Spatio-Temporal Structured Sparse Regression with Hierarchical Gaussian Process Priors

TL;DR

This paper presents a novel spatio-temporal structured Gaussian process regression framework that models evolving interdependencies in sparse signals, improving accuracy and efficiency in reconstructing dynamic patterns from various data types.

Contribution

It introduces the first hierarchical Gaussian process model for time-evolving interdependencies in sparse signals, with a new inference method and comprehensive evaluation.

Findings

Achieves 15% higher F-measure than existing methods.

Requires less memory than one-level Gaussian process models.

Effectively reconstructs dynamic patterns in synthetic, video, and EEG data.

Abstract

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian process describes such structure and the interdependencies are represented via the covariance matrices of the prior distributions. The inference is based on the expectation propagation method and the theoretical derivation of the posterior distribution is provided in the paper. The inference framework is thoroughly evaluated over synthetic, real video and electroencephalography (EEG) data where the spatio-temporal evolving patterns need to be reconstructed with high accuracy. It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and one-level Gaussian process model. Additionally, the required memory for the proposed algorithm is less than in the one-level Gaussian process model. This structured sparse regression framework is of broad applicability to source localisation and object detection problems with sparse signals.