. https://ieeexplore.ieee.org/document/8645122

@inproceedings{Nassar2018a,
  author = {Nassar, Josue and Linderman, Scott and Zhao, Yuan and Bugallo, M\'onica and Park, Il Memming},
  title = {Learning structured neural dynamics from single trial population recording},
  booktitle = {52nd Asilomar Conference on Signals, Systems and Computers},
  year = 2018,
  url = {https://ieeexplore.ieee.org/document/8645122},
  abstract = {To understand the complex nonlinear dynamics of neural circuits, we fit a structured state-space model called \textit{tree-structured recurrent switching linear dynamical system} (TrSLDS) to noisy high-dimensional neural time series. TrSLDS is a multi-scale hierarchical generative model for the state-space dynamics where each node of the latent tree captures locally linear dynamics. TrSLDS can be learned efficiently and in a fully Bayesian manner using Gibbs sampling. We showcase TrSLDS' potential of inferring low-dimensional interpretable dynamical systems on a variety of examples.},
  pdf = {Nassar2018a.pdf},
}

Zhao, Y., & Park, I. M. (2018). Accessing neural states in real time: recursive variational Bayesian dual estimation [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Zhao2018a,
  author = {Yuan Zhao and Il Memming Park},
  title = {Accessing neural states in real time: recursive variational {B}ayesian dual estimation},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2018,
}

Yates, J. L., Park, I. M., Katz, L. N., Pillow, J. W., & Huk, A. C. (2017). Functional dissection of signal and noise in MT and LIP during decision-making. Nature Neuroscience, 20, 1285–1292. https://doi.org/10.1038/nn.4611

@article{Yates2017a,
  author = {Yates, Jacob L. and Park, Il Memming and Katz, Leor N. and Pillow, Jonathan W. and Huk, Alexander C.},
  title = {Functional dissection of signal and noise in {MT} and {LIP} during decision-making},
  journal = {Nature Neuroscience},
  year = 2017,
  month = jul,
  volume = {20},
  pages = {1285--1292},
  doi = {10.1038/nn.4611},
  day = {24},
  issn = {1097-6256},
  keywords = {functional-connectivity, glm, lip, mt, noise-correlation, psychophysics},
}

Hocker, D., & Park, I. M. (2017). Multistep inference for generalized linear spiking models curbs runaway excitation. In 8th International IEEE EMBS Conference On Neural Engineering (pp. 613–616). IEEE. https://doi.org/10.1109/ner.2017.8008426

@inproceedings{Hocker2017a,
  author = {David Hocker and Il Memming Park},
  title = {Multistep inference for generalized linear spiking models curbs runaway excitation},
  booktitle = {8th International IEEE EMBS Conference On Neural Engineering},
  publisher = {IEEE},
  year = 2017,
  month = may,
  pages = {613--616},
  doi = {10.1109/ner.2017.8008426},
  isbn = {978-1-5090-4603-4},
  keywords = {autoregressive, glm, multi-step-prediction, spike-train, time-series},
  location = {Shanghai, China},
  pdf = {Hocker2017a.pdf},
}

Zhao, Y., & Park, I. M. (2017). Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains. Neural Computation, 29(5). https://doi.org/10.1162/NECO_a_00953

@article{Zhao2016a,
  author = {Zhao, Yuan and Park, Il Memming},
  title = {Variational Latent {G}aussian Process for Recovering Single-Trial Dynamics from Population Spike Trains},
  journal = {Neural Computation},
  year = 2017,
  month = may,
  volume = {29},
  number = {5},
  doi = {10.1162/NECO_a_00953},
  eprint = {1604.03053},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded populations of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent trajectories, particularly from single-trial population recordings, may help us understand the dynamics that drive neural computation. However, due to the biophysical constraints and noise in the spike trains, inferring trajectories from data is a challenging statistical problem in general. Here, we propose a practical and efficient inference method, the variational latent gaussian process (vLGP). The vLGP combines a generative model with a history-dependent point process observation, together with a smoothness prior on the latent trajectories. The vLGP improves on earlier methods for recovering latent trajectories, which assume either observation models inappropriate for point processes or linear dynamics. We compare and validate vLGP on both simulated data sets and population recordings from the primary visual cortex. In the V1 data set, we find that vLGP achieves substantially higher performance than previous methods for predicting omitted spike trains, as well as capturing both the toroidal topology of visual stimuli space and the noise correlation. These results show that vLGP is a robust method with the potential to reveal hidden neural dynamics from large-scale neural recordings.},
  code = {https://github.com/catniplab/vlgp},
  day = {22},
  keywords = {bayesian, computational-neuroscience, gaussian-process, glm, latent-dynamics, latent-variable, spike-train, statistical-neuroscience, statistics, torus, variational-bayes},
  youtube = {https://www.youtube.com/watch?v=CrY5AfNH1ik},
}

Hocker, D., & Park, I. M. (2017). Instability of the generalized linear model for spike trains [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Hocker2017b,
  author = {David Hocker and Il Memming Park},
  title = {Instability of the generalized linear model for spike trains},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2017,
}

Zhao, Y., & Park, I. M. (2017). Gotta infer'em all: dynamical features from neural trajectories [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Zhao2017a,
  author = {Yuan Zhao and Il Memming Park},
  title = {Gotta infer{'}em all: dynamical features from neural trajectories},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2017,
}

Zhao, Y., Yates, J., & Park, I. M. (2017). Low-dimensional state-space trajectory of choice at the population level in area MT [Conference abstract]. Computational and Systems Neuroscience (COSYNE).

@inproceedings{Zhao2017b,
  author = {Yuan Zhao and Jacob Yates and Il Memming Park},
  title = {Low-dimensional state-space trajectory of choice at the population level in area {MT}},
  booktitle = {Computational and Systems Neuroscience ({COSYNE})},
  year = 2017,
}

Dikecligil, G. N., Graham, D., Park, I. M., & Fontanini, A. (2016). Layer Specific Sensorimotor Activity in the Gustatory Cortex of Licking Mice [Conference abstract]. Society for Neuroscience.

@inproceedings{Dikecligil2016,
  author = {Gulce Nazli Dikecligil and Dustin Graham and Il Memming Park and Alfredo Fontanini},
  title = {Layer Specific Sensorimotor Activity in the Gustatory Cortex of Licking Mice},
  booktitle = {Society for Neuroscience},
  year = 2016,
}

Zhao, Y., & Park, I. M. (2016). Inferring low-dimensional network dynamics with variational latent Gaussian process [Conference abstract]. Organization for Computational Neuroscience (CNS).

@inproceedings{Zhao2016b,
  author = {Yuan Zhao and Il Memming Park},
  title = {Inferring low-dimensional network dynamics with variational latent {G}aussian process},
  booktitle = {Organization for Computational Neuroscience (CNS)},
  year = 2016,
}

Zhao, Y., & Park, I. M. (2016). Variational inference of latent Gaussian neural dynamics [Conference abstract]. International Conference on Machine Learning (ICML) Workshop on Computational Biology.

@inproceedings{Zhao2016c,
  author = {Yuan Zhao and Il Memming Park},
  title = {Variational inference of latent {G}aussian neural dynamics},
  booktitle = {International Conference on Machine Learning (ICML) Workshop on Computational Biology},
  year = 2016,
}

Zhao, Y., & Park, I. M. (2016). Interpretable Nonlinear Dynamic Modeling of Neural Trajectories. In Advances in Neural Information Processing Systems (NIPS). https://papers.nips.cc/paper/6543-interpretable-nonlinear-dynamic-modeling-of-neural-trajectories

@inproceedings{Zhao2016d,
  author = {Zhao, Yuan and Park, Il Memming},
  title = {Interpretable Nonlinear Dynamic Modeling of Neural Trajectories},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2016,
  url = {https://papers.nips.cc/paper/6543-interpretable-nonlinear-dynamic-modeling-of-neural-trajectories},
  eprint = {1608.06546},
  archiveprefix = {arXiv},
  primaryclass = {q-bio.QM},
  abstract = {A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.},
  keywords = {autoregressive, bifurcation, chaos, continuous-attractor, dynamics, neural-dynamics, nips, oscillation, tensorflow},
  youtube = {https://www.youtube.com/watch?v=7oWRZRpaq_I},
}

Zhao, Y. (2016). Log-linear Model Based Tree and Latent Variable Model for Count Data [Unpublished doctoral dissertation]. Stony Brook University.

