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Scott Linderman

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28 papers

1 author row

TMLR Journal 2026 Journal Article

A Bayesian Nonparametric Perspective on Mahalanobis Distance for Out of Distribution Detection

Randolph Linderman
Noah Cowan
Yiran Chen
Scott Linderman

Bayesian nonparametric methods are naturally suited to the problem of out-of-distribution (OOD) detection. However, these techniques have largely been eschewed in favor of simpler methods based on distances between pre-trained or learned embeddings of data points. Here we show a formal relationship between Bayesian nonparametric models and the relative Mahalanobis distance score (RMDS), a commonly used method for OOD detection. Building on this connection, we propose Bayesian nonparametric mixture models with hierarchical priors that generalize the RMDS. We evaluate these models on the OpenOOD detection benchmark and show that Bayesian nonparametric methods can improve upon existing OOD methods, especially in regimes where training classes differ in their covariance structure and where there are relatively few data points per class.

TMLR Journal 2026 Journal Article

A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systems

Xavier Gonzalez
E. Kelly Buchanan
Hyun Dong Lee
Jerry Weihong Liu
Ke Alexander Wang
David M. Zoltowski
Leo Kozachkov
Christopher Re

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like Newton, Picard, and Jacobi iterations. In this work, we show that these methods can be understood within a common framework based on linear dynamical systems (LDSs), where different iteration schemes arise naturally as approximate linearizations of a nonlinear recursion. Moreover, we theoretically analyze the rates of convergence of these methods, and we verify the predictions of this theory with several case studies. This unifying framework highlights shared principles behind these techniques and clarifies when particular fixed-point methods are most likely to be effective. By bridging diverse algorithms through the language of LDSs, the framework provides a clearer theoretical foundation for parallelizing sequential models and points toward new opportunities for efficient and scalable computation.

NeurIPS Conference 2025 Conference Paper

Extracting task-relevant preserved dynamics from contrastive aligned neural recordings

Yiqi Jiang
Kaiwen Sheng
Yujia Gao
Estefany Kelly Buchanan
Yu Shikano
Seung Je Woo
Yixiu Zhao
Tony Hyun Kim

Recent work indicates that low-dimensional dynamics of neural and behavioral data are often preserved across days and subjects. However, extracting these preserved dynamics remains challenging: high-dimensional neural population activity and the recorded neuron populations vary across recording sessions. While existing modeling tools can improve alignment between neural and behavioral data, they often operate on a per-subject basis or discretize behavior into categories, disrupting its natural continuity and failing to capture the underlying dynamics. We introduce $\underline{\text{C}}$ontrastive $\underline{\text{A}}$ligned $\underline{\text{N}}$eural $\underline{\text{D}}$$\underline{\text{Y}}$namics (CANDY), an end‑to‑end framework that aligns neural and behavioral data using rank-based contrastive learning, adapted for continuous behavioral variables, to project neural activity from different sessions onto a shared low-dimensional embedding space. CANDY fits a shared linear dynamical system to the aligned embeddings, enabling an interpretable model of the conserved temporal structure in the latent space. We validate CANDY on synthetic and real-world datasets spanning multiple species, behaviors, and recording modalities. Our results show that CANDY is able to learn aligned latent embeddings and preserved dynamics across neural recording sessions and subjects, and it achieves improved cross-session behavior decoding performance. We further show that the latent linear dynamical system generalizes to new sessions and subjects, achieving comparable or even superior behavior decoding performance to models trained from scratch. These advances enable robust cross‑session behavioral decoding and offer a path towards identifying shared neural dynamics that underlie behavior across individuals and recording conditions. The code and two-photon imaging data of striatal neural activity that we acquired here are available at https: //github. com/schnitzer-lab/CANDY-public. git.

