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

Zhijian Zhou · Jie Ni · Jia-He Yao · Wei Gao

Great Hall & Hall B1+B2 (level 1) #1021
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[ Paper [ Poster [ OpenReview
Wed 13 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: 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 ME$_\text{MaBiD}$, 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 ME$_\text{MaBiD}$ test. Theoretically, we present the asymptotic distribution and lower bounds of test power for our ME$_\text{MaBiD}$ 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.

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