@phdthesis{Zhao2016e,
  author = {Yuan Zhao},
  title = {Log-linear Model Based Tree and Latent Variable Model for Count Data},
  school = {Stony Brook University},
  year = 2016,
}

Archer, E., Park, I. M., Buesing, L., Cunningham, J., & Paninski, L. (2015). Black box variational inference for state space models. arXiv. https://doi.org/10.48550/arXiv.1511.07367

@unpublished{Archer2015a,
  author = {Archer, Evan and Park, Il Memming and Buesing, Lars and Cunningham, John and Paninski, Liam},
  title = {Black box variational inference for state space models},
  journal = {ArXiv e-prints},
  year = 2015,
  month = nov,
  eprint = {1511.07367},
  archiveprefix = {arXiv},
  primaryclass = {stat.ML},
  abstract = {Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering in the data, where it is assumed that meaningful correlation structure exists across time. A few highly-structured models, such as the linear dynamical system with {linear-Gaussian} observations, have closed-form inference procedures (e.g. the Kalman Filter), but this case is an exception to the general rule that exact posterior inference in more complex generative models is intractable. Consequently, much work in time-series modeling focuses on approximate inference procedures for one particular class of models. Here, we extend recent developments in stochastic variational inference to develop a `black-box' approximate inference technique for latent variable models with latent dynamical structure. We propose a structured Gaussian variational approximate posterior that carries the same intuition as the standard Kalman filter-smoother but, importantly, permits us to use the same inference approach to approximate the posterior of much more general, nonlinear latent variable generative models. We show that our approach recovers accurate estimates in the case of basic models with closed-form posteriors, and more interestingly performs well in comparison to variational approaches that were designed in a bespoke fashion for specific non-conjugate models.},
  day = {23},
  keywords = {deep-learning, machine-learning, stochastic-gradient-descent-algorithm, time-series, variational-bayes},
}

Park, I. M., Yates, J., Huk, A., & Pillow, J. (2015). Dynamic correlations between visual and decision areas during perceptual decision-making [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2015a,
  author = {Il Memming Park and Jacob Yates and Alex Huk and Jonathan Pillow},
  title = {Dynamic correlations between visual and decision areas during perceptual decision-making},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2015,
}

Wu, A., Park, I. M., & Pillow, J. (2015). Convolutional spike-triggered covariance analysis for estimating subunit models [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Wu2015a,
  author = {Anqi Wu and Il Memming Park and Jonathan Pillow},
  title = {Convolutional spike-triggered covariance analysis for estimating subunit models},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2015,
}

Wu, A., Park, I. M., & Pillow, J. (2015). Convolutional spike-triggered covariance analysis for neural subunit models. In Advances in Neural Information Processing Systems (NIPS). https://papers.nips.cc/paper/5962-convolutional-spike-triggered-covariance-analysis-for-neural-subunit-models

@inproceedings{Wu2015b,
  author = {Anqi Wu and Il Memming Park and Jonathan Pillow},
  title = {Convolutional spike-triggered covariance analysis for neural subunit models},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2015,
  url = {https://papers.nips.cc/paper/5962-convolutional-spike-triggered-covariance-analysis-for-neural-subunit-models},
}

Yates, J., Archer, E., Huk, A. C., & Park, I. M. (2015). Canonical correlations reveal co-variability between spike trains and local field potentials in area MT [Conference abstract]. Organization for Computational Neuroscience (CNS).

@inproceedings{Yates2015a,
  author = {Jacob Yates and Evan Archer and Alexander C. Huk and Il Memming Park},
  title = {Canonical correlations reveal co-variability between spike trains and local field potentials in area {MT}},
  booktitle = {Organization for Computational Neuroscience (CNS)},
  year = 2015,
}

Archer, E., Park, I. M., & Pillow, J. (2014). Bayesian Entropy Estimation for Countable Discrete Distributions. Journal of Machine Learning Research, 15, 2833–2868. http://jmlr.org/papers/v15/archer14a.html

@article{Archer2014a,
  author = {Archer, Evan and Park, Il Memming and Pillow, Jonathan},
  title = {{Bayes}ian Entropy Estimation for Countable Discrete Distributions},
  journal = {Journal of Machine Learning Research},
  year = 2014,
  month = oct,
  volume = {15},
  pages = {2833--2868},
  url = {http://jmlr.org/papers/v15/archer14a.html},
  eprint = {1302.0328},
  archiveprefix = {arXiv},
  primaryclass = {cs.IT},
  abstract = {We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The {Pitman-Yor} process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it also provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over $H$ can be computed analytically. We derive formulas for the posterior mean (Bayes' least squares estimate) and variance under Dirichlet and {Pitman-Yor} process priors. Moreover, we show that a fixed Dirichlet or {Pitman-Yor} process prior implies a narrow prior distribution over $H$, meaning the prior strongly determines the entropy estimate in the under-sampled regime. We derive a family of continuous mixing measures such that the resulting mixture of {Pitman-Yor} processes produces an approximately flat prior over $H$. We show that the resulting {Pitman-Yor} Mixture ({PYM}) entropy estimator is consistent for a large class of distributions. We explore the theoretical properties of the resulting estimator, and show that it performs well both in simulation and in application to real data.},
  day = {2},
  keywords = {bayesian, entropy-estimation, nonparametric-bayes, pitman-yor-process},
}

Park, I. M., Meister, M. L. R., Huk, A. C., & Pillow, J. W. (2014). Encoding and decoding in parietal cortex during sensorimotor decision-making. Nature Neuroscience, 17(10), 1395–1403. https://doi.org/10.1038/nn.3800

@article{Park2014d,
  author = {Park, Il Memming and Meister, Miriam L. R. and Huk, Alexander C. and Pillow, Jonathan W.},
  title = {Encoding and decoding in parietal cortex during sensorimotor decision-making},
  journal = {Nature Neuroscience},
  year = 2014,
  month = oct,
  volume = {17},
  number = {10},
  pages = {1395--1403},
  doi = {10.1038/nn.3800},
  abstract = {It has been suggested that the lateral intraparietal area (LIP) of macaques plays a fundamental role in sensorimotor decision-making. We examined the neural code in LIP at the level of individual spike trains using a statistical approach based on generalized linear models. We found that LIP responses reflected a combination of temporally overlapping task- and decision-related signals. Our model accounts for the detailed statistics of LIP spike trains and accurately predicts spike trains from task events on single trials. Moreover, we derived an optimal decoder for heterogeneous, multiplexed LIP responses that could be implemented in biologically plausible circuits. In contrast with interpretations of LIP as providing an instantaneous code for decision variables, we found that optimal decoding requires integrating LIP spikes over two distinct timescales. These analyses provide a detailed understanding of neural representations in LIP and a framework for studying the coding of multiplexed signals in higher brain areas.},
  issn = {1097-6256},
  keywords = {computational-neuroscience, decision-making, glm, lip, monkey, neural-code, neural-decoding},
  pdf = {Park2014d_typofixed.pdf},
}

Park, I. M., Bobkov, Y. V., Ache, B. W., & Príncipe, J. C. (2014). Intermittency coding in the primary olfactory system: A neural substrate for olfactory scene analysis. The Journal of Neuroscience, 34(3), 941–952. https://doi.org/10.1523/jneurosci.2204-13.2014

@article{Park2014a,
  author = {Il Memming Park and Yuriy V. Bobkov and Barry W. Ache and Jos\'e C. Pr\'incipe},
  title = {Intermittency coding in the primary olfactory system: A neural substrate for olfactory scene analysis},
  journal = {The Journal of Neuroscience},
  publisher = {Society for Neuroscience},
  year = 2014,
  month = jan,
  volume = {34},
  number = {3},
  pages = {941--952},
  doi = {10.1523/jneurosci.2204-13.2014},
  abstract = {The spatial and temporal characteristics of the visual and acoustic sensory input are indispensable attributes for animals to perform scene analysis. In contrast, research in olfaction has focused almost exclusively on how the nervous system analyzes the quality and quantity of the sensory signal and largely ignored the spatiotemporal dimension especially in longer time scales. Yet, detailed analyses of the turbulent, intermittent structure of water- and air-borne odor plumes strongly suggest that spatio-temporal information in longer time scales can provide major cues for olfactory scene analysis for animals. We show that a bursting subset of primary olfactory receptor neurons ({bORNs}) in lobster has the unexpected capacity to encode the temporal properties of intermittent odor signals. Each {bORN} is tuned to a specific range of stimulus intervals, and collectively {bORNs} can instantaneously encode a wide spectrum of intermittencies. Our theory argues for the existence of a novel peripheral mechanism for encoding the temporal pattern of odor that potentially serves as a neural substrate for olfactory scene analysis.},
  day = {15},
  issn = {1529-2401},
  keywords = {neural-code, odor-plume, olfactory, uncoupled-oscillator},
}

Huk, A., Yates, J., Katz, L., Park, I. M., & Pillow, J. (2014). Dissociated functional significance of choice-related activity across the primate dorsal stream [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Huk2014a,
  author = {Alexander Huk and Jacob Yates and Leor Katz and Il Memming Park and Jonathan Pillow},
  title = {Dissociated functional significance of choice-related activity across the primate dorsal stream},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2014,
}

Park, I. M., Archer, E., Latimer, K., & Pillow, J. (2014). Scalable nonparametric models for binary spike patterns [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2014b,
  author = {Il Memming Park and Evan Archer and Kenneth Latimer and Jonathan Pillow},
  title = {Scalable nonparametric models for binary spike patterns},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2014,
}

Park, I. M., Seth, S., & Van Vaerenbergh, S. (2014). Probabilistic Kernel Least Mean Squares Algorithms. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). IEEE. https://doi.org/10.1109/ICASSP.2014.6855214

@inproceedings{Park2014c,
  author = {Park, Il Memming and Seth, Sohan and Van Vaerenbergh, Steven},
  title = {Probabilistic Kernel Least Mean Squares Algorithms},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  publisher = {IEEE},
  year = 2014,
  doi = {10.1109/ICASSP.2014.6855214},
  url = {http://gtas.unican.es/pub/393},
}

Yates, J. L., Katz, L. N., Park, I. M., Pillow, J. W., & Huk, A. C. (2014). Correlations and choice probabilities in simultaneously recorded MT and LIP neurons [Conference abstract]. Society for Neuroscience.