NeurIPS Conference 2025 Conference Paper

Identifying multi-compartment Hodgkin-Huxley models with high-density extracellular voltage recordings

Ian Christopher Tanoh
Michael Deistler
Jakob H Macke
Scott Linderman

Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many free parameters that must be estimated for each cell, and existing fitting methods rely on intracellular voltage measurements that are highly challenging to obtain in-vivo. Recent advances in neural recording technology with high-density probes and arrays enable dense sampling of extracellular voltage from many sites surrounding a neuron, allowing indirect measurement of many compartments of a cell simultaneously. Here, we propose a method for inferring the underlying membrane voltage, biophysical parameters, and the neuron's position relative to the probe, using extracellular measurements alone. We use an Extended Kalman Filter to infer membrane voltage and channel states using efficient, differentiable simulators. Then, we learn the model parameters by maximizing the marginal likelihood using gradient-based methods. We demonstrate the performance of this approach using simulated data and real neuron morphologies.

NeurIPS Conference 2025 Conference Paper

Informed Correctors for Discrete Diffusion Models

Yixiu Zhao
Jiaxin Shi
Feng Chen
Shaul Druckmann
Lester Mackey
Scott Linderman

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the Text8 dataset, the informed corrector improves sample quality by generating text with significantly fewer errors than the baselines. On tokenized ImageNet 256x256, this approach consistently produces superior samples with fewer steps, achieving improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion.

NeurIPS Conference 2025 Conference Paper

Parallelizing MCMC Across the Sequence Length

David Zoltowski
Skyler Wu
Xavier Gonzalez
Leo Kozachkov
Scott Linderman

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence length. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem and solve for the fixed-point using a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. In several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. Additionally, we develop two new parallel quasi-Newton methods to evaluate nonlinear recursions with lower memory costs and reduced runtime. We find that the proposed parallel algorithms accelerate MCMC sampling across multiple examples, in some cases by more than an order of magnitude compared to sequential evaluation.

NeurIPS Conference 2025 Conference Paper

Predictability Enables Parallelization of Nonlinear State Space Models

Xavier Gonzalez
Leo Kozachkov
David Zoltowski
Kenneth Clarkson
Scott Linderman

The rise of parallel computing hardware has made it increasingly important to understand which nonlinear state space models can be efficiently parallelized. Recent advances like DEER and DeepPCR recast sequential evaluation as a parallelizable optimization problem, sometimes yielding dramatic speedups. However, the factors governing the difficulty of these optimization problems remained unclear, limiting broader adoption. In this work, we establish a precise relationship between a system's dynamics and the conditioning of its corresponding optimization problem, as measured by its Polyak-Łojasiewicz (PL) constant. We show that the predictability of a system, defined as the degree to which small perturbations in state influence future behavior and quantified by the largest Lyapunov exponent (LLE), impacts the number of optimization steps required for evaluation. For predictable systems, the state trajectory can be computed in at worst $\mathcal{O}((\log T)^2)$ time, where $T$ is the sequence length: a major improvement over the conventional sequential approach. In contrast, chaotic or unpredictable systems exhibit poor conditioning, with the consequence that parallel evaluation converges too slowly to be useful. Importantly, our theoretical analysis shows that predictable systems always yield well-conditioned optimization problems, whereas unpredictable systems lead to severe conditioning degradation. We validate our claims through extensive experiments, providing practical guidance on when nonlinear dynamical systems can be efficiently parallelized. We highlight predictability as a key design principle for parallelizable models.

NeurIPS Conference 2025 Conference Paper

SING: SDE Inference via Natural Gradients

Amber Hu
Henry Smith
Scott Linderman

Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior inference of the latent state path is typically intractable, motivating the use of approximate methods such as variational inference (VI). However, existing VI methods for inference in latent SDEs often suffer from slow convergence and numerical instability. Here, we propose SDE Inference via Natural Gradients (SING), a method that leverages natural gradient VI to efficiently exploit the underlying geometry of the model and variational posterior. SING enables fast and reliable inference in latent SDE models by approximating intractable integrals and parallelizing computations in time. We provide theoretical guarantees that SING will approximately optimize the intractable, continuous-time objective of interest. Moreover, we demonstrate that better state inference enables more accurate estimation of nonlinear drift functions using, for example, Gaussian process SDE models. SING outperforms prior methods in state inference and drift estimation on a variety of datasets, including a challenging application to modeling neural dynamics in freely behaving animals. Altogether, our results illustrate the potential of SING as a tool for accurate inference in complex dynamical systems, especially those characterized by limited prior knowledge and non-conjugate structure.

