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

arXiv: https://arxiv.org/abs/2608.29349 · HTML: https://mlsanity.com/paper/2608.29349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [An asymptotic analysis of distributed nonparametric methods](https://mlsanity.com/paper/1711.03149/) (2017)
- [Understanding and Comparing Scalable Gaussian Process Regression for Big Data](https://mlsanity.com/paper/1811.01159/) (2018)

## Built on by (most cited first, 1 of 1)

- [Bayesian Optimisation Using Product-of-Experts Gaussian Process Models with Uncertainty Calibration](https://mlsanity.com/paper/2609.15555/) (2026)

## Abstract (arXiv)

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.