Efficient Two-Stage Gaussian Process Regression Via Automatic Kernel Search and Subsampling

TL;DR

This paper introduces a two-stage Gaussian Process Regression framework that automatically searches for optimal kernels and employs subsampling for efficient hyperparameter tuning, significantly improving robustness and accuracy in real-world applications.

Contribution

It presents a novel two-stage GPR approach with automatic kernel search and subsampling strategies, addressing misspecification issues and enhancing computational efficiency.

Findings

Achieves competitive or superior performance with lower computational cost.

Demonstrates robustness and precision on real-world datasets.

Effectively handles mean and kernel misspecifications in GPR.

Abstract

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function, and associated hyperparameters. Severe misspecifications can lead to inaccurate results and problematic consequences, especially in safety-critical applications. However, a systematic approach to handle these misspecifications is lacking in the literature. In this work, we propose a general framework to address these issues. Firstly, we introduce a flexible two-stage GPR framework that separates mean prediction and uncertainty quantification (UQ) to prevent mean misspecification, which can introduce bias into the model. Secondly, kernel function misspecification is addressed through a novel automatic kernel search algorithm, supported by theoretical analysis, that selects the optimal kernel from a candidate set. Additionally, we propose a subsampling-based warm-start strategy for hyperparameter initialization to improve efficiency and avoid hyperparameter misspecification. With much lower computational cost, our subsampling-based strategy can yield competitive or better performance than training exclusively on the full dataset. Combining all these components, we recommend two GPR methods-exact and scalable-designed to match available computational resources and specific UQ requirements. Extensive evaluation on real-world datasets, including UCI benchmarks and a safety-critical medical case study, demonstrates the robustness and precision of our methods.