Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Formal Properties of Conditional Independence in Different Calculi of AI
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Causal networks: semantics and expressiveness
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Complete Identification Methods for the Causal Hierarchy
The Journal of Machine Learning Research
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Decision-theoretic foundations for causal reasoning
Journal of Artificial Intelligence Research
Identifiability of path-specific effects
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning
The Journal of Machine Learning Research
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
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We study the connections between causal relations and conditional independence within the settable systems extension of the Pearl causal model (PCM). Our analysis clearly distinguishes between causal notions and probabilistic notions, and it does not formally rely on graphical representations. As a foundation, we provide definitions in terms of suitable functional dependence for direct causality and for indirect and total causality via and exclusive of a set of variables. Based on these foundations, we provide causal and stochastic conditions formally characterizing conditional dependence among random vectors of interest in structural systems by stating and proving the conditional Reichenbach principle of common cause, obtaining the classical Reichenbach principle as a corollary. We apply the conditional Reichenbach principle to show that the useful tools of d-separation and D-separation can be employed to establish conditional independence within suitably restricted settable systems analogous to Markovian PCMs.