Causal Reasoning with Ancestral Graphical Models

Jiji Zhang

    Research output: Contribution to journalJournal articlepeer-review

    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)1473-1474
    Number of pages38
    JournalJournal of Machine Learning Research
    Volume9
    Publication statusPublished - Jan 2008

    Fingerprint

    Dive into the research topics of 'Causal Reasoning with Ancestral Graphical Models'. Together they form a unique fingerprint.

    Cite this