Multi-Domain Causal Discovery in Bijective Causal Models

Kasra Jalaldoust, Saber Salehkaleybar, Negar Kiyavash
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:1268-1289, 2025.

Abstract

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, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-jalaldoust25a, title = {Multi-Domain Causal Discovery in Bijective Causal Models}, author = {Jalaldoust, Kasra and Salehkaleybar, Saber and Kiyavash, Negar}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {1268--1289}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/jalaldoust25a/jalaldoust25a.pdf}, url = {https://proceedings.mlr.press/v275/jalaldoust25a.html}, abstract = {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, 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.} }
Endnote
%0 Conference Paper %T Multi-Domain Causal Discovery in Bijective Causal Models %A Kasra Jalaldoust %A Saber Salehkaleybar %A Negar Kiyavash %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-jalaldoust25a %I PMLR %P 1268--1289 %U https://proceedings.mlr.press/v275/jalaldoust25a.html %V 275 %X 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, 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.
APA
Jalaldoust, K., Salehkaleybar, S. & Kiyavash, N.. (2025). Multi-Domain Causal Discovery in Bijective Causal Models. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:1268-1289 Available from https://proceedings.mlr.press/v275/jalaldoust25a.html.

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