A KNN-Based Non-Parametric Conditional Independence Test for Mixed Data and Application in Causal Discovery

Johannes Huegle, Christopher Hagedorn, Rainer Schlosser

Abstract: Testing for Conditional Independence (CI) is a fundamental task for causal discovery but is particularly challenging in mixed discrete-continuous data. In this context, inadequate assumptions or discretization of continuous variables reduce the CI test’s statistical power, which yields incorrect learned causal structures. In this work, we present a non-parametric CI test leveraging k-nearest neighbor (kNN) methods that are adaptive to mixed discrete-continuous data. In particular, a kNN-based conditional mutual information estimator serves as the test statistic, and the p-value is calculated using a kNN-based local permutation scheme. We prove the CI test’s statistical validity and power in mixed discrete-continuous data, which yields consistency when used in constraint-based causal discovery. An extensive evaluation of synthetic and real-world data shows that the proposed CI test outperforms state-of-the-art approaches in the accuracy of CI testing and causal discovery, particularly in settings with low sample sizes.