Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
An algorithm for deciding if a set of observed independencies has a causal explanation
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Expert Systems and Probabiistic Network Models
Expert Systems and Probabiistic Network Models
Constructing the Dependency Structure of a Multiagent Probabilistic Network
IEEE Transactions on Knowledge and Data Engineering
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Construction of a Non-redundant Cover for Conditional Independencies
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
Graphs and Hypergraphs
A transformational characterization of equivalent Bayesian network structures
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Construction of a Non-redundant Cover for Conditional Independencies
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
A partial correlation-based algorithm for causal structure discovery with continuous variables
IDA'07 Proceedings of the 7th international conference on Intelligent data analysis
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Graphical models have been extensively used in probabilistic reasoning for representing conditionali ndependency (CI) information. Among them two of the well known models are undirected graphs (UGs), and directed acyclic graphs (DAGs). Given a set of CIs, it woul d be desirable to know whether this set can be perfectly represented by a UG or DAG. A necessary and sufficient condition using axioms has been found for a set of CIs that can be perfectly represented by a UG; while negative result has been shown for DAGs, i.e., there does not exist a finite set of axioms which can characterize a set of CIs having a perfect DAG. However, this does not exclude other possible ways for such a characterization. In this paper, by studying the relationship between CIs and factorizations of a joint probability distribution, we show that there does exist such a characterization for DAGs in terms of the structure of the given set of CIs. More precisely, we demonstrate that if the given set of CIs satisfies certain constraints, then it has a perfect DAG representation.