# Entropic Causal Inference: Graph Identifiability

arXiv: https://arxiv.org/abs/2509.16463 · HTML: https://mlsanity.com/paper/2509.16463/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Causal Interpretability for Machine Learning -- Problems, Methods and Evaluation](https://mlsanity.com/paper/2003.03934/) (2020)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Domain Adaptation as a Problem of Inference on Graphical Models](https://mlsanity.com/paper/2002.03278/) (2020)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Causal Imputation via Synthetic Interventions](https://mlsanity.com/paper/2011.03127/) (2020)
- [Entropic Causal Inference: Identifiability and Finite Sample Results](https://mlsanity.com/paper/2101.03501/) (2021)
- [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, 3 of 3)

- [Ordering-based Causal Discovery via Generalized Score Matching](https://mlsanity.com/paper/2601.16249/) (2026)
- [FinInvest-GTCN: Explainable Graph-Temporal-Causal Modeling for Risk-Aware Investment Decision Optimization](https://mlsanity.com/paper/2606.28933/) (2026)
- [GARLIC: Graph Attention-based Relational Learning of Multivariate Time Series in Intensive Care](https://mlsanity.com/paper/2608.10969/) (2026)

## Abstract (arXiv)

Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest entropy. In our work, we first extend the causal graph identifiability result in the two-variable setting under relaxed assumptions. We then show the first identifiability result using the entropic approach for learning causal graphs with more than two nodes. Our approach utilizes the property that ancestrality between a source node and its descendants can be determined using the bivariate entropic tests. We provide a sound sequential peeling algorithm for general graphs that relies on this property. We also propose a heuristic algorithm for small graphs that shows strong empirical performance. We rigorously evaluate the performance of our algorithms on synthetic data generated from a variety of models, observing improvement over prior work. Finally we test our algorithms on real-world datasets.