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

arXiv: https://arxiv.org/abs/2206.04356 · HTML: https://mlsanity.com/paper/2206.04356/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Testing Conditional Independence in Supervised Learning Algorithms](https://mlsanity.com/paper/1901.09917/) (2019)
- [Nonparametric independence testing via mutual information](https://mlsanity.com/paper/1711.06642/) (2017)
- [Testing Conditional Independence on Discrete Data using Stochastic Complexity](https://mlsanity.com/paper/1903.04829/) (2019)
- [Goodness of fit tests for high-dimensional linear models](https://mlsanity.com/paper/1511.03334/) (2015)
- [Symmetric Rank Covariances: a Generalised Framework for Nonparametric Measures of Dependence](https://mlsanity.com/paper/1708.05653/) (2017)
- [Measures of dependence between random vectors and tests of independence. Literature review](https://mlsanity.com/paper/1307.7383/) (2013)

## Built on by (most cited first, 4 of 4)

- [pgmpy: A Python Toolkit for Bayesian Networks](https://mlsanity.com/paper/2304.08639/) (2023)
- [How Well Does Your Tabular Generator Learn the Structure of Tabular Data?](https://mlsanity.com/paper/2503.09453/) (2025)
- [DMCD: Semantic-Statistical Framework for Causal Discovery](https://mlsanity.com/paper/2602.20333/) (2026)
- [From Unsupervised Subgroups to Hypothetical State-Intervention Policies: An Evaluation of Selected Subgrouping Methods in Observational Health Data](https://mlsanity.com/paper/2607.26521/) (2026)

## Abstract (arXiv)

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.