Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior

TL;DR

This paper introduces MultiSVGP, a scalable sparse Gaussian Process model with a novel kernel learning algorithm using a Horseshoe prior, improving efficiency and interpretability in compositional kernel learning.

Contribution

It proposes a new sparse approximation for compositional GPs and a probabilistic kernel learning algorithm that handles sparsity with a Horseshoe prior, enhancing scalability and interpretability.

Findings

Better fit for learning compositional kernels from data

Significant reduction in computational time

Competitive regression performance on real-world datasets

Abstract

Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide not only accurate prediction but also attractive interpretability through search-based methods. However, existing methods suffer from slow kernel composition learning. To tackle large-scaled data, we propose a new sparse approximate posterior for GPs, MultiSVGP, constructed from groups of inducing points associated with individual additive kernels in compositional kernels. We demonstrate that this approximation provides a better fit to learn compositional kernels given empirical observations. We also provide theoretically justification on error bound when compared to the traditional sparse GP. In contrast to the search-based approach, we present a novel probabilistic algorithm to learn a kernel composition by handling the sparsity in the kernel selection with Horseshoe prior. We demonstrate that our model can capture characteristics of time series with significant reductions in computational time and have competitive regression performance on real-world data sets.