# Entropic Causal Inference: Identifiability and Finite Sample Results

arXiv: https://arxiv.org/abs/2101.03501 · HTML: https://mlsanity.com/paper/2101.03501/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 10 Jan 2021.

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

- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [A causal framework for explaining the predictions of black-box sequence-to-sequence models](https://mlsanity.com/paper/1707.01943/) (2017)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Consistency of Causal Inference under the Additive Noise Model](https://mlsanity.com/paper/1312.5770/) (2013)
- [Interaction Information for Causal Inference: The Case of Directed Triangle](https://mlsanity.com/paper/1701.08868/) (2017)
- [Justifying Information-Geometric Causal Inference](https://mlsanity.com/paper/1402.2499/) (2014)
- [How to Find a Joint Probability Distribution of Minimum Entropy (almost) given the Marginals](https://mlsanity.com/paper/1701.05243/) (2017)
- [Entropic Causality and Greedy Minimum Entropy Coupling](https://mlsanity.com/paper/1701.08254/) (2017)

## Built on by (most cited first, 12 of 12)

- [Optimal transport for causal discovery](https://mlsanity.com/paper/2201.09366/) (2022)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Ordinal Causal Discovery](https://mlsanity.com/paper/2201.07396/) (2022)
- [Minimum Entropy Coupling with Bottleneck](https://mlsanity.com/paper/2410.21666/) (2024)
- [On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models](https://mlsanity.com/paper/2205.04641/) (2022)
- [Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation](https://mlsanity.com/paper/2209.08579/) (2022)
- [Approximate Causal Effect Identification under Weak Confounding](https://mlsanity.com/paper/2306.13242/) (2023)
- [Entropic Causal Inference: Graph Identifiability](https://mlsanity.com/paper/2509.16463/) (2025)
- [Ordering-based Causal Discovery via Generalized Score Matching](https://mlsanity.com/paper/2601.16249/) (2026)
- [Active learning of causal probability trees](https://mlsanity.com/paper/2205.08178/) (2022)
- [Probability trees and the value of a single intervention](https://mlsanity.com/paper/2205.08779/) (2022)
- [PAC-Causal Learnability: From Identification to Finite-Sample Guarantees](https://mlsanity.com/paper/2507.18903/) (2025)

## Abstract (arXiv)

Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture. Namely, we show that for almost all causal models where the exogenous variable has entropy that does not scale with the number of states of the observed variables, the causal direction is identifiable from observational data. We also consider the minimum entropy coupling-based algorithmic approach presented by Kocaoglu et al., and for the first time demonstrate algorithmic identifiability guarantees using a finite number of samples. We conduct extensive experiments to evaluate the robustness of the method to relaxing some of the assumptions in our theory and demonstrate that both the constant-entropy exogenous variable and the no latent confounder assumptions can be relaxed in practice. We also empirically characterize the number of observational samples needed for causal identification. Finally, we apply the algorithm on Tuebingen cause-effect pairs dataset.