Title

Causal Reasoning with Ancestral Graphical Models

Document Type

Journal article

Source Publication

Journal of Machine Learning Research

Publication Date

2008

Volume

9

First Page

1437

Last Page

1474

Abstract

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)'s celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993).

Print ISSN

15324435

E-ISSN

15337928

Publisher Statement

Copyright © JMLR 2008. All rights reserved.

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Recommended Citation

Zhang, J. (2008). Causal Reasoning with Ancestral Graphical Models. Journal of Machine Learning Research, 9, 1437-1474. Retrieved from http://www.jmlr.org/papers/volume9/zhang08a/zhang08a.pdf