Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations

TL;DR

This paper introduces a fast, approximate inference method using polynomial approximations for non-conjugate Gaussian Process Factor Analysis models applied to neural spike count data, enabling efficient extraction of latent neural dynamics.

Contribution

It proposes the Polynomial Approximate Log-Likelihood (PAL) method for efficient inference in non-conjugate GPFA models with count data, improving speed and accuracy over existing methods.

Findings

PAL estimators are highly accurate for spike count data.

PAL achieves faster convergence than state-of-the-art methods.

PAL hyperparameters improve variational inference accuracy.

Abstract

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as \textit{polynomial approximate log-likelihood} (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.