Gaussian Processes with Bayesian Inference of Covariate Couplings

Gaussian processes are powerful probabilistic models that are often coupled with Automatic Relevance Determination (ard) capable of uncovering the importance of individual covariates. We develop covariances characterized by affine transformations of the inputs, formalized via a precision matrix between covariates, which can uncover covariate couplings for enhanced interpretability. We study a range of couplings priors from Wishart to Horseshoe and present fully Bayesian inference of such precision matrices within sparse Gaussian processes. We empirically demonstrate the efficacy and interpretability of this approach.

Recommended citation: Mattia Rosso, Juho Ylä-Jaäski, Zheyang Shen, Markus Heinonen, & Maurizio Filippone (2025). Gaussian Processes with Bayesian Inference of Covariate Couplings. Transactions on Machine Learning Research.
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