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Využití imsetů při učení bayesovských sítí
Vomlel, Jiří ; Studený, Milan
This paper describes a modification of the greedy equivalence search (GES) algorithm. The presented modification is based on the algebraic approach to learning. The states of the search space are standard imsets. Each standard imset represents an equivalence class of Bayesian networks. For a given quality criterion the database is represented by the respective data imset. This allows a very simple update of a given quality criterion since the moves between states are represented by differential imsets. We exploit a direct characterization of lower and upper inclusion neighborhood, which allows an efficient search for the best structure in the inclusion neighborhood. The algorithm was implemented in R and is freely available.
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Characterization of inclusion neighbourhood in terms of the essential graph: Lower neighbours
Studený, Milan
The topic of the paper is to characterize inclusion neighbourhood of a given equivalence class of Bayesian networks in terms of the respective essential graph. It is shown that every inclusion neighbour is uniquely described by a pair ([a,b],C) where [a,b] is a pair of distict nodes which is not an edge and C is a disjoint set of nodes. Given such [a,b] the collection of respective sets C is the union of two tufts. The least and maximal sets of these tufts can be read from the essential graph.
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