Causal Reasoning with Ancestral Graphical Models

Research output: Journal PublicationsJournal Article (refereed)

41 Citations (Scopus)

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).
Original languageEnglish
Pages (from-to)1437-1474
Number of pages38
JournalJournal of Machine Learning Research
Volume9
Publication statusPublished - 1 Jan 2008
Externally publishedYes

Fingerprint

Equivalence classes
Graphical Models
Reasoning
Bayesian networks
Invariance
Random variables
Probability distributions
Diagram
Data mining
Equivalence class
Calculus
Directed Acyclic Graph
Graph in graph theory
Bayesian Networks
Data Mining
Probability Distribution
Random variable
Partial
Output

Cite this

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title = "Causal Reasoning with Ancestral Graphical Models",
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Causal Reasoning with Ancestral Graphical Models. / ZHANG, Jiji.

In: Journal of Machine Learning Research, Vol. 9, 01.01.2008, p. 1437-1474.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - Causal Reasoning with Ancestral Graphical Models

AU - ZHANG, Jiji

PY - 2008/1/1

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N2 - 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).

AB - 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).

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JO - Journal of Machine Learning Research

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