Robust inference using density-powered Stein operators
This work addresses robust inference for statisticians and machine learning practitioners dealing with outliers in probability models, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackled robust inference for unnormalized probability models by introducing the γ-Stein operator, a density-power weighted variant derived from γ-divergence, which down-weights outliers and enables robust score matching and applications like goodness-of-fit testing and Bayesian posterior approximation. Empirical results on contaminated Gaussian and quartic potential models showed significant outperformance over standard baselines in robustness and statistical efficiency.
We introduce a density-power weighted variant for the Stein operator, called the $γ$-Stein operator. This is a novel class of operators derived from the $γ$-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 $γ$ 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 $γ$-kernelized Stein discrepancy for robust goodness-of-fit testing, and $γ$-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.