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

TL;DR

This paper introduces a simple, unified conditional independence test for categorical and ordinal data that maintains high power and calibration in high-dimensional settings, improving model testing and structure learning.

Contribution

The paper presents a novel CI test that outperforms existing methods in high-dimensional categorical and ordinal data, with easy implementation and broad applicability.

Findings

Outperforms existing CI tests in dense models

Maintains reasonable calibration and power in high dimensions

Easy to implement and compatible with various probability models

Abstract

Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical 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 the number of conditioning variables increases. Here we propose a simple unified CI test for ordinal and categorical data that maintains reasonable calibration and power in high dimensions. We show that our test outperforms existing baselines in model testing and structure learning for dense directed graphical models while being comparable for sparse models. Our approach could be attractive for causal model testing because it is easy to implement, can be used with non-parametric or parametric probability models, has the symmetry property, and has reasonable computational requirements.