Stochastic Collapsed Variational Inference for Structured Gaussian Process Regression Network

TL;DR

This paper introduces a scalable variational inference method for structured Gaussian process regression networks that effectively handles missing data and reveals neural dynamics in electrocorticography.

Contribution

It proposes a novel stochastic collapsed variational inference framework with structured variational distributions for SGPRNs, improving efficiency and handling missing data.

Findings

Better imputation of missing data compared to state-of-the-art methods

Efficient modeling of large datasets with independent complexity from input/output size

Insightful visualization of neural population dynamics

Abstract

This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and jointly treats both the distributions of the inducing variables and hyper-parameters as variational parameters. Then we propose structured variable distributions and marginalize latent variables, which enables the decomposability of a tractable variational lower bound and leads to stochastic optimization. Our inference approach is able to model data in which outputs do not share a common input set with a computational complexity independent of the size of the inputs and outputs and thus easily handle datasets with missing values. We illustrate the performance of our method on synthetic data and real datasets and show that our model generally provides better imputation results on missing data than the state-of-the-art. We also provide a visualization approach for time-varying correlation across outputs in electrocoticography data and those estimates provide insight to understand the neural population dynamics.