MMD two-sample testing in the presence of arbitrarily missing data
OA Location
Author(s)
Zeng, Yijin
Adams, Niall
Bodenham, Dean
Type
Journal Article
Abstract
In many real-world applications, it is common that a proportion of the data may be missing or only partially observed. We develop a novel two-sample testing method based on the Maximum Mean Discrepancy (MMD) which accounts for missing data in both samples, without making assumptions about the missingness mechanism. Our approach is based on deriving the mathematically precise bounds of the MMD test statistic after accounting for all possible missing values. To the best of our knowledge, it is the only two-sample testing method that is guaranteed to control the Type I error for both univariate and multivariate data where data may be arbitrarily missing. Simulation results show that the method has good statistical power, typically for cases where 5% to 10% of the data are missing. We highlight the value of this approach when the data are missing not at random, a context in which either ignoring the missing values or using common imputation methods may not control the Type I error.
Date Acceptance
2025-12-02
Citation
Transactions on Machine Learning Research
ISSN
2835-8856
Publisher
Journal of Machine Learning Research Inc.
Journal / Book Title
Transactions on Machine Learning Research
Copyright Statement
Subject to copyright. This paper is embargoed until publication. Once published the Version of Record (VoR) will be available on immediate open access.
Publication Status
Accepted