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

• URL: http://arxiv.org/abs/2608.29349v1
• Date: Sat, 29 Aug 2026 16:13:35 GMT
• Title: Information-Based Calibration of Uncertainty Quantification in Product-of-Experts Gaussian Process Models
• Abstract summary: Product-of-experts GP models (GP-pro) combine local GP models to capture global correlations.<n>We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method.<n>Experiments show GP-pro-c achieves average reductions of 2.3% in NLL and 12.0% in ENCE compared with the uncalibrated GP-pro model.
• Score: 6.3565351281858495
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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