@inproceedings{Yates2014a,
  author = {Jacob L. Yates and Leor N. Katz and Il Memming Park and Jonathan W. Pillow and Alexander C. Huk},
  title = {Correlations and choice probabilities in simultaneously recorded {MT} and {LIP} neurons},
  booktitle = {Society for Neuroscience},
  year = 2014,
}

Park, I. M., Seth, S., & Van Vaerenbergh, S. (2013). Bayesian Extensions of Kernel Least Mean Squares. arXiv. https://doi.org/10.48550/arXiv.1310.5347

@unpublished{Park2013g,
  author = {Park, Il Memming and Seth, Sohan and Van Vaerenbergh, Steven},
  title = {{Bayes}ian Extensions of Kernel Least Mean Squares},
  journal = {ArXiv e-prints},
  year = 2013,
  month = oct,
  eprint = {1310.5347},
  archiveprefix = {arXiv},
  primaryclass = {st.ML},
  abstract = {The kernel least mean squares ({KLMS}) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the {KLMS} can be interpreted as an approximate Bayesian filtering method. This allows us to systematically develop extensions of the {KLMS} by modifying the underlying state-space and observation models. The resulting extensions introduce many desirable properties such as "forgetting", and the ability to learn from discrete data, while retaining the computational simplicity and time complexity of the original algorithm.},
  day = {20},
  keywords = {adaptive-filter, bayesian, kernel-method, klms, online-algorithm, poisson-observation},
}

Park, I. M., Seth, S., Paiva, A. R. C., Li, L., & Principe, J. C. (2013). Kernel methods on spike train space for neuroscience: a tutorial. IEEE Signal Processing Magazine, 30(4), 149–160. https://doi.org/10.1109/msp.2013.2251072

@article{Park2013a,
  author = {Park, Il Memming and Seth, Sohan and Paiva, Antonio R. C. and Li, Lin and Principe, Jose C.},
  title = {Kernel methods on spike train space for neuroscience: a tutorial},
  journal = {IEEE Signal Processing Magazine},
  year = 2013,
  month = jul,
  volume = {30},
  number = {4},
  pages = {149--160},
  doi = {10.1109/msp.2013.2251072},
  eprint = {1302.5964},
  abstract = {Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space. However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and signal processing experts. This tutorial illustrates why kernel methods can, and have already started to, change the way spike trains are analyzed and processed. The presentation incorporates simple mathematical analogies and convincing practical examples in an attempt to show the yet unexplored potential of positive definite functions to quantify point processes. It also provides a detailed overview of the current state of the art and future challenges with the hope of engaging the readers in active participation.},
  day = {24},
  issn = {1053-5888},
}

Archer, E., Park, I. M., & Pillow, J. (2013). Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data. Entropy, 15(5), 1738–1755. https://doi.org/10.3390/e15051738

@article{Archer2013c,
  author = {Archer, Evan and Park, Il Memming and Pillow, Jonathan},
  title = {{Bayes}ian and Quasi-{Bayes}ian Estimators for Mutual Information from Discrete Data},
  journal = {Entropy},
  year = 2013,
  month = may,
  volume = {15},
  number = {5},
  pages = {1738--1755},
  doi = {10.3390/e15051738},
  url = {https://www.mdpi.com/1099-4300/15/5/1738/pdf},
  abstract = {Mutual information ({MI}) quantifies the statistical dependency between a pair of random variables, and plays a central role in the analysis of engineering and biological systems. Estimation of {MI} is difficult due to its dependence on an entire joint distribution, which is difficult to estimate from samples. Here we discuss several regularized estimators for {MI} that employ priors based on the Dirichlet distribution. First, we discuss three {quasi-Bayesian} estimators that result from linear combinations of Bayesian estimates for conditional and marginal entropies. We show that these estimators are not in fact Bayesian, and do not arise from a well-defined posterior distribution and may in fact be negative. Second, we show that a fully Bayesian {MI} estimator proposed by Hutter (2002), which relies on a fixed Dirichlet prior, exhibits strong prior dependence and has large bias for small datasets. Third, we formulate a novel Bayesian estimator using a {mixture-of-Dirichlets} prior, with mixing weights designed to produce an approximately flat prior over {MI}. We examine the performance of these estimators with a variety of simulated datasets and show that, surprisingly, {quasi-Bayesian} estimators generally outperform our Bayesian estimator. We discuss outstanding challenges for {MI} estimation and suggest promising avenues for future research.},
  day = {10},
  keywords = {bayesian, entropy-estimation, estimation, information-theory, mutual-information},
}

Archer, E., Park, I. M., & Pillow, J. (2013). Semi-parametric Bayesian entropy estimation for binary spike trains [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Archer2013b,
  author = {Evan Archer and Il Memming Park and Jonathan Pillow},
  title = {Semi-parametric {Bayes}ian entropy estimation for binary spike trains},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2013,
}

Archer, E., Park, I. M., & Pillow, J. W. (2013). Bayesian entropy estimation for binary spike train data using parametric prior knowledge. In Advances in Neural Information Processing Systems (NIPS). http://papers.nips.cc/paper/4873-bayesian-entropy-estimation-for-binary-spike-train-data-using-parametric-prior-knowledge

@inproceedings{Archer2013d,
  author = {Evan Archer and Il Memming Park and Jonathan W. Pillow},
  title = {{Bayes}ian entropy estimation for binary spike train data using parametric prior knowledge},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2013,
  url = {http://papers.nips.cc/paper/4873-bayesian-entropy-estimation-for-binary-spike-train-data-using-parametric-prior-knowledge},
}

Paiva, A. R. C., Park, I., Príncipe, J. C., & Sanchez, J. (2013). Instantaneous cross-correlation analysis of neural ensembles with high temporal resolution. In D. Farina, W. Jensen, & M. Akay (Eds.), Neural engineering applied to neurorehabilitation. Wiley.

@inbook{Paiva2011,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe and Justin Sanchez},
  title = {Instantaneous cross-correlation analysis of neural ensembles with high temporal resolution},
  booktitle = {Neural engineering applied to neurorehabilitation},
  editor = {Dario Farina and Winnie Jensen and Metin Akay},
  publisher = {Wiley},
  year = 2013,
}

Park, I. M., Archer, E., Priebe, N., & Pillow, J. (2013). Got a moment or two? Neural models and linear dimensionality reduction [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2013b,
  author = {Il Memming Park and Evan Archer and Nicholas Priebe and Jonathan Pillow},
  title = {Got a moment or two? {N}eural models and linear dimensionality reduction},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2013,
}

Park, I. M., Archer, E., & Pillow, J. (2013). Bayesian entropy estimators for spike trains [Conference abstract]. Computational Neuroscience (CNS).

