Probabilistic methods for modeling decision-making dynamics and identifying structure in neural datasets

Abstract

Research in statistical neuroscience uses tools from probabilistic modeling, statistics, and machine learning to help draw scientific conclusions from complex neural datasets. In this dissertation we present multiple contributions in these areas. We begin by describing methods to identify neural dynamics during decision-making and to characterize how neural dynamics relate to models of decision-making behavior. Using these methods, we identify both discrete stepping and continuous accumulation-to-bound dynamics in various brain regions during decision-making tasks. As part of this work we also develop variational Laplace EM, a general method for fitting recurrent switching dynamical systems. We then describe approaches to address two statistical problems with modern neural data. We first use approximate sufficient statistics to enable fitting Poisson GLMs to massive neural datasets. Next, we devise methods for more accurate estimation of internal latent states underlying population calcium imaging data. Finally, we describe a new Monte Carlo gradient estimator based on slice sampling. The slice sampling reparameterization gradients apply to a wide class of unnormalized distributions, enabling lower variance Monte Carlo gradient estimates on new classes of distributions. Our contributions have provided insight into neural dynamics during decision making and the various methods we have developed have broad utility in statistical neuroscience and machine learning.