Biomarker identification by interpretable maximum mean discrepancy

In many biomedical applications, we are confronted with paired groups of samples, such as treated versus control. The aim is to detect discriminating features, i.e. biomarkers, based on high-dimensional (omics-) data. This problem can be phrased more generally as a two-sample problem requiring statistical significance testing to establish differences, and interpretations to identify distinguishing features. The multivariate maximum mean discrepancy (MMD) test quantifies group-level differences, whereas statistically significantly associated features are usually found by univariate feature selection. Currently, few general-purpose methods simultaneously perform multivariate feature selection and two-sample testing.