@inproceedings{Park2013c,
  author = {Il Memming Park and Evan Archer and Jonathan Pillow},
  title = {{B}ayesian entropy estimators for spike trains},
  booktitle = {Computational Neuroscience (CNS)},
  year = 2013,
}

Park, I. M., Archer, E., Latimer, K., & Pillow, J. W. (2013). Universal models for binary spike patterns using centered Dirichlet processes. In Advances in Neural Information Processing Systems (NIPS). http://papers.nips.cc/paper/5050-universal-models-for-binary-spike-patterns-using-centered-dirichlet-processes

@inproceedings{Park2013e,
  author = {Il Memming Park and Evan Archer and Kenneth Latimer and Jonathan W. Pillow},
  title = {Universal models for binary spike patterns using centered {D}irichlet processes},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2013,
  url = {http://papers.nips.cc/paper/5050-universal-models-for-binary-spike-patterns-using-centered-dirichlet-processes},
}

Park, I. M., Archer, E., Priebe, N., & Pillow, J. W. (2013). Spectral methods for neural characterization using generalized quadratic models. In Advances in Neural Information Processing Systems (NIPS). http://papers.nips.cc/paper/4993-spectral-methods-for-neural-characterization-using-generalized-quadratic-models

@inproceedings{Park2013f,
  author = {Il Memming Park and Evan Archer and Nicholas Priebe and Jonathan W. Pillow},
  title = {Spectral methods for neural characterization using generalized quadratic models},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2013,
  url = {http://papers.nips.cc/paper/4993-spectral-methods-for-neural-characterization-using-generalized-quadratic-models},
}

Pillow, J., & Park, I. M. (2013). Beyond Barlow: A Bayesian theory of efficient neural coding [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Pillow2013a,
  author = {Jonathan Pillow and Il Memming Park},
  title = {Beyond {B}arlow: A {Bayes}ian theory of efficient neural coding},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2013,
}

Yates, J., Park, I. M., Cormack, L., Pillow, J., & Huk, A. (2013). Precise characterization of multiple LIP neurons in relation to stimulus and behavior [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Yates2013a,
  author = {Jacob Yates and Il Memming Park and Lawrence Cormack and Jonathan Pillow and Alexander Huk},
  title = {Precise characterization of multiple {LIP} neurons in relation to stimulus and behavior},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2013,
}

Yates, J., Park, I. M., Cormack, L., Pillow, J., & Huk, A. (2013). Precise characterization of dorsal stream neural activity during decision making [Conference abstract]. Society for Neuroscience.

@inproceedings{Yates2013b,
  author = {Jacob Yates and Il Memming Park and Lawrence Cormack and Jonathan Pillow and Alexander Huk},
  title = {Precise characterization of dorsal stream neural activity during decision making},
  booktitle = {Society for Neuroscience},
  year = 2013,
}

Li, L., Park, I. M., Brockmeier, A., Chen, B., Seth, S., Francis, J. T., Sanchez, J. C., & Príncipe, J. C. (2012). Adaptive Inverse Control of Neural Spatiotemporal Spike Patterns with a Reproducing Kernel Hilbert Space (RKHS) Framework. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 21(4), 532–543. https://doi.org/10.1109/TNSRE.2012.2200300

@article{Li2012a,
  author = {Lin Li and Il Memming Park and Austin Brockmeier and Badong Chen and Sohan Seth and Joseph T. Francis and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {Adaptive Inverse Control of Neural Spatiotemporal Spike Patterns with a Reproducing Kernel {H}ilbert Space ({RKHS}) Framework},
  journal = {IEEE Transactions on Neural Systems and Rehabilitation Engineering},
  year = 2012,
  month = aug,
  volume = {21},
  number = {4},
  pages = {532--543},
  doi = {10.1109/TNSRE.2012.2200300},
  issn = {1534-4320},
  keywords = {Hilbert spaces;MIMO systems;adaptive control;adaptive signal processing;bioelectric phenomena;decoding;medical control systems;medical signal processing;multidimensional signal processing;neurophysiology;nonlinear control systems;signal representation;spatiotemporal phenomena;MIMO adaptive inverse control scheme;Schoenberg kernel maps;adaptive inverse control;control procedure;decoding accuracy;electrical stimulation;elicited system response;generalized linear model;linear algorithm;multidimensional time-varying signal representation;multiple-input multiple-output adaptive inverse control scheme;neural perturbations;neural signal representation;neural spatiotemporal spike patterns;neural stimulation;neural system plasticity;neurons;nonlinear neural system control;population spiking activity;realistic synthetic neural circuit;reproducing kernel Hilbert space framework;spike train RKHS;spikernel model;spiking responses;standard control methodology;system control problem;target system response;time-invariant homogeneous model;Adaptation models;Decoding;Integrated circuit modeling;Kernel;MIMO;Timing;Vectors;Adaptive inverse control;Schoenberg kernel;neural stimulation;spike timing representations},
}

Park, I. M., Seth, S., Rao, M., & Príncipe, J. C. (2012). Strictly positive definite spike train kernels for point process divergences. Neural Computation, 24(8), 2223–2250. https://doi.org/10.1162/NECO_a_00309

@article{Park2012a,
  author = {Il Memming Park and Sohan Seth and Murali Rao and Jos\'e C. Pr\'incipe},
  title = {Strictly positive definite spike train kernels for point process divergences},
  journal = {Neural Computation},
  year = 2012,
  month = aug,
  volume = {24},
  number = {8},
  issue = {8},
  pages = {2223--2250},
  doi = {10.1162/NECO_a_00309},
  abstract = {Exploratory tools that are sensitive to arbitrary statistical variations in spike train observations open up the possibility of novel neuroscientific discoveries. Developing such tools, however, is difficult due to the lack of Euclidean structure of the spike train space, and an experimenter usually prefers simpler tools that capture only limited statistical features of the spike train, such as mean spike count or mean firing rate. We explore strictly positive-definite kernels on the space of spike trains to offer both a structural representation of this space and a platform for developing statistical measures that explore features beyond count or rate. We apply these kernels to construct measures of divergence between two point processes and use them for hypothesis testing, that is, to observe if two sets of spike trains originate from the same underlying probability law. Although there exist positive-definite spike train kernels in the literature, we establish that these kernels are not strictly definite and thus do not induce measures of divergence. We discuss the properties of both of these existing nonstrict kernels and the novel strict kernels in terms of their computational complexity, choice of free parameters, and performance on both synthetic and real data through kernel principal component analysis and hypothesis testing.},
  pdf = {Park2012a_spd_spike_train_kernel_divergence_color.pdf},
}

Bobkov, Y., Park, I., Ukhanov, K., Príncipe, J. C., & Ache, B. W. (2012). Cellular basis for response diversity in the olfactory periphery. PLoS One, 7(4), Article e34843. https://doi.org/10.1371/journal.pone.0034843

@article{Bobkov2012a,
  author = {Yuriy Bobkov and Il Park and Kirill Ukhanov and Jos\'e C. Pr\'incipe and Barry W. Ache},
  title = {Cellular basis for response diversity in the olfactory periphery},
  journal = {PLoS One},
  year = 2012,
  month = apr,
  volume = {7},
  number = {4},
  pages = {e34843},
  doi = {10.1371/journal.pone.0034843},
  abstract = {An emerging idea in olfaction is that temporal coding of odor specificity can be intrinsic to the primary olfactory receptor neurons ({ORNs}). As a first step towards understanding whether lobster {ORNs} are capable of generating odor-specific temporal activity and what mechanisms underlie any such heterogeneity in discharge pattern, we characterized different patterns of activity in lobster {ORNs} individually and ensemble using patch-clamp recording and calcium imaging. We demonstrate that lobster {ORNs} show tonic excitation, tonic inhibition, phaso-tonic excitation, and bursting, and that these patterns are faithfully reflected in the calcium signal. We then demonstrate that the various dynamic patterns of response are inherent in the cells, and that this inherent heterogeneity is largely determined by heterogeneity in the underlying intrinsic conductances.},
  day = {13},
}

Park, I. M., Nassar, M., & Park, M. (2012). Active Bayesian Optimization: Minimizing Minimizer Entropy. arXiv. https://doi.org/10.48550/arXiv.1202.2143

@unpublished{Park2012c,
  author = {Il Memming Park and Marcel Nassar and Mijung Park},
  title = {Active {Bayes}ian Optimization: Minimizing Minimizer Entropy},
  journal = {ArXiv e-prints},
  year = 2012,
  month = feb,
  eprint = {1202.2143},
  archiveprefix = {arXiv},
  primaryclass = {stat.ME},
  abstract = {The ultimate goal of optimization is to find the minimizer of a target {function.However}, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian {processes.Our} criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately compared to conventional Bayesian optimization criteria.},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System},
  adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1202.2143M},
  code = {https://github.com/memming/gpao},
  keywords = {Statistics - Methodology, Computer Science - Learning, Statistics - Machine Learning},
}

Li, L., Park, I., Seth, S., Sanchez, J. C., & Príncipe, J. C. (2012). Functional Connectivity Dynamics Among Cortical Neurons: A Dependence Analysis. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 20(1), 18–30. https://doi.org/10.1109/TNSRE.2011.2176749

