mlsanityData to 14 Oct 2026

Multi-Domain Causal Discovery in Bijective Causal Models

arXiv 2504.21261 ↗First posted 30 Apr 2025cs.LG cs.AI stat.MEcited by 4

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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.

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

17 of 39 references.

References · 17

  1. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 536
  2. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  3. 2019Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changescited by 166
  4. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  5. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  6. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  7. 2017Invariant Causal Prediction for Sequential Datacited by 63
  8. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  9. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 55
  10. 2019Causal Discovery and Forecasting in Nonstationary Environments with State-Space Modelscited by 45
  11. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 43
  12. 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
5 more
  1. 2016Kernel-based Tests for Joint Independencecited by 40
  2. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  3. 2017Learning Causal Structures Using Regression Invariancecited by 32
  4. 2019Deep Smoothing of the Implied Volatility Surfacecited by 19
  5. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Causal Discovery via Quantile Partial Effectcited by 4
  2. 2025MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventionscited by 1
  3. 2025On the Identifiability of Causal Graphs with the Invariance Principlecited by 0
  4. 2026Causal Learning with the Invariance Principlecited by 0