论文标题
用内核Stein差异控制时刻
Controlling Moments with Kernel Stein Discrepancies
论文作者
论文摘要
内核Stein差异（KSD）测量分布近似的质量，即使目标密度具有棘手的归一化常数，也可以计算。值得注意的应用包括对近似MCMC采样器的诊断以及对不当统计模型的合适性测试。目前的工作分析了KSD的收敛控制属性。我们首先表明用于弱收敛控制的标准KSD无法控制力矩收敛。为了解决这一限制，我们接下来提供了足够的条件，在该条件下，替代扩散KSD控制力矩和弱收敛性。由于我们要开发的直接结果，对于每个$ Q> 0 $，这是已知的第一个KSD，旨在表征$ Q $ -Wasserstein Convergence。
Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant. Notable applications include the diagnosis of approximate MCMC samplers and goodness-of-fit tests for unnormalized statistical models. The present work analyzes the convergence control properties of KSDs. We first show that standard KSDs used for weak convergence control fail to control moment convergence. To address this limitation, we next provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence. As an immediate consequence we develop, for each $q > 0$, the first KSDs known to exactly characterize $q$-Wasserstein convergence.