NeurIPS Conference 2025 Conference Paper

Weaver: Shrinking the Generation-Verification Gap by Scaling Compute for Verification

Jon Saad-Falcon
Estefany Kelly Buchanan
Mayee Chen
Tzu-Heng (Brian) Huang
Brendan McLaughlin
Tanvir Bhathal
Shang Zhu
Ben Athiwaratkun

Verifiers can improve language model (LM) capabilities by providing feedback or selecting the best response from a pool of generated candidates. Currently, high-quality verifiers are either unscalable (e. g. , humans) or limited in utility (e. g. , tools like Lean for formal proofs). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers. To help close this gap, we introduce Weaver, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. First we find that weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in the verifiers. To reduce the dependency on labeled data, Weaver leverages weak supervision to estimate each verifier’s accuracy and combines their outputs into a unified score that better reflects true response quality. However, directly applying weak supervision algorithms poses several challenges, including inconsistent verifier output formats and handling low-quality verifiers. Weaver addresses these challenges by using dataset statistics to normalize outputs and filter specific verifiers. We study the effectiveness of Weaver in repeated sampling settings, where a model generates multiple candidate responses at test time and a verifier is used to select the correct one. Our evaluations demonstrate that Weaver significantly improves the pass@1 performance across several reasoning and math tasks, achieving o3-mini level accuracy with Llama 3. 3 70B Instruct (a much cheaper non-reasoning model) as the generator, and an ensemble of smaller judge and reward models as the verifiers (86. 2% average). This gain mirrors the jump achieved between GPT-4o and o3-mini (69. 0% vs. 86. 7%), which required extensive finetuning and post-training interventions. To make Weaver more efficient, we train a compact 400M cross-encoder using Weaver's combined output scores. This distilled model retains 98. 7% of Weaver's full accuracy while reducing verification compute by up to 99. 97%.

NeurIPS Conference 2024 Conference Paper

Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems

Amber Hu
David Zoltowski
Aditya Nair
David Anderson
Lea Duncker
Scott Linderman

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

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NeurIPS Conference 2023 Conference Paper

Convolutional State Space Models for Long-Range Spatiotemporal Modeling

Jimmy Smith
Shalini De Mello
Jan Kautz
Scott Linderman
Wonmin Byeon

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training $3\times$ faster than ConvLSTM and generating samples $400\times$ faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

NeurIPS Conference 2023 Conference Paper

NAS-X: Neural Adaptive Smoothing via Twisting

Dieterich Lawson
Michael Li
Scott Linderman

Sequential latent variable models (SLVMs) are essential tools in statistics and machine learning, with applications ranging from healthcare to neuroscience. As their flexibility increases, analytic inference and model learning can become challenging, necessitating approximate methods. Here we introduce neural adaptive smoothing via twisting (NAS-X), a method that extends reweighted wake-sleep (RWS) to the sequential setting by using smoothing sequential Monte Carlo (SMC) to estimate intractable posterior expectations. Combining RWS and smoothing SMC allows NAS-X to provide low-bias and low-variance gradient estimates, and fit both discrete and continuous latent variable models. We illustrate the theoretical advantages of NAS-X over previous methods and explore these advantages empirically in a variety of tasks, including a challenging application to mechanistic models of neuronal dynamics. These experiments show that NAS-X substantially outperforms previous VI- and RWS-based methods in inference and model learning, achieving lower parameter error and tighter likelihood bounds.

