Computational Test for Conditional Independence (with Categorical Variables)

Conditional Independence (CI) testing is fundamental in statistical analysis. For example, CI testing helps validate causal graphs or longitudinal data analysis with repeated measures in causal inference. CI testing is difficult, especially when testing involves categorical variables conditioned on a mixture of continuous and categorical variables. Current parametric and non-parametric testing methods designed for continuous variables and can quickly fall short in the categorical case. This paper presents a computational approach for CI testing for categorical data types, which we call computational conditional independence (CCI) testing. The test procedure is based on permutation and combines machine learning prediction algorithms and Monte Carlo Cross-Validation. We evaluated the approach through simulation studies and assessed the performance against alternative methods; the generalized covariance measure (GCM) test, the kernel conditional independence (KCI) test, and testing with multinomial regression. We find that the computational approach to testing has utility over the alternative methods, and we can achieve better control over type-I-error rates. We hope this work can expand the toolkit for CI testing for practitioners and researchers.