arXiv subjects

Jonathan W. Pillow

Publications and source records attributed to Jonathan W. Pillow.

17 recordsLinked to original sources

arXiv2025

Modeling Neural Activity with Conditionally Linear Dynamical Systems

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task.

q-bio.NC↗

arXiv2025

State-switching navigation strategies in C. elegans are beneficial for chemotaxis

Animals employ different strategies for relating sensory input to behavioral output to navigate sensory environments, but what strategy to use, when to switch and why remain unclear. In C. elegans, navigation is composed of 'steering' and 'turns', corresponding to small heading changes and large reorientation events, respectively. It is unclear whether transitions between these elements are driven solely by sensory input or are influenced by internal states that persist over time. It also remains unknown how worms accomplish seemingly surprising feats of navigation--for example, worms appear to exit turns correctly oriented toward a goal, despite their presumed lack of spatial awareness during the turn. Here, we resolve these questions using detailed measurements of sensory-guided navigation and a novel statistical model of state-dependent navigation. We show that the worm's navigation is well described by a sensory-driven state-switching model with two distinct states, each persisting over many seconds and producing different mixtures of sensorimotor relations. One state is enriched for steering, while the other is enriched for turning. This hierarchical, temporal organization of strategies challenges the previous assumption that strategies are static over time and driven solely by immediate sensory input. Sensory input causally drives transitions between these persistent internal states, and creates the appearance of 'directed turns.' Genetic perturbations and a data-constrained reinforcement learning model demonstrate that state-switching enhances gradient-climbing performance. By combining measurement, perturbation, and modeling, we show that state-switching plays a functionally beneficial role in organizing behavior over time--a principle likely to generalize across species and contexts.

q-bio.NC↗

arXiv2025

Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic state-space model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finite-horizon setting. We further illustrate the performance of our methodology through numerical examples.

math.OC↗

arXiv2024

Olfactory learning alters navigation strategies and behavioral variability in C. elegans

Animals adjust their behavioral response to sensory input adaptively depending on past experiences. The flexible brain computation is crucial for survival and is of great interest in neuroscience. The nematode C. elegans modulates its navigation behavior depending on the association of odor butanone with food (appetitive training) or starvation (aversive training), and will then climb up the butanone gradient or ignore it, respectively. However, the exact change in navigation strategy in response to learning is still unknown. Here we study the learned odor navigation in worms by combining precise experimental measurement and a novel descriptive model of navigation. Our model consists of two known navigation strategies in worms: biased random walk and weathervaning. We infer weights on these strategies by applying the model to worm navigation trajectories and the exact odor concentration it experiences. Compared to naive worms, appetitive trained worms up-regulate the biased random walk strategy, and aversive trained worms down-regulate the weathervaning strategy. The statistical model provides prediction with $>90 \%$ accuracy of the past training condition given navigation data, which outperforms the classical chemotaxis metric. We find that the behavioral variability is altered by learning, such that worms are less variable after training compared to naive ones. The model further predicts the learning-dependent response and variability under optogenetic perturbation of the olfactory neuron AWC$^\mathrm{ON}$. Lastly, we investigate neural circuits downstream from AWC$^\mathrm{ON}$ that are differentially recruited for learned odor-guided navigation. Together, we provide a new paradigm to quantify flexible navigation algorithms and pinpoint the underlying neural substrates.

q-bio.NC↗

arXiv2023

Spectral learning of Bernoulli linear dynamical systems models

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.

stat.ML↗

arXiv2023

Bayesian Active Learning for Discrete Latent Variable Models

Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap by proposing a novel framework for maximum-mutual-information input selection for discrete latent variable regression models. We first apply our method to a class of models known as "mixtures of linear regressions" (MLR). While it is well known that active learning confers no advantage for linear-Gaussian regression models, we use Fisher information to show analytically that active learning can nevertheless achieve large gains for mixtures of such models, and we validate this improvement using both simulations and real-world data. We then consider a powerful class of temporally structured latent variable models given by a Hidden Markov Model (HMM) with generalized linear model (GLM) observations, which has recently been used to identify discrete states from animal decision-making data. We show that our method substantially reduces the amount of data needed to fit GLM-HMM, and outperforms a variety of approximate methods based on variational and amortized inference. Infomax learning for latent variable models thus offers a powerful for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond.

cs.LG↗

arXiv2022

Correcting motion induced fluorescence artifacts in two-channel neural imaging

Imaging neural activity in a behaving animal presents unique challenges in part because motion from an animal's movement creates artifacts in fluorescence intensity time-series that are difficult to distinguish from neural signals of interest. One approach to mitigating these artifacts is to image two channels; one that captures an activity-dependent fluorophore, such as GCaMP, and another that captures an activity-independent fluorophore such as RFP. Because the activity-independent channel contains the same motion artifacts as the activity-dependent channel, but no neural signals, the two together can be used to remove the artifacts. Existing approaches for this correction, such as taking the ratio of the two channels, do not account for channel independent noise in the measured fluorescence. Moreover, no systematic comparison has been made of existing approaches that use two-channel signals. Here, we present Two-channel Motion Artifact Correction (TMAC), a method which seeks to remove artifacts by specifying a generative model of the fluorescence of the two channels as a function of motion artifact, neural activity, and noise. We further present a novel method for evaluating ground-truth performance of motion correction algorithms by comparing the decodability of behavior from two types of neural recordings; a recording that had both an activity-dependent fluorophore (GCaMP and RFP) and a recording where both fluorophores were activity-independent (GFP and RFP). A successful motion-correction method should decode behavior from the first type of recording, but not the second. We use this metric to systematically compare five methods for removing motion artifacts from fluorescent time traces. We decode locomotion from a GCaMP expressing animal 15x more accurately on average than from control when using TMAC inferred activity and outperform all other methods of motion correction tested.

