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Hierarchical Markov network model: ...

Wu, Dan.

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Hierarchical Markov network model: A hypergraph representation of Bayesian networks.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hierarchical Markov network model: A hypergraph representation of Bayesian networks./
作者:	Wu, Dan.
面頁冊數:	164 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4122.
Contained By:	Dissertation Abstracts International65-08B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ92831
ISBN:	0612928314

Hierarchical Markov network model: A hypergraph representation of Bayesian networks.
Wu, Dan.

Hierarchical Markov network model: A hypergraph representation of Bayesian networks. - 164 p.

Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4122.

Thesis (Ph.D.)--The University of Regina (Canada), 2004.

Bayesian networks have been successfully established as a framework for managing uncertainty using probability. A Bayesian network is graphically represented by a directed acyclic graph (DAG). However, it has been pointed out even in the early development of Bayesian networks that in the strictest sense, Bayesian networks are not ordinary (directed) graphs, but hypergraphs.

ISBN: 0612928314Subjects--Topical Terms:

626642
Computer Science.

Hierarchical Markov network model: A hypergraph representation of Bayesian networks.
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245 1 0 $a Hierarchical Markov network model: A hypergraph representation of Bayesian networks.
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500 $a Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4122.
500 $a Adviser: S. K. Michael Wong.
502 $a Thesis (Ph.D.)--The University of Regina (Canada), 2004.
520 $a Bayesian networks have been successfully established as a framework for managing uncertainty using probability. A Bayesian network is graphically represented by a directed acyclic graph (DAG). However, it has been pointed out even in the early development of Bayesian networks that in the strictest sense, Bayesian networks are not ordinary (directed) graphs, but hypergraphs.
520 $a Motivated by this interesting comment, in this dissertation, a new probabilistic graphical model, namely, the hierarchical Markov network (HMN) model is proposed. A hierarchical Markov network features a tree hierarchy of acyclic hypergraphs. A procedure which transforms any given Bayesian network into a unique HMN is introduced. In other words, a hypergraph representation of Bayesian networks is provided. Moreover, the conditional independency information encoded in the DAG of the given Bayesian network and the transformed HMN are equivalent to each other so that no information is ever lost during the transformation. This makes HMN a faithful hypergraph representation of a Bayesian network. Furthermore, by taking full advantage of techniques developed for answering relational database queries, how belief updating in a HMN can be performed on a tree hierarchy of acyclic hypergraphs in a more convenient and flexible manner than the conventional belief updating in a Bayesian network which is performed on a single acyclic hypergraph is demonstrated.
520 $a The idea of a tree hierarchy of acyclic hypergraphs representing a Bayesian network is inspired by an algebraic study of Bayesian networks. A necessary and sufficient condition under which a marginal factorization of a joint probability distribution defines a Bayesian network is given. This algebraic study naturally leads to the development of the HMN model. The belief updating method in HMN is inspired by a relational database approach for belief updating in Bayesian networks. Well developed techniques originally used in the relational database community are adopted for our purpose of belief updating in a Bayesian network. This adoption can then be further tailored to solve the problem of belief updating in a HMN.
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