Bivariate Causal Discovery using Bayesian Model Selection

Anish Dhir, Samuel Power, Mark Van Der Wilk
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:10710-10735, 2024.

Abstract

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-dhir24a, title = {Bivariate Causal Discovery using {B}ayesian Model Selection}, author = {Dhir, Anish and Power, Samuel and Van Der Wilk, Mark}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {10710--10735}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/dhir24a/dhir24a.pdf}, url = {https://proceedings.mlr.press/v235/dhir24a.html}, abstract = {Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.} }
Endnote
%0 Conference Paper %T Bivariate Causal Discovery using Bayesian Model Selection %A Anish Dhir %A Samuel Power %A Mark Van Der Wilk %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-dhir24a %I PMLR %P 10710--10735 %U https://proceedings.mlr.press/v235/dhir24a.html %V 235 %X Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.
APA
Dhir, A., Power, S. & Van Der Wilk, M.. (2024). Bivariate Causal Discovery using Bayesian Model Selection. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:10710-10735 Available from https://proceedings.mlr.press/v235/dhir24a.html.

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