提出新型鲁棒推断方法，用密度加权提升模型抗干扰能力。
Robust inference using density-powered Stein operators
- 基于γ-散度设计加权斯坦算子，通过模型密度调整观测权重。
- 在污染数据下保持稳定，γ>0时比传统方法更鲁棒，γ=0时效率最优。
- 适用于方向模型、混合模型等复杂分布，适合高噪声场景研究者。
我们引入一种新的密度幂加权斯坦算子，称为γ-斯坦算子，用于未归一化概率模型的鲁棒推断。该算子源于γ-散度在无穷小援引传输下的第一变分，通过正幂次的模型密度对常规斯坦场进行加权，从而降低低密度区域观测的影响，实现有原则的鲁棒性，同时保持评分匹配中无需归一化常数的结构。我们推导出相应的γ-评分匹配估计方程，并讨论其非可积、广义矩方法的特性。进一步研究了两个扩展：γ-核化斯坦分歧，可作为鲁棒诊断或污染零假设拟合优度检验；以及γ-斯坦变分梯度下降，用于鲁棒后验逼近。数值实验在方向模型、混合模型和四次势模型上展示了鲁棒性与效率的权衡：正γ值能在靶向污染下稳定推断，而γ=0在干净且正确设定的模型下仍为优选。
原文摘要 · Abstract (English)
We introduce a density-power weighted variant of the Stein operator, called the $γ$-Stein operator, for robust inference with unnormalized probability models. The operator is motivated by the first variation of the $γ$-divergence under infinitesimal escort transport and weights the usual Stein field by a positive power of the model density. This weighting down-weights observations in low model-density regions, providing a principled robustness mechanism while retaining the normalizing-constant-free structure of score matching. We develop the resulting $γ$-score matching estimating equations and discuss their non-integrable, generalized-method-of-moments character. We further study two extensions: a $γ$-kernelized Stein discrepancy, interpreted as a robust diagnostic or contaminated-null goodness-of-fit procedure, and $γ$-Stein variational gradient descent for robust posterior approximation. Numerical examples on directional, mixture, and quartic-potential models illustrate the robustness--efficiency trade-off: positive $γ$ can stabilize inference under targeted contamination, whereas $γ=0$ remains preferable under clean well-specified models.
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