NeurIPS Conference 2023 Conference Paper

Switching Autoregressive Low-rank Tensor Models

Hyun Dong Lee
andrew warrington
Joshua Glaser
Scott Linderman

An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation, but are parameter intensive when modeling long dependencies, and hence are prone to overfitting. In contrast, SLDSs can capture long-range dependencies in a parameter efficient way through Markovian latent dynamics, but present an intractable likelihood and a challenging parameter estimation task. In this paper, we propose switching autoregressive low-rank tensor SALT models, which retain the advantages of both approaches while ameliorating the weaknesses. SALT parameterizes the tensor of an ARHMM with a low-rank factorization to control the number of parameters and allow longer range dependencies without overfitting. We prove theoretical and discuss practical connections between SALT, linear dynamical systems, and SLDSs. We empirically demonstrate quantitative advantages of SALT models on a range of simulated and real prediction tasks, including behavioral and neural datasets. Furthermore, the learned low-rank tensor provides novel insights into temporal dependencies within each discrete state.

NeurIPS Conference 2022 Conference Paper

Distinguishing discrete and continuous behavioral variability using warped autoregressive HMMs

Julia Costacurta
Lea Duncker
Blue Sheffer
Winthrop Gillis
Caleb Weinreb
Jeffrey Markowitz
Sandeep R Datta
Alex Williams

A core goal in systems neuroscience and neuroethology is to understand how neural circuits generate naturalistic behavior. One foundational idea is that complex naturalistic behavior may be composed of sequences of stereotyped behavioral syllables, which combine to generate rich sequences of actions. To investigate this, a common approach is to use autoregressive hidden Markov models (ARHMMs) to segment video into discrete behavioral syllables. While these approaches have been successful in extracting syllables that are interpretable, they fail to account for other forms of behavioral variability, such as differences in speed, which may be better described as continuous in nature. To overcome these limitations, we introduce a class of warped ARHMMs (WARHMM). As is the case in the ARHMM, behavior is modeled as a mixture of autoregressive dynamics. However, the dynamics under each discrete latent state (i. e. each behavioral syllable) are additionally modulated by a continuous latent ``warping variable. '' We present two versions of warped ARHMM in which the warping variable affects the dynamics of each syllable either linearly or nonlinearly. Using depth-camera recordings of freely moving mice, we demonstrate that the failure of ARHMMs to account for continuous behavioral variability results in duplicate cluster assignments. WARHMM achieves similar performance to the standard ARHMM while using fewer behavioral syllables. Further analysis of behavioral measurements in mice demonstrates that WARHMM identifies structure relating to response vigor.

NeurIPS Conference 2022 Conference Paper

SIXO: Smoothing Inference with Twisted Objectives

Dieterich Lawson
Allan Raventós
andrew warrington
Scott Linderman

Sequential Monte Carlo (SMC) is an inference algorithm for state space models that approximates the posterior by sampling from a sequence of target distributions. The target distributions are often chosen to be the filtering distributions, but these ignore information from future observations, leading to practical and theoretical limitations in inference and model learning. We introduce SIXO, a method that instead learns target distributions that approximate the smoothing distributions, incorporating information from all observations. The key idea is to use density ratio estimation to fit functions that warp the filtering distributions into the smoothing distributions. We then use SMC with these learned targets to define a variational objective for model and proposal learning. SIXO yields provably tighter log marginal lower bounds and offers more accurate posterior inferences and parameter estimates in a variety of domains.

NeurIPS Conference 2021 Conference Paper

Generalized Shape Metrics on Neural Representations

Alex H Williams
Erin Kunz
Simon Kornblith
Scott Linderman

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates---such as architecture, anatomical brain region, and model organism---impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of metric spaces that quantify representational dissimilarity. Using this framework, we modify existing representational similarity measures based on canonical correlation analysis and centered kernel alignment to satisfy the triangle inequality, formulate a novel metric that respects the inductive biases in convolutional layers, and identify approximate Euclidean embeddings that enable network representations to be incorporated into essentially any off-the-shelf machine learning method. We demonstrate these methods on large-scale datasets from biology (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101). In doing so, we identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.

