Advanced Tutorial: Label-Efficient Two-Sample Tests

Abstract: Hypothesis testing is a statistical inference approach used to determine whether data supports a specific hypothesis. An important type is the two-sample test, which evaluates whether two sets of data points are from identical distributions. This test is widely used, such as by clinical researchers comparing treatment effectiveness. This tutorial explores two-sample testing in a context where an analyst has many features from two samples, but determining the sample membership (or labels) of these features is costly. In machine learning, a similar scenario is studied in active learning. This tutorial extends active learning concepts to two-sample testing within this \textit{label-costly} setting while maintaining statistical validity and high testing power. Additionally, the tutorial discusses practical applications of these label-efficient two-sample tests.