Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Optimal decomposition by clique separators
Discrete Mathematics
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Computing Minimal Triangulations in Time O(n\alpha \log n) = o(n2.376)
SIAM Journal on Discrete Mathematics
Decomposition of search for v-structures in DAGs
Journal of Multivariate Analysis
A Recursive Method for Structural Learning of Directed Acyclic Graphs
The Journal of Machine Learning Research
Decomposition of structural learning about directed acyclic graphs
Artificial Intelligence
A wide-range algorithm for minimal triangulation from an arbitrary ordering
Journal of Algorithms
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Structural learning of a Bayesian network is often decomposed into problems related to its subgraphs, although many approaches without decomposition were proposed. In 2006, Xie, Geng and Zhao proposed using a d-separation tree to improve the power of conditional independence tests and the efficiency of structural learning. In our research note, we study a minimal d-separation tree under a partial ordering, by which the maximal efficiency can be obtained. Our results demonstrate that a minimal d-separation tree of a directed acyclic graph (DAG) can be constructed by searching for the clique tree of a minimal triangulation of the moral graph for the DAG.