NeurIPS Conference 2021 Conference Paper

Reverse engineering recurrent neural networks with Jacobian switching linear dynamical systems

Jimmy Smith
Scott Linderman
David Sussillo

Recurrent neural networks (RNNs) are powerful models for processing time-series data, but it remains challenging to understand how they function. Improving this understanding is of substantial interest to both the machine learning and neuroscience communities. The framework of reverse engineering a trained RNN by linearizing around its fixed points has provided insight, but the approach has significant challenges. These include difficulty choosing which fixed point to expand around when studying RNN dynamics and error accumulation when reconstructing the nonlinear dynamics with the linearized dynamics. We present a new model that overcomes these limitations by co-training an RNN with a novel switching linear dynamical system (SLDS) formulation. A first-order Taylor series expansion of the co-trained RNN and an auxiliary function trained to pick out the RNN's fixed points govern the SLDS dynamics. The results are a trained SLDS variant that closely approximates the RNN, an auxiliary function that can produce a fixed point for each point in state-space, and a trained nonlinear RNN whose dynamics have been regularized such that its first-order terms perform the computation, if possible. This model removes the post-training fixed point optimization and allows us to unambiguously study the learned dynamics of the SLDS at any point in state-space. It also generalizes SLDS models to continuous manifolds of switching points while sharing parameters across switches. We validate the utility of the model on two synthetic tasks relevant to previous work reverse engineering RNNs. We then show that our model can be used as a drop-in in more complex architectures, such as LFADS, and apply this LFADS hybrid to analyze single-trial spiking activity from the motor system of a non-human primate.

NeurIPS Conference 2020 Conference Paper

Point process models for sequence detection in high-dimensional neural spike trains

Alex Williams
Anthony Degleris
Yixin Wang
Scott Linderman

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising recent work utilized a convolutive nonnegative matrix factorization model to tackle this challenge. However, this model requires spike times to be discretized, utilizes a sub-optimal least-squares criterion, and does not provide uncertainty estimates for model predictions or estimated parameters. We address each of these shortcomings by developing a point process model that characterizes fine-scale sequences at the level of individual spikes and represents sequence occurrences as a small number of marked events in continuous time. This ultra-sparse representation of sequence events opens new possibilities for spike train modeling. For example, we introduce learnable time warping parameters to model sequences of varying duration, which have been experimentally observed in neural circuits. We demonstrate these advantages on recordings from songbird higher vocal center and rodent hippocampus.

NeurIPS Conference 2020 Conference Paper

Recurrent Switching Dynamical Systems Models for Multiple Interacting Neural Populations

Joshua Glaser
Matthew Whiteway
John P. Cunningham
Liam Paninski
Scott Linderman

Modern recording techniques can generate large-scale measurements of multiple neural populations over extended time periods. However, it remains a challenge to model non-stationary interactions between high-dimensional populations of neurons. To tackle this challenge, we develop recurrent switching linear dynamical systems models for multiple populations. Here, each high-dimensional neural population is represented by a unique set of latent variables, which evolve dynamically in time. Populations interact with each other through this low-dimensional space. We allow the nature of these interactions to change over time by using a discrete set of dynamical states. Additionally, we parameterize these discrete state transition rules to capture which neural populations are responsible for switching between interaction states. To fit the model, we use variational expectation-maximization with a structured mean-field approximation. After validating the model on simulations, we apply it to two different neural datasets: spiking activity from motor areas in a non-human primate, and calcium imaging from neurons in the nematode \textit{C. elegans}. In both datasets, the model reveals behaviorally-relevant discrete states with unique inter-population interactions and different populations that predict transitioning between these states.

