Generalized Do-Calculus with Testable Causal Assumptions

Jiji Zhang
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:667-674, 2007.

Abstract

A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus (Pearl 1995) gives a set of rules that govern the identification of such post-intervention probabilities in terms of (estimable) pre-intervention probabilities, assuming available a directed acyclic graph (DAG) that represents the underlying causal structure. However, a DAG causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph (PAG) that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-zhang07a, title = {Generalized Do-Calculus with Testable Causal Assumptions}, author = {Zhang, Jiji}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {667--674}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/zhang07a/zhang07a.pdf}, url = {https://proceedings.mlr.press/v2/zhang07a.html}, abstract = {A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus (Pearl 1995) gives a set of rules that govern the identification of such post-intervention probabilities in terms of (estimable) pre-intervention probabilities, assuming available a directed acyclic graph (DAG) that represents the underlying causal structure. However, a DAG causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph (PAG) that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations.} }
Endnote
%0 Conference Paper %T Generalized Do-Calculus with Testable Causal Assumptions %A Jiji Zhang %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-zhang07a %I PMLR %P 667--674 %U https://proceedings.mlr.press/v2/zhang07a.html %V 2 %X A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus (Pearl 1995) gives a set of rules that govern the identification of such post-intervention probabilities in terms of (estimable) pre-intervention probabilities, assuming available a directed acyclic graph (DAG) that represents the underlying causal structure. However, a DAG causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph (PAG) that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations.
RIS
TY - CPAPER TI - Generalized Do-Calculus with Testable Causal Assumptions AU - Jiji Zhang BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-zhang07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 667 EP - 674 L1 - http://proceedings.mlr.press/v2/zhang07a/zhang07a.pdf UR - https://proceedings.mlr.press/v2/zhang07a.html AB - A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus (Pearl 1995) gives a set of rules that govern the identification of such post-intervention probabilities in terms of (estimable) pre-intervention probabilities, assuming available a directed acyclic graph (DAG) that represents the underlying causal structure. However, a DAG causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph (PAG) that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations. ER -
APA
Zhang, J.. (2007). Generalized Do-Calculus with Testable Causal Assumptions. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:667-674 Available from https://proceedings.mlr.press/v2/zhang07a.html.

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