On the Exploration of Local Significant Differences For Two-Sample Test

Recent years have witnessed increasing attentions on two-sample test with diverse real applications, while this work takes one more step on the exploration of local significant differences for two-sample test. We propose the MEMaBiD, an effective test for two-sample testing, and the basic idea is to exploit local information by multiple Mahalanobis kernels and introduce bi-directional hypothesis for testing. On the exploration of local significant differences, we first partition the embedding space into several rectangle regions via a new splitting criterion, which is relevant to test power and data correlation. We then explore local significant differences based on our bi-directional masked p-value together with the MEMaBiD test. Theoretically, we present the asymptotic distribution and lower bounds of test power for our MEMaBiD test, and control the familywise error rate on the exploration of local significant differences. We finally conduct extensive experiments to validate the effectiveness of our proposed methods on two-sample test and the exploration of local significant differences.