NeurIPS Conference 2019 Conference Paper

BehaveNet: nonlinear embedding and Bayesian neural decoding of behavioral videos

Eleanor Batty
Matthew Whiteway
Shreya Saxena
Dan Biderman
Taiga Abe
Simon Musall
Winthrop Gillis
Jeffrey Markowitz

A fundamental goal of systems neuroscience is to understand the relationship between neural activity and behavior. Behavior has traditionally been characterized by low-dimensional, task-related variables such as movement speed or response times. More recently, there has been a growing interest in automated analysis of high-dimensional video data collected during experiments. Here we introduce a probabilistic framework for the analysis of behavioral video and neural activity. This framework provides tools for compression, segmentation, generation, and decoding of behavioral videos. Compression is performed using a convolutional autoencoder (CAE), which yields a low-dimensional continuous representation of behavior. We then use an autoregressive hidden Markov model (ARHMM) to segment the CAE representation into discrete "behavioral syllables. " The resulting generative model can be used to simulate behavioral video data. Finally, based on this generative model, we develop a novel Bayesian decoding approach that takes in neural activity and outputs probabilistic estimates of the full-resolution behavioral video. We demonstrate this framework on two different experimental paradigms using distinct behavioral and neural recording technologies.

NeurIPS Conference 2019 Conference Paper

Mutually Regressive Point Processes

Ifigeneia Apostolopoulou
Scott Linderman
Kyle Miller
Artur Dubrawski

Many real-world data represent sequences of interdependent events unfolding over time. They can be modeled naturally as realizations of a point process. Despite many potential applications, existing point process models are limited in their ability to capture complex patterns of interaction. Hawkes processes admit many efficient inference algorithms, but are limited to mutually excitatory effects. Non- linear Hawkes processes allow for more complex influence patterns, but for their estimation it is typically necessary to resort to discrete-time approximations that may yield poor generative models. In this paper, we introduce the first general class of Bayesian point process models extended with a nonlinear component that allows both excitatory and inhibitory relationships in continuous time. We derive a fully Bayesian inference algorithm for these processes using Polya-Gamma augmentation and Poisson thinning. We evaluate the proposed model on single and multi-neuronal spike train recordings. Results demonstrate that the proposed model, unlike existing point process models, can generate biologically-plausible spike trains, while still achieving competitive predictive likelihoods.

NeurIPS Conference 2019 Conference Paper

Poisson-Randomized Gamma Dynamical Systems

Aaron Schein
Scott Linderman
Mingyuan Zhou
David Blei
Hanna Wallach

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.

NeurIPS Conference 2019 Conference Paper

Scalable Bayesian inference of dendritic voltage via spatiotemporal recurrent state space models

Ruoxi Sun
Scott Linderman
Ian Kinsella
Liam Paninski

Recent advances in optical voltage sensors have brought us closer to a critical goal in cellular neuroscience: imaging the full spatiotemporal voltage on a dendritic tree. However, current sensors and imaging approaches still face significant limitations in SNR and sampling frequency; therefore statistical denoising and interpolation methods remain critical for understanding single-trial spatiotemporal dendritic voltage dynamics. Previous denoising approaches were either based on an inadequate linear voltage model or scaled poorly to large trees. Here we introduce a scalable fully Bayesian approach. We develop a generative nonlinear model that requires few parameters per compartment of the cell but is nonetheless flexible enough to sample realistic spatiotemporal data. The model captures different dynamics in each compartment and leverages biophysical knowledge to constrain intra- and inter-compartmental dynamics. We obtain a full posterior distribution over spatiotemporal voltage via an augmented Gibbs sampling algorithm. The nonlinear smoother model outperforms previously developed linear methods, and scales to much larger systems than previous methods based on sequential Monte Carlo approaches.

