# Distinguishing Cause from Effect on Categorical Data: The Uniform Channel Model

arXiv: https://arxiv.org/abs/2303.08572 · HTML: https://mlsanity.com/paper/2303.08572/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Learning Bayesian Networks: A Unification for Discrete and Gaussian Domains](https://mlsanity.com/paper/1302.4957/) (2013)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Multireference Alignment using Semidefinite Programming](https://mlsanity.com/paper/1308.5256/) (2013)
- [Causal Inference on Discrete Data via Estimating Distance Correlations](https://mlsanity.com/paper/1803.07712/) (2018)
- [Causal Inference by Stochastic Complexity](https://mlsanity.com/paper/1702.06776/) (2017)
- [Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation](https://mlsanity.com/paper/2209.08579/) (2022)

## Built on by (most cited first, 1 of 1)

- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)

## Abstract (arXiv)

Distinguishing cause from effect using observations of a pair of random variables is a core problem in causal discovery. Most approaches proposed for this task, namely additive noise models (ANM), are only adequate for quantitative data. We propose a criterion to address the cause-effect problem with categorical variables (living in sets with no meaningful order), inspired by seeing a conditional probability mass function (pmf) as a discrete memoryless channel. We select as the most likely causal direction the one in which the conditional pmf is closer to a uniform channel (UC). The rationale is that, in a UC, as in an ANM, the conditional entropy (of the effect given the cause) is independent of the cause distribution, in agreement with the principle of independence of cause and mechanism. Our approach, which we call the uniform channel model (UCM), thus extends the ANM rationale to categorical variables. To assess how close a conditional pmf (estimated from data) is to a UC, we use statistical testing, supported by a closed-form estimate of a UC channel. On the theoretical front, we prove identifiability of the UCM and show its equivalence with a structural causal model with a low-cardinality exogenous variable. Finally, the proposed method compares favorably with recent state-of-the-art alternatives in experiments on synthetic, benchmark, and real data.