Multiple Testing of Conditional Independence Hypotheses Using Information-Theoretic Approach

In the paper we study the multiple testing problem for which individual hypotheses of interest correspond to conditional independence of the two variables X and Y given each of the several conditioning variables. Approaches to such problems avoiding inflation of probability of spurious rejections are widely studied and applied. Here we introduce a direct approach based on Joint Mutual Information (JMI) statistics which restates the problem as a problem of testing of a single hypothesis. The distribution of the test statistics JMI is established and shown to be well numerically approximated for a single data sample. The corresponding test is studied on artificial data sets and is shown to work promisingly when compared to general purpose multiple testing methods such as Bonferroni or Simes procedures.