@article{Li2011a,
  author = {Lin Li and Il Park and Sohan Seth and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {Functional Connectivity Dynamics Among Cortical Neurons: A Dependence Analysis},
  journal = {IEEE Transactions on Neural Systems and Rehabilitation Engineering},
  year = 2012,
  month = jan,
  volume = {20},
  number = {1},
  pages = {18--30},
  doi = {10.1109/TNSRE.2011.2176749},
  issn = {1534-4320},
  keywords = {behavior task;cortical neurons;cross correlation;dependence analysis;firing rates;food reaching task;functional connectivity dynamics;mean square contingency;monkey cortex;movement states;mutual information;neural assembly functional connectivity;neural ensemble recordings;pairwise functional connectivity;phase synchronization;phase-based metrics;robust estimators;statistical analysis;temporal resolutions;time 100 ms to 1000 ms;bioelectric potentials;biomechanics;brain;correlation methods;estimation theory;medical signal processing;neurophysiology;statistical analysis;synchronisation;},
}

Archer, E., Park, I. M., & Pillow, J. (2012). Bayesian entropy estimation for infinite neural alphabets [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE). http://papers.nips.cc/paper/4521-bayesian-estimation-of-discrete-entropy-with-mixtures-of-stick-breaking-priors

@inproceedings{Archer2012a,
  author = {Evan Archer and Il Memming Park and Jonathan Pillow},
  title = {{Bayes}ian entropy estimation for infinite neural alphabets},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2012,
  url = {http://papers.nips.cc/paper/4521-bayesian-estimation-of-discrete-entropy-with-mixtures-of-stick-breaking-priors},
}

Archer, E., Park, I. M., & Pillow, J. W. (2012). Bayesian estimation of discrete entropy with mixtures of stick breaking priors. In Advances in Neural Information Processing Systems (NIPS). https://papers.nips.cc/paper/4521-bayesian-estimation-of-discrete-entropy-with-mixtures-of-stick-breaking-priors

@inproceedings{Archer2012b,
  author = {Evan Archer and Il Memming Park and Jonathan W. Pillow},
  title = {{Bayes}ian estimation of discrete entropy with mixtures of stick breaking priors},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2012,
  url = {https://papers.nips.cc/paper/4521-bayesian-estimation-of-discrete-entropy-with-mixtures-of-stick-breaking-priors},
}

Park, I. M., & Pillow, J. (2012). Bayesian spike-triggered covariance and the elliptical LNP model [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2012b,
  author = {Il Memming Park and Jonathan Pillow},
  title = {{Bayes}ian spike-triggered covariance and the elliptical {LNP} model},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2012,
}

Park, I. M., Meister, M. L. R., Huk, A. C., & Pillow, J. W. (2012). Deciphering the code for sensorimotor decision-making at the level of single neurons in parietal cortex [Conference abstract]. Society for Neuroscience.

@inproceedings{Park2012e,
  author = {Il Memming Park and Miriam L. R. Meister and Alexander C. Huk and Jonathan W. Pillow},
  title = {Deciphering the code for sensorimotor decision-making at the level of single neurons in parietal cortex},
  booktitle = {Society for Neuroscience},
  year = 2012,
  note = {(oral presentation)},
}

Seth, S., Rao, M., Park, I., & Príncipe, J. C. (2011). A Unified Framework for Quadratic Measures of Independence. IEEE Transactions on Signal Processing, 59(8), 3624–3635. https://doi.org/10.1109/TSP.2011.2153197

@article{Seth2011a,
  author = {Sohan Seth and Murali Rao and Il Park and Jos\'e C. Pr\'incipe},
  title = {A Unified Framework for Quadratic Measures of Independence},
  journal = {IEEE Transactions on Signal Processing},
  year = 2011,
  month = aug,
  volume = {59},
  issue = {8},
  pages = {3624--3635},
  doi = {10.1109/TSP.2011.2153197},
}

Park, I., Seth, S., Rao, M., & Principe, J. C. (2011). Estimation of symmetric chi-square divergence for point processes. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) (pp. 2016–2019). IEEE. https://doi.org/10.1109/ICASSP.2011.5946907

@inproceedings{Park2011d,
  author = {Park, Il and Seth, Sohan and Rao, Murali and Principe, Jos\'e C.},
  title = {Estimation of symmetric chi-square divergence for point processes},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  publisher = {IEEE},
  year = 2011,
  month = may,
  pages = {2016--2019},
  doi = {10.1109/ICASSP.2011.5946907},
  isbn = {978-1-4577-0538-0},
  issn = {1520-6149},
  keywords = {divergence, hypothesis-test, point-process},
}

Li, L., Park, I. M., Seth, S., Choi, J., Francis, J. T., Sanchez, J. C., & Príncipe, J. C. (2011). An adaptive decoder from spike trains to micro-stimulation using kernel least-mean-square (KLMS) algorithm. In IEEE International Workshop on Machine Learning for Signal Processing (MLSP). https://doi.org/10.1109/MLSP.2011.6064603

@conference{Li2011b,
  author = {Lin Li and Il Memming Park and Sohan Seth and John Choi and Joseph T. Francis and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {An adaptive decoder from spike trains to micro-stimulation using kernel least-mean-square ({KLMS}) algorithm},
  booktitle = {IEEE International Workshop on Machine Learning for Signal Processing (MLSP)},
  year = 2011,
  doi = {10.1109/MLSP.2011.6064603},
}

Park, I. M., Meister, M., Huk, A., & Pillow, J. W. (2011). Detailed encoding and decoding of choice-related information from LIP spike trains [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2011a,
  author = {Il Memming Park and Miriam Meister and Alexander Huk and Jonathan W Pillow},
  title = {Detailed encoding and decoding of choice-related information from {LIP} spike trains},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience ({COSYNE})},
  year = 2011,
}

Park, I. M., Seth, S., & Príncipe, J. C. (2011). Spike Train Kernel Methods for Neuroscience [Conference abstract]. Joint Statistical Meeting.

@conference{Park2011b,
  author = {Il Memming Park and Sohan Seth and Jos\'e C. Pr\'incipe},
  title = {Spike Train Kernel Methods for Neuroscience},
  booktitle = {Joint Statistical Meeting},
  year = 2011,
  abstract = {Positive definite kernels has been widely used in the context of machine learning by the, so called, kernel machines such as the support vector machine and the kernel principal component analysis. An attractive property of a kernel machine is that it can be applied to arbitrary spaces as long as appropriate kernel is provided. We have developed spike train kernels and analyzed their properties in the context of two-sample problem, probability embedding as well as regression and classification. We discuss strictly positive definite kernels that provide theoretical foundation for its power.},
}

Park, I. M., & Pillow, J. W. (2011). Bayesian Spike Triggered Covariance Analysis. In Advances in Neural Information Processing Systems (NIPS). http://papers.nips.cc/paper/4411-bayesian-spike-triggered-covariance-analysis

@inproceedings{Park2011c,
  author = {Il Memming Park and Jonathan W. Pillow},
  title = {{Bayes}ian Spike Triggered Covariance Analysis},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2011,
  url = {http://papers.nips.cc/paper/4411-bayesian-spike-triggered-covariance-analysis},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2010). A Comparison of Binless Spike Train Measures. Neural Computing & Applications, 19(3), 405–419. https://doi.org/10.1007/s00521-009-0307-6

@article{Paiva2009a,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {A Comparison of Binless Spike Train Measures},
  journal = {Neural Computing \& Applications},
  year = 2010,
  month = sep,
  volume = {19},
  issue = {3},
  pages = {405--419},
  doi = {10.1007/s00521-009-0307-6},
}

Park, I. M. (2010). Capturing spike train similarity structure: A point process divergence approach [Unpublished doctoral dissertation]. The University of Florida.

@phdthesis{Park2010a,
  author = {Il Memming Park},
  title = {Capturing spike train similarity structure: A point process divergence approach},
  school = {The University of Florida},
  year = 2010,
  month = Aug,
  abstract = {Neurons mostly communicate via stereotypical events called action potentials (or spikes for short) giving rise to a time series called the neural spike train. Spike trains are random in nature, and hence one needs to deal with the probability law over the spike trains space (point process). Rich statistical descriptors are a prerequisite for statistical learning in the spike train domain; this provides necessary analysis tools for neural decoding, change detection, and neuron model fitting. The first and second order statistics prevalently used in neuroscience -- such as mean firing rate function, and correlation function -- do not fully describe the randomness, thus are partial statistics. However, restricting the study to these basic statistics implicitly limit what can be discovered. We propose three families of statistical divergences that enable non-Poisson, and more over, distribution-free spike train analysis. We extend the Kolmogorov-Smirnov test, $\phi$-divergence, and kernel based divergence to point processes. This is possible through the development of novel mathematical foundations for point process representations. Compared to the similarity or distance measures for spike trains that assumes predefined stochasticity and hence are not flexible, divergences applied to sets of spike trains capture the underlying probability law and measures the statistical similarity. Therefore, divergences are more robust, and assumption free. We apply the methodology on real data from neuronal cultures as well as anesthetized animals for neuroscience and neuroengineering applications posed as statistical inferences to evaluate their usefulness.},
}

Bobkov, Y., Ukhanov, K., Park, I., Príncipe, J. C., & Ache, B. (2010). Measuring Ensemble Activity in Lobster ORNs through Calcium Imaging [Conference abstract]. Association for Chemoreception (AChemS) Annual Meeting.

