# Multi-Domain Causal Discovery in Bijective Causal Models

arXiv: https://arxiv.org/abs/2504.21261 · HTML: https://mlsanity.com/paper/2504.21261/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [Deep Smoothing of the Implied Volatility Surface](https://mlsanity.com/paper/1906.05065/) (2019)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)

## Built on by (most cited first, 4 of 4)

- [Causal Discovery via Quantile Partial Effect](https://mlsanity.com/paper/2509.12981/) (2025)
- [MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions](https://mlsanity.com/paper/2510.22298/) (2025)
- [On the Identifiability of Causal Graphs with the Invariance Principle](https://mlsanity.com/paper/2510.13583/) (2025)
- [Causal Learning with the Invariance Principle](https://mlsanity.com/paper/2605.13589/) (2026)

## Abstract (arXiv)

We consider the problem of causal discovery (a.k.a., causal structure learning) in a multi-domain setting. We assume that the causal functions are invariant across the domains, while the distribution of the exogenous noise may vary. Under causal sufficiency (i.e., no confounders exist), we show that the causal diagram can be discovered under less restrictive functional assumptions compared to previous work. What enables causal discovery in this setting is bijective generation mechanisms (BGM), which ensures that the functional relation between the exogenous noise E and the endogenous variable Y is bijective and differentiable in both directions at every level of the cause variable X = x. BGM generalizes a variety of models including additive noise model, LiNGAM, post-nonlinear model, and location-scale noise model. Further, we derive a statistical test to find the parents set of the target variable. Experiments on various synthetic and real-world datasets validate our theoretical findings.