Nonstationary and Sparsely-Correlated Multioutput Gaussian Process with Spike-and-Slab Prior

Multioutput 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, because some outputs may lack correlation, transferring information among them may lead to negative transfer. To address these issues, this study proposes a nonstationary 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 real cases demonstrate its efficacy in capturing dynamic and sparse correlation structure and mitigating negative transfer for high-dimensional time-series data modeling. A mountain-car reinforcement learning case highlights that transferring knowledge from source expertise can enhance the efficiency of the target decision-making process. Our method holds promise for application in more complex multitask decision-making challenges within nonstationary environments in the future. History: Rema Padman served as the senior editor for this article. Funding: This work was supported by NSFC [Grants NSFC-72171003, NSFC-71932006, and NSFC-72101147]. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://doi.org/10.24433/CO.4010696.v1 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0022 ).