@inproceedings{Bobkov2010a,
  author = {Yuriy Bobkov and Kirill Ukhanov and Il Park and Jos\'e C. Pr\'incipe and Barry Ache},
  title = {Measuring Ensemble Activity in Lobster {ORN}s through Calcium Imaging},
  booktitle = {Association for Chemoreception (AChemS) Annual Meeting},
  year = 2010,
  abstract = {Lobster ORNs can be imaged in the olfactory organ in situ, thereby maintaining the normal polarity of the cells and the ionic environment of the olfactory cilia. The preparation gives simultaneous access to hundreds of ORNs that are viable for hours, thereby allowing rigorous characterization of their steadystate and dynamic properties. Odorants change the level of cytoplasmic Ca2+ in a dose-dependent manner in ORNs loaded with Ca2+-sensitive indicator either through bath application or via a patch electrode. The kinetics and amplitude of the odorantevoked Ca2+ signal correlate with the excitatory inward current, the degree of membrane depolarization, and the number of evoked action potentials, thereby establishing the physiological relevance of the Ca2+ signal. Spontaneous periodic Ca2+ transients in many ORNs correlate with spontaneous bursts of action potentials measured in single cells in the same cluster. We are using signal processing algorithms to analyze the level of correlated activity between these ORNs and the extent to which periodic calcium oscillations in different ORNs are synchronized by common intermittent excitatory input to test the predictions of our computational model for ensemble burst coding in these cells and the potential relevance of bursting input to olfactory scene analysis.},
}

Brockmeier, A. J., Park, I., Mahmoudi, B., Sanchez, J. C., & Príncipe, J. C. (2010). Spatio-Temporal Clustering of Firing Rates for Neural State Estimation. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS).

@inproceedings{Brockmeier2010a,
  author = {Austin J. Brockmeier and Il Park and Babak Mahmoudi and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {Spatio-Temporal Clustering of Firing Rates for Neural State Estimation},
  booktitle = {Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS)},
  year = 2010,
}

Li, L., Park, I., Seth, S., Sanchez, J. C., & Príncipe, J. C. (2010). Neuronal Functional Connectivity Dynamics in Cortex: An MSC-based Analysis. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS).

@inproceedings{Li2010a,
  author = {Lin Li and Il Park and Sohan Seth and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {Neuronal Functional Connectivity Dynamics in Cortex: An {MSC}-based Analysis},
  booktitle = {Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS)},
  year = 2010,
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2010). Optimization in Reproducing Kernel Hilbert Spaces of Spike Trains. In W. A. Chaovalitwongse, P. Pardalos, & P. Xanthopoulos (Eds.), Computational Neuroscience (pp. 3–29). Springer New York. https://doi.org/10.1007/978-0-387-88630-5_1

@inbook{Paiva2010a,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {Optimization in Reproducing Kernel {H}ilbert Spaces of Spike Trains},
  booktitle = {Computational Neuroscience},
  editor = {W. Art Chaovalitwongse and Panos Pardalos and Petros Xanthopoulos},
  publisher = {Springer New York},
  year = 2010,
  pages = {3--29},
  doi = {10.1007/978-0-387-88630-5_1},
  abstract = {This chapter presents a framework based on reproducing kernel Hilbert spaces (RKHS) for optimization with spike trains. To establish the RKHS for optimization we start by introducing kernels for spike trains. It is shown that spike train kernels can be built from ideas of kernel methods or from the intensity functions underlying the spike trains. However, the later approach shall be the main focus of this study. We introduce the memoryless cross-intensity (mCI) kernel as an example of an inner product of spike trains, which defines the RKHS bottom-up as an inner product of intensity functions. Being defined in terms of the intensity functions, this approach toward defining spike train kernels has the advantage that points in the RKHS incorporate a statistical description of the spike trains, and the statistical model is explicitly stated. Some properties of the mCI kernel and the RKHS it induces will be given to show that this RKHS has the necessary structure for optimization. The issue of estimation from data is also addressed. We finalize with an example of optimization in the RKHS by deriving an algorithm for principal component analysis (PCA) of spike trains.},
  address = {New York, NY},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2010). Inner Products for Representation and Learning in the Spike Train Domain. In K. G. Oweiss (Ed.), Statistical Signal Processing for Neuroscience. Academic Press.

@inbook{Paiva2010b,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {Inner Products for Representation and Learning in the Spike Train Domain},
  booktitle = {Statistical Signal Processing for Neuroscience},
  editor = {Karim G. Oweiss},
  publisher = {Academic Press},
  year = 2010,
  isbn = {978-0123750273},
}

Paiva, A. R. C., & Park, I. (2010). Which measure should we use for unsupervised spike train learning? [Conference abstract]. Statistical Analysis of Neuronal Data (SAND5).

@conference{Paiva2010c,
  author = {Ant\'onio R. C. Paiva and Il Park},
  title = {Which measure should we use for unsupervised spike train learning?},
  booktitle = {Statistical Analysis of Neuronal Data (SAND5)},
  year = 2010,
}

Park, I., & Príncipe, J. C. (2010). Quantification of Inter-trial Non-stationarity in Spike Trains from Periodically Stimulated Neural Cultures. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) (pp. 5442–5445). https://doi.org/10.1109/ICASSP.2010.5494920

@inproceedings{Park2010b,
  author = {Il Park and Jos\'e C. Pr\'incipe},
  title = {Quantification of Inter-trial Non-stationarity in Spike Trains from Periodically Stimulated Neural Cultures},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  year = 2010,
  pages = {5442--5445},
  note = {Special session on Multivariate Analysis of Brain Signals: Methods and Applications},
  doi = {10.1109/ICASSP.2010.5494920},
}

Príncipe, J. C. (2010). Information Theoretic Learning. Springer. http://www.springer.com/us/book/9781441915696

@book{Principe2010,
  author = {Jos\'e C. Pr\'incipe},
  title = {Information Theoretic Learning},
  publisher = {Springer},
  year = 2010,
  url = {http://www.springer.com/us/book/9781441915696},
  isbn = {1441915699},
}

Seth, S., Park, I., Brockmeier, A. J., Semework, M., Choi, J., Francis, J., & Príncipe, J. C. (2010). A novel family of non-parametric cumulative based divergences for point processes. In Advances in Neural Information Processing Systems (NIPS) (pp. 2119–2127). http://papers.nips.cc/paper/4126-a-novel-family-of-non-parametric-cumulative-based-divergences-for-point-processes

@inproceedings{Seth2010a,
  author = {Sohan Seth and Il Park and Austin J. Brockmeier and Mulugeta Semework and John Choi and Joe Francis and Jos\'e C. Pr\'incipe},
  title = {A novel family of non-parametric cumulative based divergences for point processes},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = 2010,
  pages = {2119--2127},
  url = {http://papers.nips.cc/paper/4126-a-novel-family-of-non-parametric-cumulative-based-divergences-for-point-processes},
}

Príncipe, J. C., Xu, J. W., Jenssen, R., Paiva, A., & Park, I. (2010). A Reproducing Kernel Hilbert Space Framework for Information-Theoretic Learning. In J. C. Príncipe (Ed.), Information Theoretic Learning. Springer.

