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

Neural systems exhibit multiple firing states that reflect an organism's 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.