Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior

TL;DR

This paper introduces a non-stationary multi-output Gaussian process model with a spike-and-slab prior to effectively capture dynamic, sparse correlations among outputs, improving transfer learning and decision-making in complex time-series data.

Contribution

It proposes a novel non-stationary MGP with a spike-and-slab prior and an EM algorithm for efficient fitting, addressing dynamic and sparse correlations in multivariate data.

Findings

Effectively captures dynamic and sparse output correlations.

Reduces negative transfer in high-dimensional time-series.

Demonstrates improved decision-making in reinforcement learning.

Abstract

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for subsequent decision-making tasks. However, traditional MGP may not be sufficiently flexible to handle multivariate data with dynamic characteristics, particularly when dealing with complex temporal correlations. Additionally, since some outputs may lack correlation, transferring information among them may lead to negative transfer. To address these issues, this study proposes a non-stationary MGP model that can capture both the dynamic and sparse correlation among outputs. Specifically, the covariance functions of MGP are constructed using convolutions of time-varying kernel functions. Then a dynamic spike-and-slab prior is placed on correlation parameters to automatically decide which sources are informative to the target output in the training process. An expectation-maximization (EM) algorithm is proposed for efficient model fitting. Both numerical studies and a real case demonstrate its efficacy in capturing dynamic and sparse correlation structure and mitigating negative transfer for high-dimensional time-series data. Finally, a mountain-car reinforcement learning case highlights its potential application in decision making problems.