arXiv subjects

Jonathan Pillow

Publications and source records attributed to Jonathan Pillow.

7 recordsLinked to original sources

arXiv2025

Reduced rank regression for neural communication: a tutorial for neuroscientists

Reduced rank regression (RRR) is a statistical method for finding a low-dimensional linear mapping between a set of high-dimensional inputs and outputs. In recent years, RRR has found numerous applications in neuroscience, in particular for identifying "communication subspaces" governing the interactions between brain regions. This tutorial article seeks to provide an introduction to RRR and its mathematical foundations, with a particular emphasis on neural communication. We discuss RRR's relationship to alternate dimensionality reduction techniques such as singular value decomposition (SVD), principal components analysis (PCA), principal components regression (PCR), and canonical correlation analysis (CCA). We also derive important extensions to RRR, including ridge regularization and non-spherical noise. Finally, we introduce new metrics for quantifying communication strength as well as the alignment between communication axes and the principal modes of neural activity. By the end of this article, readers should have a clear understanding of RRR and the practical considerations involved in applying it to their own data.

q-bio.NC↗

arXiv2025

Flexible inference for animal learning rules using neural networks

Understanding how animals learn is a central challenge in neuroscience, with growing relevance to the development of animal- or human-aligned artificial intelligence. However, existing approaches tend to assume fixed parametric forms for the learning rule (e.g., Q-learning, policy gradient), which may not accurately describe the complex forms of learning employed by animals in realistic settings. Here we address this gap by developing a framework to infer learning rules directly from behavioral data collected during de novo task learning. We assume that animals follow a decision policy parameterized by a generalized linear model (GLM), and we model their learning rule -- the mapping from task covariates to per-trial weight updates -- using a deep neural network (DNN). This formulation allows flexible, data-driven inference of learning rules while maintaining an interpretable form of the decision policy itself. To capture more complex learning dynamics, we introduce a recurrent neural network (RNN) variant that relaxes the Markovian assumption that learning depends solely on covariates of the current trial, allowing for learning rules that integrate information over multiple trials. Simulations demonstrate that the framework can recover ground-truth learning rules. We applied our DNN and RNN-based methods to a large behavioral dataset from mice learning to perform a sensory decision-making task and found that they outperformed traditional RL learning rules at predicting the learning trajectories of held-out mice. The inferred learning rules exhibited reward-history-dependent learning dynamics, with larger updates following sequences of rewarded trials. Overall, these methods provide a flexible framework for inferring learning rules from behavioral data in de novo learning tasks, setting the stage for improved animal training protocols and the development of behavioral digital twins.

cs.LG↗

arXiv2023

System Identification for Continuous-time Linear Dynamical Systems

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 It\^o 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.

cs.LG↗

arXiv2021

Probing the relationship between linear dynamical systems and low-rank recurrent neural network models

A large body of work has suggested that neural populations exhibit low-dimensional dynamics during behavior. However, there are a variety of different approaches for modeling low-dimensional neural population activity. One approach involves latent linear dynamical system (LDS) models, in which population activity is described by a projection of low-dimensional latent variables with linear dynamics. A second approach involves low-rank recurrent neural networks (RNNs), in which population activity arises directly from a low-dimensional projection of past activity. Although these two modeling approaches have strong similarities, they arise in different contexts and tend to have different domains of application. Here we examine the precise relationship between latent LDS models and linear low-rank RNNs. When can one model class be converted to the other, and vice versa? We show that latent LDS models can only be converted to RNNs in specific limit cases, due to the non-Markovian property of latent LDS models. Conversely, we show that linear RNNs can be mapped onto LDS models, with latent dimensionality at most twice the rank of the RNN.

q-bio.NC↗

arXiv2021

Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity

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

cs.LG↗

arXiv2019

Fast shared response model for fMRI data

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.

cs.CV↗

arXiv2014

Bayesian Entropy Estimation for Countable Discrete Distributions

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.

cs.IT↗