Robust inference using density-powered Stein operators

arXiv:2511.03963v2 Announce Type: replace-cross Abstract: We introduce a density-power weighted variant for the Stein operator, called the gamma-Stein operator. This is a novel class of operators derived from the gamma-divergence, designed to build robust inference methods for unnormalized probability models. The operator's construction (weighting by the model density raised to a positive power gamma inherently down-weights the influence of outliers, providing a principled mechanism for robustness. Applying this operator yields a robust generalization of score matching that retains the crucial property of being independent of the model's normalizing constant. We extend this framework to develop two key applications: the gamma-kernelized Stein discrepancy for robust goodness-of-fit testing, and gamma-Stein variational gradient descent for robust Bayesian posterior approximation. Empirical results on contaminated Gaussian and quartic potential models show our methods significantly outperform standard baselines in both robustness and statistical efficiency.

Source: arXiv cs.LG | 2026-05-26