Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Conditional independence structures examined via minors
Annals of Mathematics and Artificial Intelligence
Causal networks: semantics and expressiveness
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
A transformational characterization of equivalent Bayesian network structures
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
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The inclusion problem deals with how to characterize (in graphical terms) whether all independence statements in the model induced by a DAG K are in the model induced by a second DAG L. Meek (1997) conjectured that this inclusion holds iff there exists a sequence of DAGs from L to K such that only certain 'legal' arrow reversal and 'legal' arrow adding operations are performed to get the next DAG in the sequence. In this paper we give several characterizations of inclusion of DAG models and verify Meek's conjecture in the case that the DAGs K and L differ in at most one adjacency. As a warming up a rigorous proof of graphical characterizations of equivalence of DAGs is given.