Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Optimal structure identification with greedy search
The Journal of Machine Learning Research
A Linear Non-Gaussian Acyclic Model for Causal Discovery
The Journal of Machine Learning Research
A transformational characterization of equivalent Bayesian network structures
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Causal inference and causal explanation with background knowledge
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Strong completeness and faithfulness in Bayesian networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Introduction to Causal Inference
The Journal of Machine Learning Research
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
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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).