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Conditional independence (CI) tests underlie many approaches to model testingand structure learning in causal inference. Most existing CI tests forcategorical and ordinal data stratify the sample by the conditioning variables,perform simple independence tests in each stratum, and combine the results.Unfortunately, the statistical power of this approach degrades rapidly as thenumber of conditioning variables increases. Here we propose a simple unified CItest for ordinal and categorical data that maintains reasonable calibration andpower in high dimensions. We show that our test outperforms existing baselinesin model testing and structure learning for dense directed graphical modelswhile being comparable for sparse models. Our approach could be attractive forcausal model testing because it is easy to implement, can be used withnon-parametric or parametric probability models, has the symmetry property, andhas reasonable computational requirements.

A Simple Unified Approach to Testing High-Dimensional Conditional Independences for Categorical and Ordinal Data