Bayesian Hierarchical Invariant Prediction

Francisco Madaleno, Pernille Julie Viuff Sand, Francisco C. Pereira, Sergio Hernan Garrido Mejia
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:324-352, 2026.

Abstract

We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. We evaluate BHIP on both synthetic and real-world datasets, demonstrating its potential as an alternative inference method to ICP and related methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-madaleno26a, title = {Bayesian Hierarchical Invariant Prediction}, author = {Madaleno, Francisco and Sand, Pernille Julie Viuff and Pereira, Francisco C. and Mejia, Sergio Hernan Garrido}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {324--352}, 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/madaleno26a/madaleno26a.pdf}, url = {https://proceedings.mlr.press/v323/madaleno26a.html}, abstract = {We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. We evaluate BHIP on both synthetic and real-world datasets, demonstrating its potential as an alternative inference method to ICP and related methods.} }
Endnote
%0 Conference Paper %T Bayesian Hierarchical Invariant Prediction %A Francisco Madaleno %A Pernille Julie Viuff Sand %A Francisco C. Pereira %A Sergio Hernan Garrido Mejia %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-madaleno26a %I PMLR %P 324--352 %U https://proceedings.mlr.press/v323/madaleno26a.html %V 323 %X We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. We evaluate BHIP on both synthetic and real-world datasets, demonstrating its potential as an alternative inference method to ICP and related methods.
APA
Madaleno, F., Sand, P.J.V., Pereira, F.C. & Mejia, S.H.G.. (2026). Bayesian Hierarchical Invariant Prediction. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:324-352 Available from https://proceedings.mlr.press/v323/madaleno26a.html.

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