q-bio.NC↗

arXiv2022

Loss-calibrated expectation propagation for approximate Bayesian decision-making

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.

stat.ML↗

arXiv2020

Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as \textit{polynomial approximate log-likelihood} (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.

stat.ML↗

arXiv2020

High-contrast "gaudy" images improve the training of deep neural network models of visual cortex

A key challenge in understanding the sensory transformations of the visual system is to obtain a highly predictive model of responses from visual cortical neurons. Deep neural networks (DNNs) provide a promising candidate for such a model. However, DNNs require orders of magnitude more training data than neuroscientists can collect from real neurons because experimental recording time is severely limited. This motivates us to find images that train highly-predictive DNNs with as little training data as possible. We propose gaudy images---high-contrast binarized versions of natural images---to efficiently train DNNs. In extensive simulation experiments, we find that training DNNs with gaudy images substantially reduces the number of training images needed to accurately predict the simulated responses of visual cortical neurons. We also find that gaudy images, chosen before training, outperform images chosen during training by active learning algorithms. Thus, gaudy images overemphasize features of natural images, especially edges, that are the most important for efficiently training DNNs. We believe gaudy images will aid in the modeling of visual cortical neurons, potentially opening new scientific questions about visual processing, as well as aid general practitioners that seek ways to improve the training of DNNs.

cs.CV↗

arXiv2020

Unifying and generalizing models of neural dynamics during decision-making

An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit the number of these models that we can fit to neural data. Here we propose a unifying framework for modeling neural activity during decision-making tasks. The framework includes the canonical drift-diffusion model and enables extensions such as multi-dimensional accumulators, variable and collapsing boundaries, and discrete jumps. Our framework is based on constraining the parameters of recurrent state-space models, for which we introduce a scalable variational Laplace-EM inference algorithm. We applied the modeling approach to spiking responses recorded from monkey parietal cortex during two decision-making tasks. We found that a two-dimensional accumulator better captured the trial-averaged responses of a set of parietal neurons than a single accumulator model. Next, we identified a variable lower boundary in the responses of an LIP neuron during a random dot motion task.

q-bio.NC↗

arXiv2019

Shared Representational Geometry Across Neural Networks

Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representational similarity matrix, and their neural activity patterns are connected by orthogonal transformations. However, it is unclear if this holds for non-linear networks. Using a shared response model, we show that different neural networks encode the same input examples as different orthogonal transformations of an underlying shared representation. We test this claim using both standard convolutional neural networks and residual networks on CIFAR10 and CIFAR100.

cs.LG↗

arXiv2019

Dependent relevance determination for smooth and structured sparse regression

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), which model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop Laplace approximation and Monte Carlo Markov Chain (MCMC) sampling to provide efficient inference for the posterior. Furthermore, a two-stage convex relaxation of the Laplace approximation approach is also provided to relax the inevitable non-convexity during the optimization. We finally show substantial improvements over comparable methods for both simulated and real datasets from brain imaging.

stat.ML↗

arXiv2018

Exploiting gradients and Hessians in Bayesian optimization and Bayesian quadrature

An exciting branch of machine learning research focuses on methods for learning, optimizing, and integrating unknown functions that are difficult or costly to evaluate. A popular Bayesian approach to this problem uses a Gaussian process (GP) to construct a posterior distribution over the function of interest given a set of observed measurements, and selects new points to evaluate using the statistics of this posterior. Here we extend these methods to exploit derivative information from the unknown function. We describe methods for Bayesian optimization (BO) and Bayesian quadrature (BQ) in settings where first and second derivatives may be evaluated along with the function itself. We perform sampling-based inference in order to incorporate uncertainty over hyperparameters, and show that both hyperparameter and function uncertainty decrease much more rapidly when using derivative information. Moreover, we introduce techniques for overcoming ill-conditioning issues that have plagued earlier methods for gradient-enhanced Gaussian processes and kriging. We illustrate the efficacy of these methods using applications to real and simulated Bayesian optimization and quadrature problems, and show that exploting derivatives can provide substantial gains over standard methods.

stat.ML↗

arXiv2017

Capturing the dynamical repertoire of single neurons with generalized linear models

A key problem in computational neuroscience is to find simple, tractable models that are nevertheless flexible enough to capture the response properties of real neurons. Here we examine the capabilities of recurrent point process models known as Poisson generalized linear models (GLMs). These models are defined by a set of linear filters, a point nonlinearity, and conditionally Poisson spiking. They have desirable statistical properties for fitting and have been widely used to analyze spike trains from electrophysiological recordings. However, the dynamical repertoire of GLMs has not been systematically compared to that of real neurons. Here we show that GLMs can reproduce a comprehensive suite of canonical neural response behaviors, including tonic and phasic spiking, bursting, spike rate adaptation, type I and type II excitation, and two forms of bistability. GLMs can also capture stimulus-dependent changes in spike timing precision and reliability that mimic those observed in real neurons, and can exhibit varying degrees of stochasticity, from virtually deterministic responses to greater-than-Poisson variability. These results show that Poisson GLMs can exhibit a wide range of dynamic spiking behaviors found in real neurons, making them well suited for qualitative dynamical as well as quantitative statistical studies of single-neuron and population response properties.

q-bio.NC↗

arXiv2016

Bayesian latent structure discovery from multi-neuron recordings

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.

stat.ML↗

arXiv2015

The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex.

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