Harmony of Gröbner Bases and the Modern Industrial Society - The Second CREST-CSBM International Conference 2012
DOI: 10.1142/9789814383462_0020
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Polyhedral Approach to Statistical Learning Graphical Models

Abstract: The aim of the talk will be to explain how the statistical task to learn so-called Bayesian network structure from data leads to the study of a special polyhedron, and to report on what was found out about that polyhedron so far.

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(2 citation statements)
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“…Because learning decomposable models with cliques of cardinality at most three is already NP-hard (cf. [30]), this can appear to be a non-trivial generalization of the greedy procedure for learning undirected forests.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Because learning decomposable models with cliques of cardinality at most three is already NP-hard (cf. [30]), this can appear to be a non-trivial generalization of the greedy procedure for learning undirected forests.…”
Section: Discussionmentioning
confidence: 99%
“…The point is that the procedure for computing the remaining components of c G from those for sets of cardinality at most three is non-linear. More specifically, for a set S ⊆ N of cardinality at least four, one has c G (S) = 1 iff at least three subsets T ⊂ S of cardinality |S| − 1 exist such that c G (T) = 1, see Lemma 4.1 [30] for details. Therefore, if we omit the "superfluous" components of c G the quality criterion Q becomes a non-linear function of the restricted characteristic imset.…”
Section: Lemma 1 Every Score Equivalent and Additively Decomposable mentioning
confidence: 99%