Negative Binomial LDS via Polya-Gamma Augmentation for Neural Spike Count Modeling

In this paper we extend well-studied Bayesian Latent State Space Time Series models to be able to account for discrete observation data using \PG Augmentation. In particular, we describe extensions of Linear Dynamical Systems (Gaussian distributed latent state space with linear dynamics and observations) and Hidden Markov Models (discrete state space with categorical transitions and linear observations) to be able to account for observations with bernoulli and negative binomial distributions. We then describe inference algorithms for these models, and evaluate both algorithmic performance on fitting synthetic data, and model fit on hippocampal data. We find that the ability to fit a negative binomial distribution improves on standard Poisson Observations, and that the Bayesian model provides a more accurate distribution over possible observations than a standard Expectation Maximization based approach.