# Learning Causal Structures Using Regression Invariance

arXiv: https://arxiv.org/abs/1705.09644 · HTML: https://mlsanity.com/paper/1705.09644/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2017.

## Built on by (most cited first, 30 of 32)

- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Optimization-based Causal Estimation from Heterogenous Environments](https://mlsanity.com/paper/2109.11990/) (2021)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Incorporating Causal Graphical Prior Knowledge into Predictive Modeling via Simple Data Augmentation](https://mlsanity.com/paper/2103.00136/) (2021)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis](https://mlsanity.com/paper/2311.18048/) (2023)
- [Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data](https://mlsanity.com/paper/2312.06091/) (2023)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [Counterfactual Maximum Likelihood Estimation for Training Deep Networks](https://mlsanity.com/paper/2106.03831/) (2021)
- [Variance Minimization in the Wasserstein Space for Invariant Causal Prediction](https://mlsanity.com/paper/2110.07064/) (2021)
- [Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting](https://mlsanity.com/paper/2303.03187/) (2023)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Selecting Treatment Effects Models for Domain Adaptation Using Causal Knowledge](https://mlsanity.com/paper/2102.06271/) (2021)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Multi-Domain Causal Discovery in Bijective Causal Models](https://mlsanity.com/paper/2504.21261/) (2025)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)
- [The Implicit Bias of Heterogeneity towards Invariance: A Study of Multi-Environment Matrix Sensing](https://mlsanity.com/paper/2403.01420/) (2024)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [Characterization and Learning of Causal Graphs from Hard Interventions](https://mlsanity.com/paper/2505.01037/) (2025)
- [Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments](https://mlsanity.com/paper/2506.11756/) (2025)
- [Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data](https://mlsanity.com/paper/2509.25800/) (2025)
- [A step towards the applicability of algorithms based on invariant causal learning on observational data](https://mlsanity.com/paper/2304.02286/) (2023)
- [A Subsampling-Based Method for Causal Discovery on Discrete Data](https://mlsanity.com/paper/2108.13984/) (2021)
- [Learning Linear Gaussian Polytree Models with Interventions](https://mlsanity.com/paper/2311.04636/) (2023)

## Abstract (arXiv)

We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We introduce the idea of using the invariance of the functional relations of the variables to their causes across a set of environments. We define a notion of completeness for a causal inference algorithm in this setting and prove the existence of such algorithm by proposing the baseline algorithm. Additionally, we present an alternate algorithm that has significantly improved computational and sample complexity compared to the baseline algorithm. The experiment results show that the proposed algorithm outperforms the other existing algorithms.