Two-sample testing decides whether two datasets are generated from the same
distribution. This paper studies variable selection for two-sample testing, the
task being to identify the variables (or dimensions) responsible for the
discrepancies between the two distributions. This task is relevant to many
problems of pattern analysis and machine learning, such as dataset shift
adaptation, causal inference and model validation. Our approach is based on a
two-sample test based on the Maximum Mean Discrepancy (MMD). We optimise the
Automatic Relevance Detection (ARD) weights defined for individual variables to
maximise the power of the MMD-based test. For this optimisation, we introduce
sparse regularisation and propose two methods for dealing with the issue of
selecting an appropriate regularisation parameter. One method determines the
regularisation parameter in a data-driven way, and the other aggregates the
results of different regularisation parameters. We confirm the validity of the
proposed methods by systematic comparisons with baseline methods, and
demonstrate their usefulness in exploratory analysis of high-dimensional
traffic simulation data. Preliminary theoretical analyses are also provided,
including a rigorous definition of variable selection for two-sample testing.

这篇研究论文研究了在两样本检验中的变量选择问题，基于最大平均差异（MMD）的两样本检验的能力，通过优化自适应相关检测（ARD）权重来确定引起两个分布差异的变量，提出了考虑稀疏正则化的两种方法以解决选择适当正则化参数的问题，并通过与基线方法的系统比较验证了所提出方法的有效性，在高维交通仿真数据的探索性分析中展示了所提方法的实用性，同时也提供了变量选择在两样本检验中的严格定义的初步理论分析。