Uncovering internal states with a robust shared-state multi-neuron GLM-HMM framework

Abstract

Neural systems exhibit multiple firing states that reflect an organisms internal state and modulate the relationship between external environmental stimuli and behavior. Several studies have inferred these latent states by supplementing the traditional hidden Markov Model (HMM) with generalized linear models (GLMs) with non-Poisson behavioral observations. However, understanding the relationship between internal brain states and behavior also requires modeling the neural activity. Nonetheless, fitting multi-neuron GLM-HMMs is non-trivial due to high sparsity, collinearity, and low trial counts in neuronal datasets. Therefore, we built a robust multi-neuron GLM-HMM framework that uncovers latent states from population activity while incorporating the influence of time-stamped task variables and spike histories. To obtain reliable model parameters, we employ a modified expectation-maximization procedure. Specifically, we show that incorporating neuron-adaptive penalization in the maximization step overcomes the covariate co-linearity issues typical of time-stamped events and sparse spiking, yielding stable estimates of Poisson GLM coefficients. Furthermore, we incorporate a trust-region algorithm to ensure stable M-step convergence in the presence of ill-conditioned Hessians that can lead to unstable Newton-Raphson updates. We further demonstrate the utility of leave-one-out cross-validation analysis for evaluating model performance on datasets with low trial counts and without breaking their temporal structure. We evaluate our framework on three electrophysiological datasets from primates and rodents as they perform a decision-making task, demonstrate stable model convergence, and discuss the behavioral relevance of the inferred states. Author SummaryNeural systems evolve over time: not only do the individual neurons influence each other across the network, but the network and interconnections themselves change as an animal enters different behaviors (e.g., attentive vs. disengaged) or states (e.g., hungry or tired). Analyzing the neural activity that guides behavior thus must incorporate the time-varying nature of the brain. Recent modeling work has extended the popular Generalized Linear Model, a model that can connect task and behavior to recorded neural action potentials, to incorporate a latent Hidden Markov Model. This extension allows the resulting GLM-HMM to exhibit several different relationships (different GLMs) that are switched between over time to account for the animals changing patterns. While GLM-HMMs have been applied extensively on behavioral data (e.g., task choice in a decision making paradigm), neural data is much more difficult due to the smaller sample sizes, sparser activity, and larger parameter space. Our work presents a new fitting approach and best practices to robustly fit GLM-HMMs to neural data. We demonstrate through numerous applications to a variety of neural datasets that by robustly fitting GLM-HMMs to data, we can identify important features of neural activity that let us better understand its relationship to behavior.