Factorizing Probabilistic Graphical Models Using Co-occurrence Rate

Zhemin Zhu

Research output: Book/ReportReportOther research output

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Abstract

Factorization is of fundamental importance in the area of Probabilistic Graphical Models (PGMs). In this paper, we theoretically develop a novel mathematical concept, \textbf{C}o-occurrence \textbf{R}ate (CR), for factorizing PGMs. CR has three obvious advantages: (1) CR provides a unified mathematical foundation for factorizing different types of PGMs. We show that Bayesian Network Factorization (BN-F), Conditional Random Field Factorization (CRF-F), Markov Random Field Factorization (MRF-F) and Refined Markov Random Field Factorization (RMRF-F) are all special cases of CR Factorization (CR-F); (2) CR has simple probability definition and clear intuitive interpretation. CR-F tells not only the scopes of the factors, but also the exact probability functions of these factors; (3) CR connects probability factorization and graph operations perfectly. The factorization process of CR-F can be visualized as applying a sequence of graph operations including partition, merge, duplicate and condition to a PGM graph. We further obtain an important result: by CR-F, on TCG graphs the scopes of factors can be exactly over maximal cliques without any default configuration. This improves the results of (R)MRF-F which need default configurations, and also indicates that (R)MRF-F, as special cases of CR-F, can not always achieve the optimal results of CR-F.
Original languageUndefined
Place of PublicationEnschede
PublisherCentre for Telematics and Information Technology (CTIT)
Number of pages9
Publication statusPublished - 1 May 2011

Publication series

NameCTIT technical report series
PublisherCentre for Telematics and Information Technology, University of Twente
No.TR-CTIT-12-30
ISSN (Print)1381-3625

Keywords

  • EWI-22603
  • IR-84372

Cite this

Zhu, Z. (2011). Factorizing Probabilistic Graphical Models Using Co-occurrence Rate. (CTIT technical report series; No. TR-CTIT-12-30). Enschede: Centre for Telematics and Information Technology (CTIT).
Zhu, Zhemin. / Factorizing Probabilistic Graphical Models Using Co-occurrence Rate. Enschede : Centre for Telematics and Information Technology (CTIT), 2011. 9 p. (CTIT technical report series; TR-CTIT-12-30).
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abstract = "Factorization is of fundamental importance in the area of Probabilistic Graphical Models (PGMs). In this paper, we theoretically develop a novel mathematical concept, \textbf{C}o-occurrence \textbf{R}ate (CR), for factorizing PGMs. CR has three obvious advantages: (1) CR provides a unified mathematical foundation for factorizing different types of PGMs. We show that Bayesian Network Factorization (BN-F), Conditional Random Field Factorization (CRF-F), Markov Random Field Factorization (MRF-F) and Refined Markov Random Field Factorization (RMRF-F) are all special cases of CR Factorization (CR-F); (2) CR has simple probability definition and clear intuitive interpretation. CR-F tells not only the scopes of the factors, but also the exact probability functions of these factors; (3) CR connects probability factorization and graph operations perfectly. The factorization process of CR-F can be visualized as applying a sequence of graph operations including partition, merge, duplicate and condition to a PGM graph. We further obtain an important result: by CR-F, on TCG graphs the scopes of factors can be exactly over maximal cliques without any default configuration. This improves the results of (R)MRF-F which need default configurations, and also indicates that (R)MRF-F, as special cases of CR-F, can not always achieve the optimal results of CR-F.",
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Zhu, Z 2011, Factorizing Probabilistic Graphical Models Using Co-occurrence Rate. CTIT technical report series, no. TR-CTIT-12-30, Centre for Telematics and Information Technology (CTIT), Enschede.

Factorizing Probabilistic Graphical Models Using Co-occurrence Rate. / Zhu, Zhemin.

Enschede : Centre for Telematics and Information Technology (CTIT), 2011. 9 p. (CTIT technical report series; No. TR-CTIT-12-30).

Research output: Book/ReportReportOther research output

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N2 - Factorization is of fundamental importance in the area of Probabilistic Graphical Models (PGMs). In this paper, we theoretically develop a novel mathematical concept, \textbf{C}o-occurrence \textbf{R}ate (CR), for factorizing PGMs. CR has three obvious advantages: (1) CR provides a unified mathematical foundation for factorizing different types of PGMs. We show that Bayesian Network Factorization (BN-F), Conditional Random Field Factorization (CRF-F), Markov Random Field Factorization (MRF-F) and Refined Markov Random Field Factorization (RMRF-F) are all special cases of CR Factorization (CR-F); (2) CR has simple probability definition and clear intuitive interpretation. CR-F tells not only the scopes of the factors, but also the exact probability functions of these factors; (3) CR connects probability factorization and graph operations perfectly. The factorization process of CR-F can be visualized as applying a sequence of graph operations including partition, merge, duplicate and condition to a PGM graph. We further obtain an important result: by CR-F, on TCG graphs the scopes of factors can be exactly over maximal cliques without any default configuration. This improves the results of (R)MRF-F which need default configurations, and also indicates that (R)MRF-F, as special cases of CR-F, can not always achieve the optimal results of CR-F.

AB - Factorization is of fundamental importance in the area of Probabilistic Graphical Models (PGMs). In this paper, we theoretically develop a novel mathematical concept, \textbf{C}o-occurrence \textbf{R}ate (CR), for factorizing PGMs. CR has three obvious advantages: (1) CR provides a unified mathematical foundation for factorizing different types of PGMs. We show that Bayesian Network Factorization (BN-F), Conditional Random Field Factorization (CRF-F), Markov Random Field Factorization (MRF-F) and Refined Markov Random Field Factorization (RMRF-F) are all special cases of CR Factorization (CR-F); (2) CR has simple probability definition and clear intuitive interpretation. CR-F tells not only the scopes of the factors, but also the exact probability functions of these factors; (3) CR connects probability factorization and graph operations perfectly. The factorization process of CR-F can be visualized as applying a sequence of graph operations including partition, merge, duplicate and condition to a PGM graph. We further obtain an important result: by CR-F, on TCG graphs the scopes of factors can be exactly over maximal cliques without any default configuration. This improves the results of (R)MRF-F which need default configurations, and also indicates that (R)MRF-F, as special cases of CR-F, can not always achieve the optimal results of CR-F.

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Zhu Z. Factorizing Probabilistic Graphical Models Using Co-occurrence Rate. Enschede: Centre for Telematics and Information Technology (CTIT), 2011. 9 p. (CTIT technical report series; TR-CTIT-12-30).