# Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation

arXiv: https://arxiv.org/abs/2209.08579 · HTML: https://mlsanity.com/paper/2209.08579/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 18 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Entropic Causal Inference: Identifiability and Finite Sample Results](https://mlsanity.com/paper/2101.03501/) (2021)
- [Causal Inference on Discrete Data via Estimating Distance Correlations](https://mlsanity.com/paper/1803.07712/) (2018)
- [Ordinal Causal Discovery](https://mlsanity.com/paper/2201.07396/) (2022)
- [Non-linear Causal Inference using Gaussianity Measures](https://mlsanity.com/paper/1409.4573/) (2014)
- [Identifiability of an Integer Modular Acyclic Additive Noise Model and its Causal Structure Discovery](https://mlsanity.com/paper/1401.5625/) (2014)

## Built on by (most cited first, 3 of 3)

- [Global Optimality in Bivariate Gradient-based DAG Learning](https://mlsanity.com/paper/2306.17378/) (2023)
- [Distinguishing Cause from Effect on Categorical Data: The Uniform Channel Model](https://mlsanity.com/paper/2303.08572/) (2023)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)

## Abstract (arXiv)

Causal discovery for quantitative data has been extensively studied but less is known for categorical data. We propose a novel causal model for categorical data based on a new classification model, termed classification with optimal label permutation (COLP). By design, COLP is a parsimonious classifier, which gives rise to a provably identifiable causal model. A simple learning algorithm via comparing likelihood functions of causal and anti-causal models suffices to learn the causal direction. Through experiments with synthetic and real data, we demonstrate the favorable performance of the proposed COLP-based causal model compared to state-of-the-art methods. We also make available an accompanying R package COLP, which contains the proposed causal discovery algorithm and a benchmark dataset of categorical cause-effect pairs.