A0986
Title: MATES: Multi-view aggregated two-sample test
Authors: Doudou Zhou - National University of Singapore (Singapore) [presenting]
Zexi Cai - Columbia University (United States)
Abstract: The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional assumptions. However, many existing methods tend to be more effective when the two distributions differ primarily in their first and/or second moments. In many real-world scenarios, distributional differences may arise in higher-order moments, rendering traditional methods less powerful. To address this limitation, a novel framework is proposed to aggregate information from multiple moments to build a test statistic. Each moment is regarded as one view of the data and contributes to the detection of some specific type of discrepancy, thus allowing the test statistic to capture more complex distributional differences. The novel multi-view aggregated two-sample TESt (MATES) leverages a graph-based approach, where the test statistic is constructed from the weighted similarity graphs of the pooled sample. Under mild conditions on the multi-view weighted similarity graphs, theoretical properties of MATES are established, including a distribution-free limiting distribution under the null hypothesis, which enables straightforward type-I error control.