@inbook{bookch2010a,
  author = {Jos\'e C. Pr\'incipe and Jian Wu Xu and Robert Jenssen and Antonio Paiva and Il Park},
  title = {A Reproducing Kernel {H}ilbert Space Framework for Information-Theoretic Learning},
  booktitle = {Information Theoretic Learning},
  editor = {Jos\'e C. Pr\'incipe},
  chapter = {9},
  publisher = {Springer},
  year = 2010,
  isbn = {978-1441915696},
}

Liu, W., Park, I., & Príncipe, J. C. (2009). An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters. IEEE Transactions on Neural Network, 20(12), 1950–1961. https://doi.org/10.1109/TNN.2009.2033676

@article{Liu2009b,
  author = {Weifeng Liu and Il Park and Jos\'e C. Pr\'incipe},
  title = {An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters},
  journal = {IEEE Transactions on Neural Network},
  year = 2009,
  month = dec,
  volume = {20},
  number = {12},
  pages = {1950--1961},
  doi = {10.1109/TNN.2009.2033676},
}

Liu, W., Park, I., Wang, Y., & Príncipe, J. C. (2009). Extended Kernel Recursive Least Squares Algorithm. IEEE Transactions on Signal Processing, 57(10), 3801–3814. https://doi.org/10.1109/TSP.2009.2022007

@article{Liu2009a,
  author = {Weifeng Liu and Il Park and Yiwen Wang and Jos\'e C. Pr\'incipe},
  title = {Extended Kernel Recursive Least Squares Algorithm},
  journal = {IEEE Transactions on Signal Processing},
  year = 2009,
  month = oct,
  volume = {57},
  number = {10},
  pages = {3801--3814},
  doi = {10.1109/TSP.2009.2022007},
}

Dockendorf, K., Park, I., He, P., Príncipe, J. C., & DeMarse, T. B. (2009). Liquid State Machines and Cultured Cortical Networks: The Separation Property. Biosystems, 95(2), 90–97. https://doi.org/10.1016/j.biosystems.2008.08.001

@article{Dockendorf2008,
  author = {Karl Dockendorf and Il Park and Ping He and Jos\'e C. Pr\'incipe and Thomas B. DeMarse},
  title = {Liquid State Machines and Cultured Cortical Networks: The Separation Property},
  journal = {Biosystems},
  year = 2009,
  month = feb,
  volume = {95},
  number = {2},
  pages = {90--97},
  doi = {10.1016/j.biosystems.2008.08.001},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2009). A Reproducing Kernel Hilbert Space framework for Spike Trains. Neural Computation, 21(2), 424–449. https://doi.org/10.1162/neco.2008.09-07-614

@article{Paiva2008b,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {A Reproducing Kernel {H}ilbert Space framework for Spike Trains},
  journal = {Neural Computation},
  year = 2009,
  month = feb,
  volume = {21},
  number = {2},
  pages = {424--449},
  doi = {10.1162/neco.2008.09-07-614},
}

Bobkov, Y., Park, I., Ukhanov, K., Príncipe, J. C., & Ache, B. W. (2009). Population coding within an ensemble of rhythmically active primary olfactory receptor [Conference abstract]. Society for Neuroscience.

@inproceedings{Bobkov2009a,
  author = {Yuriy Bobkov and Il Park and Kirill Ukhanov and Jos\'e C. Pr\'incipe and Barry W. Ache},
  title = {Population coding within an ensemble of rhythmically active primary olfactory receptor},
  booktitle = {Society for Neuroscience},
  year = 2009,
}

Li, L., Seth, S., Park, I., Sanchez, J. C., & Príncipe, J. C. (2009). Estimation and Visualization of Neuronal Functional Connectivity in Motor Tasks. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS). https://doi.org/10.1109/IEMBS.2009.5333991

@inproceedings{Li2009,
  author = {Lin Li and Sohan Seth and Il Park and Justin C. Sanchez and Jos\'e C. Pr\'incipe},
  title = {Estimation and Visualization of Neuronal Functional Connectivity in Motor Tasks},
  booktitle = {Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS)},
  year = 2009,
  doi = {10.1109/IEMBS.2009.5333991},
  abstract = {In brain-machine interface (BMI) modeling, the firing patterns of hundreds of neurons are used to reconstruct a variety of kinematic variables. The large number of neurons produces an explosion in the number of free parameters, which affects model generalization. This paper proposes a model-free measure of pairwise neural dependence to rank the importance of neurons in neural to motor mapping. Compared to a model-dependent approach such as sensitivity analysis, sixty percent of the neurons with the strongest dependence coincide with the top 10 most sensitive neurons trained through the model. Using this data-driven approach that operates on the input data alone, it is possible to perform neuron selection in a more efficient way that is not subject to assumptions about decoding models. To further understand the functional dependencies that influence neural to motor mapping, we use an open source available graph visualization toolkit called Prefuse to visualize the neural dependency graph and quantify the functional connectivity in motor cortex. This tool when adapted to the analysis of neuronal recordings has the potential to easily display the relationships in data of large dimension.},
}

Park, I., Rao, M., DeMarse, T. B., & Príncipe, J. C. (2009). Point Process Model for Precisely Timed Spike Trains [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE). https://doi.org/10.3389/conf.neuro.06.2009.03.227

@inproceedings{Park2009a,
  author = {Il Park and Murali Rao and Thomas B. DeMarse and Jos\'e C. Pr\'incipe},
  title = {Point Process Model for Precisely Timed Spike Trains.},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE)},
  year = 2009,
  doi = {10.3389/conf.neuro.06.2009.03.227},
}

Park, I., Bobkov, Y., Ukhanov, K., Ache, B. W., & Príncipe, J. C. (2009). Input Driven Synchrony of Oscillating Olfactory Receptor Neurons: A Computational Modeling Study [Conference abstract]. Association for Chemoreception (AChemS) Annual Meeting.

@inproceedings{Park2009b,
  author = {Il Park and Yuriy Bobkov and Kirill Ukhanov and Barry W. Ache and Jos\'e C. Pr\'incipe},
  title = {Input Driven Synchrony of Oscillating Olfactory Receptor Neurons: A Computational Modeling Study},
  booktitle = {Association for Chemoreception (AChemS) Annual Meeting},
  year = 2009,
}

Park, I., & Príncipe, J. C. (2009). Significance test for spike trains based on finite point process estimation [Conference abstract]. Society for Neuroscience.

@inproceedings{Park2009c,
  author = {Il Park and Jos\'e C. Pr\'incipe},
  title = {Significance test for spike trains based on finite point process estimation},
  booktitle = {Society for Neuroscience},
  year = 2009,
}

Seth, S., Park, I., & Príncipe, J. C. (2009). A new nonparametric measure of conditional independence. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). https://doi.org/10.1109/ICASSP.2009.4960250

@inproceedings{Seth2009a,
  author = {Sohan Seth and Il Park and Jos\'e C. Pr\'incipe},
  title = {A new nonparametric measure of conditional independence},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  year = 2009,
  doi = {10.1109/ICASSP.2009.4960250},
}

Xu, J. W., Paiva, A. R. C., Park, I., & Príncipe, J. C. (2008). A Reproducing Kernel Hilbert Space Framework for Information-Theoretic Learning. IEEE Transactions on Signal Processing, 56(12), 5891–5902. https://doi.org/10.1109/TSP.2008.2005085

@article{Xu2008,
  author = {Xu, Jian Wu and Paiva, Ant\'onio R. C. and Park, Il and Pr\'incipe, Jos\'e C.},
  title = {A Reproducing Kernel {H}ilbert Space Framework for Information-Theoretic Learning},
  journal = {IEEE Transactions on Signal Processing},
  year = 2008,
  month = aug,
  volume = {56},
  number = {12},
  pages = {5891--5902},
  doi = {10.1109/TSP.2008.2005085},
  abstract = {This paper provides a functional analysis perspective of information-theoretic learning (ITL) by defining bottom-up a reproducing kernel Hilbert space (RKHS) uniquely determined by the symmetric nonnegative definite kernel function known as the cross-information potential (CIP). The CIP as an integral of the product of two probability density functions characterizes similarity between two stochastic functions. We prove the existence of a one-to-one congruence mapping between the ITL RKHS and the Hilbert space spanned by square integrable probability density functions. Therefore, all the statistical descriptors in the original information-theoretic learning formulation can be rewritten as algebraic computations on deterministic functional vectors in the ITL RKHS, instead of limiting the functional view to the estimators as is commonly done in kernel methods. A connection between the ITL RKHS and kernel approaches interested in quantifying the statistics of the projected data is also established.},
  keywords = {cnel, itl, rkhs},
}

Park, I., Paiva, A. R. C., DeMarse, T. B., & Príncipe, J. C. (2008). An efficient algorithm for continuous-time cross correlogram of spike trains. Journal of Neuroscience Methods, 168(2), 514–523. https://doi.org/10.1016/j.jneumeth.2007.10.005

@article{Park2008a,
  author = {Il Park and Ant\'onio R. C. Paiva and Thomas B. DeMarse and Jos\'e C. Pr\'incipe},
  title = {An efficient algorithm for continuous-time cross correlogram of spike trains},
  journal = {Journal of Neuroscience Methods},
  year = 2008,
  month = mar,
  volume = {168},
  number = {2},
  pages = {514--523},
  doi = {10.1016/j.jneumeth.2007.10.005},
  abstract = {We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram-based correlogram estimations, the proposed algorithm operates on continuous time and does not bin either the spike train nor the correlogram. Hence it can be more precise in detecting the effective delay between two recording sites. Moreover, it can take advantage of the higher temporal resolution of the spike times provided by the current recording methods. The Laplacian kernel for smoothing enables efficient computation of the algorithm. We also provide the basic statistics of the estimator and a guideline for choosing the kernel size. This new technique is demonstrated by estimating the effective delays in a neuronal network from synthetic data and recordings of dissociated cortical tissue.},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2008). Reproducing Kernel Hilbert Spaces for Spike Train Analysis. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). https://doi.org/10.1109/ICASSP.2008.4518834

