# Differentiable Invariant Causal Discovery

arXiv: https://arxiv.org/abs/2205.15638 · HTML: https://mlsanity.com/paper/2205.15638/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 54 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 27 of 27)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [RUBi: Reducing Unimodal Biases in Visual Question Answering](https://mlsanity.com/paper/1906.10169/) (2019)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Integer Programming for Learning Directed Acyclic Graphs from Continuous Data](https://mlsanity.com/paper/1904.10574/) (2019)
- [Advances in Learning Bayesian Networks of Bounded Treewidth](https://mlsanity.com/paper/1406.1411/) (2014)
- [Learning DAGs without imposing acyclicity](https://mlsanity.com/paper/2006.03005/) (2020)

## Built on by (most cited first, 3 of 3)

- [Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting](https://mlsanity.com/paper/2303.03187/) (2023)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Distributed Dynamic Invariant Causal Prediction in Environmental Time Series](https://mlsanity.com/paper/2603.02902/) (2026)

## Abstract (arXiv)

Learning causal structure from observational data is a fundamental challenge in machine learning. However, the majority of commonly used differentiable causal discovery methods are non-identifiable, turning this problem into a continuous optimization task prone to data biases. In many real-life situations, data is collected from different environments, in which the functional relations remain consistent across environments, while the distribution of additive noises may vary. This paper proposes Differentiable Invariant Causal Discovery (DICD), utilizing the multi-environment information based on a differentiable framework to avoid learning spurious edges and wrong causal directions. Specifically, DICD aims to discover the environment-invariant causation while removing the environment-dependent correlation. We further formulate the constraint that enforces the target structure equation model to maintain optimal across the environments. Theoretical guarantees for the identifiability of proposed DICD are provided under mild conditions with enough environments. Extensive experiments on synthetic and real-world datasets verify that DICD outperforms state-of-the-art causal discovery methods up to 36% in SHD. Our code will be open-sourced.