Robust inference using density-powered Stein operators

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.