Sparse within Sparse Gaussian Processes using Neighbor Information

TL;DR

This paper introduces a hierarchical prior for sparse Gaussian processes that leverages neighbor information to efficiently handle many inducing variables, enabling scalable inference with large datasets.

Contribution

It proposes a novel hierarchical prior that induces sparsity among inducing variables based on neighbor information, improving scalability of sparse GPs.

Findings

Significant computational gains over standard sparse GPs.

Effective handling of large numbers of inducing points.

Validated through extensive experiments.

Abstract

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.