Characteristic imset: A simple algebraic representative of a Bayesian network structure

Milan Studený, Raymond Hemmecke, Silvia Lindner

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

14 Zitate (Scopus)

Abstract

First, we recall the basic idea of an algebraic and geometric approach to learning a Bayesian network (BN) structure proposed in (Studený, Vomlel and Hemmecke, 2010): to represent every BN structure by a certain uniquely determined vector. The original proposal was to use a so-called standard imset which is a vector having integers as components, as an algebraic representative of a BN structure. In this paper we propose an even simpler algebraic representative called the characteristic imset. It is 0-1-vector obtained from the standard imset by an affine transformation. This implies that every reasonable quality criterion is an affine function of the characteristic imset. The characteristic imset is much closer to the graphical description: we establish a simple relation to any chain graph without flags that defines the BN structure. In particular, we are interested in the relation to the essential graph, which is a classic graphical BN structure representative. In the end, we discuss two special cases in which the use of characteristic imsets particularly simplifies things: learning decomposable models and (undirected) forests.

OriginalspracheEnglisch
TitelProceedings of the 5th European Workshop on Probabilistic Graphical Models, PGM 2010
Seiten257-264
Seitenumfang8
PublikationsstatusVeröffentlicht - 2010
Veranstaltung5th European Workshop on Probabilistic Graphical Models, PGM 2010 - Helsinki, Finnland
Dauer: 13 Sept. 201015 Sept. 2010

Publikationsreihe

NameProceedings of the 5th European Workshop on Probabilistic Graphical Models, PGM 2010

Konferenz

Konferenz5th European Workshop on Probabilistic Graphical Models, PGM 2010
Land/GebietFinnland
OrtHelsinki
Zeitraum13/09/1015/09/10

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