@inproceedings{Paiva2008a,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {Reproducing Kernel {H}ilbert Spaces for Spike Train Analysis},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  year = 2008,
  doi = {10.1109/ICASSP.2008.4518834},
  abstract = {This paper introduces a generalized cross-correlation (GCC) measure for spike train analysis derived from reproducing kernel Hilbert spaces (RKHS) theory. An estimator for GCC is derived that does not depend on binning or a specific kernel and it operates directly and efficiently on spike times. For instantaneous analysis as required for real-time use, an instantaneous estimator is proposed and proved to yield the GCC on average. We finalize with two experiments illustrating the usefulness of the techniques derived.},
}

Paiva, A. R. C., Park, I., Sanchez, J., & Príncipe, J. C. (2008). Peri-event Cross-Correlation over Time for Analysis of Interactions in Neuronal Firing. In International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

@inproceedings{Paiva2008c,
  author = {Ant\'onio R. C. Paiva and Il Park and Justin Sanchez and Jos\'e C. Pr\'incipe},
  title = {Peri-event Cross-Correlation over Time for Analysis of Interactions in Neuronal Firing},
  journal = {International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)},
  year = 2008,
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2008). Reproducing Kernel Hilbert Spaces for Spike Train Analysis [Conference abstract]. Conference on Computational Neuroscience.

@inproceedings{Paiva2008e,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos{\'e} C. Pr{\'i}ncipe},
  title = {Reproducing Kernel {H}ilbert Spaces for Spike Train Analysis},
  booktitle = {Conference on Computational Neuroscience},
  year = 2008,
  abstract = {This paper introduces a generalized cross-correlation (GCC) measure for spike train analysis derived from reproducing kernel Hilbert spaces (RKHS) theory. An estimator for GCC is derived that does not depend on binning or a specific kernel and it operates directly and efficiently on spike times. For instantaneous analysis as required for real-time use, an instantaneous estimator is proposed and proved to yield the GCC on average. We finalize with two experiments illustrating the usefulness of the techniques derived.},
}

Park, I., & Príncipe, J. C. (2008). Correntropy based Granger causality. In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). https://doi.org/10.1109/ICASSP.2008.4518432

@inproceedings{Park2008b,
  author = {Il Park and Jos\'e C. Pr\'incipe},
  title = {Correntropy based Granger causality},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  year = 2008,
  doi = {10.1109/ICASSP.2008.4518432},
  abstract = {We propose a novel nonlinear extension to Granger causality. It is derived from a nonlinear mapping of a stochastic process using the recently introduced generalized correlation measure called correntropy. The method is demonstrated by detecting the direction of coupling in a chaotic system where the original Granger causality failed.},
}

Paiva, A. R. C., Rao, S., Park, I., & Príncipe, J. C. (2007). Spectral Clustering of Synchronous Spike Trains. In IEEE International Joint Conference on Neural Networks (IJCNN) (pp. 1831–1835). https://doi.org/10.1109/IJCNN.2007.4371236

@inproceedings{Paiva2007a,
  author = {Ant\'onio R. C. Paiva and Sudhir Rao and Il Park and Jos\'e C. Pr\'incipe},
  title = {Spectral Clustering of Synchronous Spike Trains},
  booktitle = {{IEEE} International Joint Conference on Neural Networks ({IJCNN})},
  year = 2007,
  month = aug,
  pages = {1831--1835},
  doi = {10.1109/IJCNN.2007.4371236},
  url = {http://dx.doi.org/10.1109/IJCNN.2007.4371236},
  abstract = {In this paper a clustering algorithm that learns the groups of synchronized spike trains directly from data is proposed. Clustering of spike trains based on the presence of synchronous neural activity is of high relevance in neurophys-iological studies. In this context such activity is thought to be associated with functional structures in the brain. In addition, clustering has the potential to analyze large volumes of data. The algorithm couples a distance between two spike trains recently proposed in the literature with spectral clustering. Finally, the algorithm is illustrated in sets of computer generated spike trains and analyzed for the dependence on its parameters and accuracy with respect to features of interest.},
  address = {Orlando, FL, USA},
  issn = {2161-4407},
  keywords = {Neurons;Clustering algorithms;Neuroscience;Data analysis;Random processes;Clustering methods;Algorithm design and analysis;Design methodology;Unsupervised learning;Machine learning},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (2007). Innovating Signal Processing for Spike Train Data. In International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

@inproceedings{Paiva2007b,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {Innovating Signal Processing for Spike Train Data},
  booktitle = {International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)},
  year = 2007,
  address = {Lyon, France},
}

Park, I., Paiva, A. R. C., DeMarse, T. B., Príncipe, J. C., & Harris, J. (2007). A Closed Form Solution for Multiple-Input Spike Based Adaptive Filters. In IEEE International Joint Conference on Neural Networks (IJCNN).

@inproceedings{Park2007,
  author = {Il Park and Ant\'onio R. C. Paiva and Thomas B. DeMarse and Jose C. Pr\'incipe and John Harris},
  title = {A Closed Form Solution for Multiple-Input Spike Based Adaptive Filters},
  booktitle = {IEEE International Joint Conference on Neural Networks (IJCNN)},
  year = 2007,
}

Park, I., Paiva, A. R. C., Príncipe, J. C., & DeMarse, T. B. (2007). An Efficient Computation of Continuous-time Correlogram of Spike Trains [Conference abstract]. Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE).

@inproceedings{Park2007b,
  author = {Il Park and Ant\'onio R. C. Paiva and Jos\'e C. Pr\'incipe and Thomas B. DeMarse},
  title = {An Efficient Computation of Continuous-time Correlogram of Spike Trains},
  booktitle = {Frontiers in Systems Neuroscience. Conference Abstract: Computational and Systems Neuroscience (COSYNE)},
  year = 2007,
}

Park, I. (2007). Continuous time correlation analysis techniques for spike trains [Unpublished master's thesis]. The University of Florida.

@mastersthesis{ParkMSThesis2007,
  author = {Park, Il},
  title = {Continuous time correlation analysis techniques for spike trains},
  school = {The University of Florida},
  year = 2007,
}

Park, I., Xu, D., DeMarse, T. B., & Príncipe, J. C. (2006). Modeling of Synchronized Burst in Dissociated Cortical Tissue: An Exploration of Parameter Space. In IEEE International Joint Conference on Neural Networks (IJCNN). https://doi.org/10.1109/IJCNN.2006.246734

@inproceedings{Park2006,
  author = {Il Park and Dongming Xu and Thomas B. DeMarse and Jos\'e C. Pr\'incipe},
  title = {Modeling of Synchronized Burst in Dissociated Cortical Tissue: An Exploration of Parameter Space},
  booktitle = {IEEE International Joint Conference on Neural Networks (IJCNN)},
  year = 2006,
  doi = {10.1109/IJCNN.2006.246734},
}

Park, I., & Park, J. C. (2005). Modeling Causality in Biological Pathways for Logical Identification of Drug Targets. In Bioinfo.

@inproceedings{Park2005,
  author = {Il Park and Jong C. Park},
  title = {Modeling Causality in Biological Pathways for Logical Identification of Drug Targets},
  booktitle = {Bioinfo},
  year = 2005,
  month = sep,
  address = {Busan, Korea},
}

Paiva, A. R. C., Park, I., & Príncipe, J. C. (n.d.). Optimization in Reproducing Kernel Hilbert Spaces of Spike Trains [Unpublished manuscript].

@unpublished{Paiva2008d,
  author = {Ant\'onio R. C. Paiva and Il Park and Jos\'e C. Pr\'incipe},
  title = {Optimization in Reproducing Kernel {H}ilbert Spaces of Spike Trains},
  note = {Unpublished manuscript},
  abstract = {This chapter presents a framework based on reproducing kernel Hilbert spaces (RKHS) for optimization with spike trains. To establish the RKHS for optimization we start by introducing kernels for spike trains. It is shown that spike train kernels can be built from ideas of kernel methods or from the intensity functions underlying the spike trains. However, the later approach shall be the main focus of this study. We introduce the memoryless cross-intensity (mCI) kernel as an example of an inner product of spike trains, which defines the RKHS bottom-up as an inner product of intensity functions. Being defined in terms of the intensity functions, this approach toward defining spike train kernels has the advantage that points in the RKHS incorporate a statistical description of the spike trains, and the statistical model is explicitly stated. Some properties of the mCI kernel and the RKHS it induces will be given to show that this RKHS has the necessary structure for optimization. The issue of estimation from data is also addressed. We finalize with an example of optimization in the RKHS by deriving an algorithm for principal component analysis (PCA) of spike trains.},
}