A Sparse Expansion For Deep Gaussian Processes

TL;DR

This paper introduces a hierarchical expansion of Tensor Markov Gaussian Processes (TMGP) to create a deep DTMGP model that offers accurate inference and significantly improved computational efficiency for complex stochastic processes.

Contribution

It proposes a novel hierarchical expansion of TMGPs and a deep DTMGP model that reduces computational complexity in inference and training for deep Gaussian processes.

Findings

DTMGP achieves superior computational efficiency compared to existing DGP models.

The hierarchical expansion enables scalable inference for complex stochastic processes.

Numerical experiments validate the effectiveness of DTMGP on synthetic and real datasets.

Abstract

In this work, we use Deep Gaussian Processes (DGPs) as statistical surrogates for stochastic processes with complex distributions. Conventional inferential methods for DGP models can suffer from high computational complexity as they require large-scale operations with kernel matrices for training and inference. In this work, we propose an efficient scheme for accurate inference and efficient training based on a range of Gaussian Processes, called the Tensor Markov Gaussian Processes (TMGP). We construct an induced approximation of TMGP referred to as the hierarchical expansion. Next, we develop a deep TMGP (DTMGP) model as the composition of multiple hierarchical expansion of TMGPs. The proposed DTMGP model has the following properties: (1) the outputs of each activation function are deterministic while the weights are chosen independently from standard Gaussian distribution; (2) in training or prediction, only polylog(M) (out of M) activation functions have non-zero outputs, which significantly boosts the computational efficiency. Our numerical experiments on synthetic models and real datasets show the superior computational efficiency of DTMGP over existing DGP models.