Title: Permutation methods for comparing distributions

Speaker: 김일문 (Assistant Professor, Yonsei University)

Abstract: The advent of large-scale, high-dimensional, and complex datasets has posed significant challenges for classical inference methods, which frequently yield unreliable results when applied to modern datasets. These challenges call for new tools and theoretical frameworks better suited to contemporary data environments. In this talk, we consider permutation tests as a promising alternative to address these issues and discuss their utility in modern applications. In the first part of this talk, we build on permutation tests to present a flexible framework for comparing distributions that can leverage any classification or regression algorithms. Depending on the selected classification or regression model, the proposed framework can efficiently handle different types of variables and data structures, demonstrating competitive power across many practical scenarios. In the second part, we introduce a theoretical framework for analyzing the power of permutation tests. Despite their growing popularity and empirical success, the theoretical properties of permutation tests, particularly regarding power, remain underexplored beyond simple cases. We aim to partly fill this gap by presenting a general non-asymptotic framework for analyzing the minimax power of permutation tests. We illustrate the utility of our proposed framework in two-sample and independence testing, showing that permutation tests can achieve minimax optimality in diverse settings.

Zoom Link: *https://us06web.zoom.us/j/4564461054?pwd=TVUt6ys0rcjoVTMNAkaUmN8YJUiK8T.1&omn=88642237048