# Causal Graph Learning via Distributional Invariance of Cause-Effect Relationship

arXiv: https://arxiv.org/abs/2602.03353 · HTML: https://mlsanity.com/paper/2602.03353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences](https://mlsanity.com/paper/1407.8088/) (2014)

## Abstract (arXiv)

This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of those causes. This insight enables a direct test for potential causal relationships by checking the variance of their corresponding effect-cause conditional distributions across multiple downsampled subsets of the data. These subsets are selected to reflect different prior cause distributions, while preserving the effect-cause conditional relationships. Using this invariance test and exploiting an (empirical) sparsity of most causal graphs, we develop an algorithm that efficiently uncovers causal relationships with quadratic complexity in the number of observational variables, reducing the processing time by up to 25x compared to state-of-the-art methods. Our empirical experiments on a varied benchmark of large-scale datasets show superior or equivalent performance compared to existing works, while achieving enhanced scalability.