Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation

TL;DR

This paper tackles the challenge of non-conjugacy in Gaussian Process Factor Analysis for spike-count data by introducing conditionally-conjugate GPFA (ccGPFA) through a comprehensive data-augmentation scheme. By augmenting with variables from Pólya-gamma, Polya-Inverse Gamma, and Power Truncated Normal families, the authors render the likelihood Gaussian in a transformed space, enabling closed-form, variational EM updates for all latent variables and parameters, including the NB dispersion $r_n$. The approach supports scalable inference via sparse GP priors and natural-gradient updates, and it demonstrates superior performance and efficiency on real neural data compared with established baselines. The resulting framework provides a principled, fully Bayesian, tractable solution for modeling smooth latent trajectories driving spike counts, with practical scalability to large neural recordings. Overall, ccGPFA combines rigorous augmentation-based conjugacy with scalable inference to advance spike-count GPFA in real-world neuroscience datasets.

Abstract

Gaussian process factor analysis (GPFA) is a latent variable modeling technique commonly used to identify smooth, low-dimensional latent trajectories underlying high-dimensional neural recordings. Specifically, researchers model spiking rates as Gaussian observations, resulting in tractable inference. Recently, GPFA has been extended to model spike count data. However, due to the non-conjugacy of the likelihood, the inference becomes intractable. Prior works rely on either black-box inference techniques, numerical integration or polynomial approximations of the likelihood to handle intractability. To overcome this challenge, we propose a conditionally-conjugate Gaussian process factor analysis (ccGPFA) resulting in both analytically and computationally tractable inference for modeling neural activity from spike count data. In particular, we develop a novel data augmentation based method that renders the model conditionally conjugate. Consequently, our model enjoys the advantage of simple closed-form updates using a variational EM algorithm. Furthermore, due to its conditional conjugacy, we show our model can be readily scaled using sparse Gaussian Processes and accelerated inference via natural gradients. To validate our method, we empirically demonstrate its efficacy through experiments.

Figures (2)

• Figure 1: Plate diagram representing our ccGPFA model. Dashed circles indicate the variable is augmented.
• Figure 2: (Top) inferred mean firing rates by our method of a neuron across time along with peri-stimulus time histogram; (Left) orthonormalized latent processes; (Right) loading weights identified by our method ccGPFA for the first 10 neurons.