Information-Based Calibration of Uncertainty Quantification in Product-of-Experts Gaussian Process Models

2026-08-29

AI Summary

为解决高斯过程模型中局部专家导致的后验方差过高问题，提出了一种基于信息的方法GP-pro-c来校准不确定性量化，同时保持预测准确性并降低计算复杂度。

Abstract

Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3% in NLL and 12.0% in ENCE compared with the uncalibrated GP-pro model. The proposed method mitigates posterior variance overestimation while maintaining predictive accuracy and reducing computational complexity. GP-pro-c provides a promising approach for uncertainty estimation in scalable GP models and may serve as a useful surrogate model for Bayesian optimisation with high-dimensional and large-scale data.

Problem

• Gaussian Process
• Product-of-Experts
• Uncertainty Quantification
• Posterior Variance
• Calibration

Innovation

• information-based calibration
• product-of-experts GP models
• posterior variance overestimation
• monotonicity and submodularity of information gain