Abstract

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modeling the difference between kernel mean embeddings in the reproducing kernel Hilbert space using the framework established by Flaxman et al. The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e., testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach. Supplementary materials for this article are available online.

摘要

在现代数据分析中，随机变量之间差异的非参数测量尤为重要。该主题在常客文献中得到了充分研究，而贝叶斯设置的发展受到限制，因为应用程序通常仅限于单变量情况。在这里，我们提出了一种贝叶斯核双样本测试程序，该程序基于使用 Flaxman 等人建立的框架对再生核希尔伯特空间中的核均值嵌入之间的差异进行建模。核方法的使用使其能够应用于多元欧几里德空间之外的一般域中的随机变量。所提出的过程导致后验推理方案，允许自动选择与手头问题相关的内核参数。在一系列合成实验和两个真实数据实验（即，从高维数据测试网络异质性和六元单环构象比较）中，我们说明了我们方法的优势。本文的补充材料可在线获取。