# Ordinal Causal Discovery

arXiv: https://arxiv.org/abs/2201.07396 · HTML: https://mlsanity.com/paper/2201.07396/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [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)
- [Non-linear Causal Inference using Gaussianity Measures](https://mlsanity.com/paper/1409.4573/) (2014)
- [Learning Bayesian Networks from Ordinal Data](https://mlsanity.com/paper/2010.15808/) (2020)
- [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, 6 of 6)

- [Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation](https://mlsanity.com/paper/2209.08579/) (2022)
- [CDFM: Towards a General-Purpose Causal Discovery Foundation Model](https://mlsanity.com/paper/2607.11508/) (2026)
- [Ordering-based Causal Discovery via Generalized Score Matching](https://mlsanity.com/paper/2601.16249/) (2026)
- [On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models](https://mlsanity.com/paper/2609.17942/) (2026)
- [Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms](https://mlsanity.com/paper/2609.20676/) (2026)
- [DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables](https://mlsanity.com/paper/2610.06086/) (2026)

## Abstract (arXiv)

Causal discovery for purely observational, categorical data is a long-standing challenging problem. Unlike continuous data, the vast majority of existing methods for categorical data focus on inferring the Markov equivalence class only, which leaves the direction of some causal relationships undetermined. This paper proposes an identifiable ordinal causal discovery method that exploits the ordinal information contained in many real-world applications to uniquely identify the causal structure. The proposed method is applicable beyond ordinal data via data discretization. Through real-world and synthetic experiments, we demonstrate that the proposed ordinal causal discovery method combined with simple score-and-search algorithms has favorable and robust performance compared to state-of-the-art alternative methods in both ordinal categorical and non-categorical data. An accompanied R package OrdCD is freely available on CRAN and at https://web.stat.tamu.edu/~yni/files/OrdCD_1.0.0.tar.gz.