Bayesian Transformed Gaussian Processes

Published: 14 Apr 2023, Last Modified: 14 Apr 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: The Bayesian transformed Gaussian (BTG) model, proposed by Kedem and Oliviera in 1997, was developed as a Bayesian approach to trans-Kriging in the spatial statistics community. In this paper, we revisit BTG in the context of modern Gaussian process literature by framing it as a fully Bayesian counterpart to the Warped Gaussian process that marginalizes out a joint prior over input warping and kernel hyperparameters. As with any other fully Bayesian approach, this treatment introduces prohibitively expensive computational overhead; unsurprisingly, the BTG posterior predictive distribution, itself estimated through high-dimensional integration, must be inverted in order to perform model prediction. To address these challenges, we introduce principled numerical techniques for computing with BTG efficiently using a combination of doubly sparse quadrature rules, tight quantile bounds, and rank-one matrix algebra to enable both fast model prediction and model selection. These efficient methods allow us to compute with higher-dimensional datasets and apply BTG with layered transformations that greatly improve its expressibility. We demonstrate that BTG achieves superior empirical performance over MLE-based models in the low-data regime ---situations in which MLE tends to overfit.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: We moved all table captions above the table content.
Assigned Action Editor: ~Roman_Garnett1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 792