A Bayesian Approach to Constraint Based Causal Inference

Tom Claassen, Tom Heskes
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:205-214, 2012.

Abstract

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while others are very adept at handling and representing uncertainty, but need to rely on undesirable assumptions. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of con icts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It can also indicate which causal decisions in the output have high reliability and which do not.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-claassen12a, title = {A {B}ayesian Approach to Constraint Based Causal Inference}, author = {Claassen, Tom and Heskes, Tom}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {205--214}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/claassen12a/claassen12a.pdf}, url = {https://proceedings.mlr.press/r10/claassen12a.html}, abstract = {We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while others are very adept at handling and representing uncertainty, but need to rely on undesirable assumptions. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of con icts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It can also indicate which causal decisions in the output have high reliability and which do not.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Bayesian Approach to Constraint Based Causal Inference %A Tom Claassen %A Tom Heskes %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-claassen12a %I PMLR %P 205--214 %U https://proceedings.mlr.press/r10/claassen12a.html %V R10 %X We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while others are very adept at handling and representing uncertainty, but need to rely on undesirable assumptions. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of con icts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It can also indicate which causal decisions in the output have high reliability and which do not. %Z Reissued by PMLR on 04 October 2026.
APA
Claassen, T. & Heskes, T.. (2012). A Bayesian Approach to Constraint Based Causal Inference. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:205-214 Available from https://proceedings.mlr.press/r10/claassen12a.html. Reissued by PMLR on 04 October 2026.

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