When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow learning to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths. We establish the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, derive stochastic Riemannian gradient descent algorithms for their efficient optimization, and demonstrate their advantages over score matching in models with non-smooth densities or heavy tailed distributions.

本文提出了一种统一的视角来描述和设计基于最小Stein距离的估计器，并使用这种方法来设计新的扩散核Stein距离（DKSD）和扩散分数匹配（DSM）估计器，证明了它们的一致性、渐近正常性和鲁棒性，并为它们的高效优化推导了随机黎曼梯度下降算法。该方法的主要优势在于其灵活性，使我们能够通过仔细选择Stein距离来为特定的模型设计具有理想性质的估计器，并在一些具有挑战性的问题上进行了演示，例如光滑、重尾或轻尾密度的分数匹配。

最小斯坦（Stein）差异估计量