### Abstract

Original language | English |
---|---|

Pages (from-to) | 1437-1474 |

Number of pages | 38 |

Journal | Journal of Machine Learning Research |

Volume | 9 |

Publication status | Published - 1 Jan 2008 |

Externally published | Yes |

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*Journal of Machine Learning Research*,

*9*, 1437-1474.

}

*Journal of Machine Learning Research*, vol. 9, pp. 1437-1474.

**Causal Reasoning with Ancestral Graphical Models.** / ZHANG, Jiji.

Research output: Journal Publications › Journal Article (refereed)

TY - JOUR

T1 - Causal Reasoning with Ancestral Graphical Models

AU - ZHANG, Jiji

PY - 2008/1/1

Y1 - 2008/1/1

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).

UR - http://www.jmlr.org/papers/volume9/zhang08a/zhang08a.pdf

UR - http://commons.ln.edu.hk/sw_master/4152

M3 - Journal Article (refereed)

VL - 9

SP - 1437

EP - 1474

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1532-4435

ER -