Bayesian Discovery of Linear Acyclic Causal Models

Patrik Hoyer, Antti Hyttinen
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:240-248, 2009.

Abstract

Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accuracy is as good as or better than existing methods. We provide a complete code package (in R) which implements all algorithms and performs all of the analysis provided in the paper, and hope that this will further the application of these methods to solving causal inference problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-hoyer09a, title = {{B}ayesian Discovery of Linear Acyclic Causal Models}, author = {Hoyer, Patrik and Hyttinen, Antti}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {240--248}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/hoyer09a/hoyer09a.pdf}, url = {https://proceedings.mlr.press/r7/hoyer09a.html}, abstract = {Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accuracy is as good as or better than existing methods. We provide a complete code package (in R) which implements all algorithms and performs all of the analysis provided in the paper, and hope that this will further the application of these methods to solving causal inference problems.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Bayesian Discovery of Linear Acyclic Causal Models %A Patrik Hoyer %A Antti Hyttinen %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-hoyer09a %I PMLR %P 240--248 %U https://proceedings.mlr.press/r7/hoyer09a.html %V R7 %X Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accuracy is as good as or better than existing methods. We provide a complete code package (in R) which implements all algorithms and performs all of the analysis provided in the paper, and hope that this will further the application of these methods to solving causal inference problems. %Z Reissued by PMLR on 04 October 2026.
APA
Hoyer, P. & Hyttinen, A.. (2009). Bayesian Discovery of Linear Acyclic Causal Models. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:240-248 Available from https://proceedings.mlr.press/r7/hoyer09a.html. Reissued by PMLR on 04 October 2026.

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