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.
| Comments: | Revised version |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2511.03963 [stat.ML] |
| (or arXiv:2511.03963v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2511.03963 arXiv-issued DOI via DataCite |
From: Shinto Eguchi [view email]
[v1]
Thu, 6 Nov 2025 01:32:17 UTC (469 KB)
[v2]
Sun, 24 May 2026 02:22:46 UTC (177 KB)
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