Bayesian Causal Discovery Networks for Linear Mixed Data

Moabi Mokhoro, Ioan Gabriel Bucur, Tom Heskes, Jildau Bouwman, Tom Claassen
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:1526-1544, 2026.

Abstract

Causal discovery from observational data is challenging due to limited sample sizes and noise, motivating probabilistic approaches that represent uncertainty over causal structures and parameters. Bayesian Causal Discovery Networks (BCD Nets) and related methods approximate posterior distributions over graphs, but existing approaches primarily focus on continuous data, with limited support for mixed discrete–continuous settings common in healthcare and economics. In this work, we extend BCD Nets to handle linear mixed data. Our approach incorporates an appropriate likelihood function for mixed data into the BCD Nets framework, enabling it to jointly model discrete and continuous variables. Experiments on synthetic and real-world datasets show that our method significantly outperforms a state-of-the-art causal discovery model for mixed data in both structural and causal effects accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-mokhoro26a, title = {Bayesian Causal Discovery Networks for Linear Mixed Data}, author = {Mokhoro, Moabi and Bucur, Ioan Gabriel and Heskes, Tom and Bouwman, Jildau and Claassen, Tom}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {1526--1544}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/mokhoro26a/mokhoro26a.pdf}, url = {https://proceedings.mlr.press/v323/mokhoro26a.html}, abstract = {Causal discovery from observational data is challenging due to limited sample sizes and noise, motivating probabilistic approaches that represent uncertainty over causal structures and parameters. Bayesian Causal Discovery Networks (BCD Nets) and related methods approximate posterior distributions over graphs, but existing approaches primarily focus on continuous data, with limited support for mixed discrete–continuous settings common in healthcare and economics. In this work, we extend BCD Nets to handle linear mixed data. Our approach incorporates an appropriate likelihood function for mixed data into the BCD Nets framework, enabling it to jointly model discrete and continuous variables. Experiments on synthetic and real-world datasets show that our method significantly outperforms a state-of-the-art causal discovery model for mixed data in both structural and causal effects accuracy.} }
Endnote
%0 Conference Paper %T Bayesian Causal Discovery Networks for Linear Mixed Data %A Moabi Mokhoro %A Ioan Gabriel Bucur %A Tom Heskes %A Jildau Bouwman %A Tom Claassen %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-mokhoro26a %I PMLR %P 1526--1544 %U https://proceedings.mlr.press/v323/mokhoro26a.html %V 323 %X Causal discovery from observational data is challenging due to limited sample sizes and noise, motivating probabilistic approaches that represent uncertainty over causal structures and parameters. Bayesian Causal Discovery Networks (BCD Nets) and related methods approximate posterior distributions over graphs, but existing approaches primarily focus on continuous data, with limited support for mixed discrete–continuous settings common in healthcare and economics. In this work, we extend BCD Nets to handle linear mixed data. Our approach incorporates an appropriate likelihood function for mixed data into the BCD Nets framework, enabling it to jointly model discrete and continuous variables. Experiments on synthetic and real-world datasets show that our method significantly outperforms a state-of-the-art causal discovery model for mixed data in both structural and causal effects accuracy.
APA
Mokhoro, M., Bucur, I.G., Heskes, T., Bouwman, J. & Claassen, T.. (2026). Bayesian Causal Discovery Networks for Linear Mixed Data. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:1526-1544 Available from https://proceedings.mlr.press/v323/mokhoro26a.html.

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