Robust inference using density-powered Stein operators

TL;DR

This paper introduces a new density-power Stein operator that enhances robustness in statistical inference, enabling more reliable model fitting and testing in the presence of outliers.

Contribution

The paper proposes the $oldsymbol{ extgamma}$-Stein operator derived from $oldsymbol{ extgamma}$-divergence, providing a robust alternative to traditional score matching and related methods.

Findings

Outperforms standard methods in contaminated Gaussian models

Provides robust goodness-of-fit testing via $oldsymbol{ extgamma}$-kernelized Stein discrepancy

Enhances Bayesian inference with $oldsymbol{ extgamma}$-Stein variational gradient descent

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.