NeurIPS Conference 2018 Conference Paper

Point process latent variable models of larval zebrafish behavior

Anuj Sharma
Robert Johnson
Florian Engert
Scott Linderman

A fundamental goal of systems neuroscience is to understand how neural activity gives rise to natural behavior. In order to achieve this goal, we must first build comprehensive models that offer quantitative descriptions of behavior. We develop a new class of probabilistic models to tackle this challenge in the study of larval zebrafish, an important model organism for neuroscience. Larval zebrafish locomote via sequences of punctate swim bouts--brief flicks of the tail--which are naturally modeled as a marked point process. However, these sequences of swim bouts belie a set of discrete and continuous internal states, latent variables that are not captured by standard point process models. We incorporate these variables as latent marks of a point process and explore various models for their dynamics. To infer the latent variables and fit the parameters of this model, we develop an amortized variational inference algorithm that targets the collapsed posterior distribution, analytically marginalizing out the discrete latent variables. With a dataset of over 120, 000 swim bouts, we show that our models reveal interpretable discrete classes of swim bouts and continuous internal states like hunger that modulate their dynamics. These models are a major step toward understanding the natural behavioral program of the larval zebrafish and, ultimately, its neural underpinnings.

NeurIPS Conference 2016 Conference Paper

Bayesian latent structure discovery from multi-neuron recordings

Scott Linderman
Ryan Adams
Jonathan Pillow

Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

JMLR Journal 2016 Journal Article

Cross-Corpora Unsupervised Learning of Trajectories in Autism Spectrum Disorders

Huseyin Melih Elibol
Vincent Nguyen
Scott Linderman
Matthew Johnson
Amna Hashmi
Finale Doshi-Velez

Patients with developmental disorders, such as autism spectrum disorder (ASD), present with symptoms that change with time even if the named diagnosis remains fixed. For example, language impairments may present as delayed speech in a toddler and difficulty reading in a school-age child. Characterizing these trajectories is important for early treatment. However, deriving these trajectories from observational sources is challenging: electronic health records only reflect observations of patients at irregular intervals and only record what factors are clinically relevant at the time of observation. Meanwhile, caretakers discuss daily developments and concerns on social media. In this work, we present a fully unsupervised approach for learning disease trajectories from incomplete medical records and social media posts, including cases in which we have only a single observation of each patient. In particular, we use a dynamic topic model approach which embeds each disease trajectory as a path in $\mathbb{R}^D$. A Polya- gamma augmentation scheme is used to efficiently perform inference as well as incorporate multiple data sources. We learn disease trajectories from the electronic health records of 13,435 patients with ASD and the forum posts of 13,743 caretakers of children with ASD, deriving interesting clinical insights as well as good predictions. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

NeurIPS Conference 2015 Conference Paper

Dependent Multinomial Models Made Easy: Stick-Breaking with the Polya-gamma Augmentation

Scott Linderman
Matthew Johnson
Ryan Adams

Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at one position in the DNA strand may depend on the preceding nucleotides, children's names are highly correlated from year to year, and topics in text may be correlated and dynamic. These dependencies are not naturally captured by the typical Dirichlet-multinomial formulation. Here, we leverage a logistic stick-breaking representation and recent innovations in P\'{o}lya-gamma augmentation to reformulate the multinomial distribution in terms of latent variables with jointly Gaussian likelihoods, enabling us to take advantage of a host of Bayesian inference techniques for Gaussian models with minimal overhead.

NeurIPS Conference 2014 Conference Paper

A framework for studying synaptic plasticity with neural spike train data

Scott Linderman
Christopher Stock
Ryan Adams

Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling arbitrary synaptic plasticity rules on spike train data in populations of interconnected neurons. We treat synaptic weights as a (potentially nonlinear) dynamical system embedded in a fully-Bayesian generalized linear model (GLM). In addition, we provide an algorithm for inferring synaptic weight trajectories alongside the parameters of the GLM and of the learning rules. Using this method, we perform model comparison of two proposed variants of the well-known spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a substantial role. On synthetic data generated from the biophysical simulator NEURON, we show that we can recover the weight trajectories, the pattern of connectivity, and the underlying learning rules.