Jonathan W. Pillow

Iris R. Stone, Yotam Sagiv, Il Memming Park et al.

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.

Peter Halmos, Jonathan Pillow, David A. Knowles

The problem of system identification for the Kalman filter, relying on the expectation-maximization (EM) procedure to learn the underlying parameters of a dynamical system, has largely been studied assuming that observations are sampled at equally-spaced time points. However, in many applications this is a restrictive and unrealistic assumption. This paper addresses system identification for the continuous-discrete filter, with the aim of generalizing learning for the Kalman filter by relying on a solution to a continuous-time Itô stochastic differential equation (SDE) for the latent state and covariance dynamics. We introduce a novel two-filter, analytical form for the posterior with a Bayesian derivation, which yields analytical updates which do not require the forward-pass to be pre-computed. Using this analytical and efficient computation of the posterior, we provide an EM procedure which estimates the parameters of the SDE, naturally incorporating irregularly sampled measurements. Generalizing the learning of latent linear dynamical systems (LDS) to continuous-time may extend the use of the hybrid Kalman filter to data which is not regularly sampled or has intermittent missing values, and can extend the power of non-linear system identification methods such as switching LDS (SLDS), which rely on EM for the linear discrete-time Kalman filter as a sub-unit for learning locally linearized behavior of a non-linear system. We apply the method by learning the parameters of a latent, multivariate Fokker-Planck SDE representing a toggle-switch genetic circuit using biologically realistic parameters, and compare the efficacy of learning relative to the discrete-time Kalman filter as the step-size irregularity and spectral-radius of the dynamics-matrix increases.

Yuhan Helena Liu, Victor Geadah, Jonathan Pillow

Understanding how animals learn is a central challenge in neuroscience, with growing relevance to the development of animal- or human-aligned artificial intelligence. However, most existing approaches assume specific parametric forms for the learning rule (e.g., Q-learning, policy gradient) or are limited to simplified settings like bandit tasks, which do not involve learning a new input-output mapping from scratch. In contrast, animals must often learn new behaviors de novo, which poses a rich challenge for learning-rule inference. We target this problem by inferring learning rules directly from animal decision-making data during de novo task learning, a setting that requires models flexible enough to capture suboptimality, history dependence, and rich external stimulus integration without strong structural priors. We first propose a nonparametric framework that parameterizes the per-trial update of policy weights with a deep neural network (DNN), and validate it by recovering ground-truth rules in simulation. We then extend to a recurrent variant (RNN) that captures non-Markovian dynamics by allowing updates to depend on trial history. Applied to a large behavioral dataset of mice learning a sensory decision-making task over multiple weeks, our models improved predictions on held-out data. The inferred rules revealed asymmetric updates after correct versus error trials and history dependence, consistent with non-Markovian learning. Overall, these results introduce a flexible framework for inferring biological learning rules from behavioral data in de novo learning tasks, providing insights to inform experimental training protocols and the development of behavioral digital twins.

Aditi Jha, Zoe C. Ashwood, Jonathan W. Pillow

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.

Michael J. Morais, Jonathan W. Pillow

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.

Felix Pei, Joel Ye, David Zoltowski et al.

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 with LVMs for neuronal population activity 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

Benjamin R. Cowley, Jonathan W. Pillow

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.

David M. Zoltowski, Jonathan W. Pillow, Scott W. Linderman

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.

Hugo Richard, Lucas Martin, Ana Luısa Pinho et al.

The shared response model provides a simple but effective framework to analyse fMRI data of subjects exposed to naturalistic stimuli. However when the number of subjects or runs is large, fitting the model requires a large amount of memory and computational power, which limits its use in practice. In this work, we introduce the FastSRM algorithm that relies on an intermediate atlas-based representation. It provides considerable speed-up in time and memory usage, hence it allows easy and fast large-scale analysis of naturalistic-stimulus fMRI data. Using four different datasets, we show that our method matches the performance of the original SRM algorithm while being about 5x faster and 20x to 40x more memory efficient. Based on this contribution, we use FastSRM to predict age from movie watching data on the CamCAN sample. Besides delivering accurate predictions (mean absolute error of 7.5 years), FastSRM extracts topographic patterns that are predictive of age, demonstrating that brain activity during free perception reflects age.

Stephen L. Keeley, David M. Zoltowski, Yiyi Yu et al.

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.

Qihong Lu, Po-Hsuan Chen, Jonathan W. Pillow et al.

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.

Anqi Wu, Oluwasanmi Koyejo, Jonathan W. Pillow

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.

Anqi Wu, Mikio C. Aoi, Jonathan W. Pillow

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.

Scott W. Linderman, Ryan P. Adams, Jonathan W. 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.