GP‑Pro‑c Improves Posterior Variance Estimation by 5%

A team led by Yean Hoon Ong, Paolo Barucca, Wei Pan and Jun Wang introduced a product‑of‑experts Gaussian process model called GP‑pro‑c in an article published on August 15, 2026 in the Journal of Artificial Intelligence Research ¹.

The authors address the tendency for local experts trained on disjoint data subsets to inflate posterior uncertainty estimates—a problem that arises because training a single global Gaussian process incurs cubic computational cost and limits scalability to large datasets. Product‑of‑experts models split the data into smaller regions, train independent local GPs, and combine their predictions; however, each expert sees only part of the full dataset, which can lead to overestimated posterior variances.

To correct this, GP‑pro‑c uses an information‑based calibration scheme. By exploiting monotonicity and submodularity properties of information gain—how much additional data reduces uncertainty—the method assigns a calibration ratio to each local GP that proportionally shrinks its estimated variance.

This adjustment is applied iteratively during inference without requiring retraining of all experts; instead it relies solely on per‑step information calculations.

Experimental results show that GP‑pro‑c improves negative log‑likelihood (NLL) by up to 5% across several benchmark datasets compared with baseline product‑of‑expert approaches, and also reports reductions in root mean squared error (RMSE) and expected normalized confidence intervals, indicating tighter uncertainty estimates translate into more accurate point predictions ¹.

Expert commentary frames the work as building upon long‑standing challenges first highlighted in Murphy’s Bayesian Hierarchical Modelling (2003). Earlier attempts to correct overestimation often incurred prohibitive computational costs; GP‑pro‑c offers a practical alternative that preserves scalability while delivering measurable gains in likelihood metrics ¹.