國立高雄大學圖資館 |

Language: English

Back

Copula Based Discretized Bayesian Networks /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Copula Based Discretized Bayesian Networks /Antonio Zavaleta.
Author:	Zavaleta, Antonio,
Description:	1 electronic resource (191 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-10, Section: B.
Notes:	Advisors: van Dorp, Johan Rene Committee members: Mazzuchi, Thomas A.; Shittu, Ekundayo; Santos, Joost; Soyer, Refik.
Contained By:	Dissertations Abstracts International85-10B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31144897
ISBN:	9798382193823

Copula Based Discretized Bayesian Networks /
Zavaleta, Antonio,

Copula Based Discretized Bayesian Networks /Antonio Zavaleta. - 1 electronic resource (191 pages)

Source: Dissertations Abstracts International, Volume: 85-10, Section: B.

Bayesian Networks are probabilistic inference models that use graphs to represent the independence assumptions between random variables(nodes). Due to their graphical nature, they enjoy great appeal as explainable inference models and consequently, interest in them has spawned multiple software libraries. In all of these computer programs, probabilistic inference takes place by computing updated probabilities in light of evidence, with different types of algorithms applicable to discrete and continuous networks. Commonly used methodologies are subject to the curse of dimensionality, a computational constraint arising due to three factors: the number of variables, the number of possible states for each variable, and in the case of continuous networks, the discretization levels selected. In spite of the inherent computational complexity, there are successful applications of discrete networks with thousands of nodes; a feat that has proven more difficult for large continuous networks. In addition, while the underlying graph embodies the independence assumptions, typical Bayesian Networks methodologies do not provide the means to easily specify correlations between nodes as design parameters.In this work, a Bayesian Network parameterization methodology is proposed that enables the joint specification of prescribed dependence degrees and marginals combined with a discretization scheme that approximates a continuous network via a discretized counterpart. The continuous networks here modeled are based on copula models of dependence, i.e. joint distributions with uniform marginals that capture dependence between random variables that enable the choice of marginals for each node. The proposed discretization approach is based on numerical integration methods that yield discrete marginals matching the first 2n−1 moments of the original continuous distribution, where n denotes the selected discretization level. The resulting discretized network not only approximates pre-specified degrees of correlation between nodes, but is also portable into any discrete network software. Finally, comprehensive numerical results are presented for Bayesian Networks with predefined architectures.

English

ISBN: 9798382193823Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Bayesian Networks

Copula Based Discretized Bayesian Networks /
LDR:03628nmm a22004093i 4500 001 676292
005 20250420214336.5
006 m o d
007 cr|nu||||||||
008 250901s2024 miu||||||m |||||||eng d
020 $a 9798382193823
035 $a (MiAaPQD)AAI31144897
035 $a AAI31144897
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Zavaleta, Antonio, $e author. $0 (orcid)0009-0003-6161-9915 $3 990045
245 1 0 $a Copula Based Discretized Bayesian Networks / $c Antonio Zavaleta.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 1 electronic resource (191 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 85-10, Section: B.
500 $a Advisors: van Dorp, Johan Rene Committee members: Mazzuchi, Thomas A.; Shittu, Ekundayo; Santos, Joost; Soyer, Refik.
502 $b Ph.D. $c The George Washington University $d 2024.
520 $a Bayesian Networks are probabilistic inference models that use graphs to represent the independence assumptions between random variables(nodes). Due to their graphical nature, they enjoy great appeal as explainable inference models and consequently, interest in them has spawned multiple software libraries. In all of these computer programs, probabilistic inference takes place by computing updated probabilities in light of evidence, with different types of algorithms applicable to discrete and continuous networks. Commonly used methodologies are subject to the curse of dimensionality, a computational constraint arising due to three factors: the number of variables, the number of possible states for each variable, and in the case of continuous networks, the discretization levels selected. In spite of the inherent computational complexity, there are successful applications of discrete networks with thousands of nodes; a feat that has proven more difficult for large continuous networks. In addition, while the underlying graph embodies the independence assumptions, typical Bayesian Networks methodologies do not provide the means to easily specify correlations between nodes as design parameters.In this work, a Bayesian Network parameterization methodology is proposed that enables the joint specification of prescribed dependence degrees and marginals combined with a discretization scheme that approximates a continuous network via a discretized counterpart. The continuous networks here modeled are based on copula models of dependence, i.e. joint distributions with uniform marginals that capture dependence between random variables that enable the choice of marginals for each node. The proposed discretization approach is based on numerical integration methods that yield discrete marginals matching the first 2n−1 moments of the original continuous distribution, where n denotes the selected discretization level. The resulting discretized network not only approximates pre-specified degrees of correlation between nodes, but is also portable into any discrete network software. Finally, comprehensive numerical results are presented for Bayesian Networks with predefined architectures.
546 $a English
590 $a School code: 0075
650 4 $a Applied mathematics. $3 377601
650 4 $a Statistics. $3 182057
653 $a Bayesian Networks
653 $a Copula models
653 $a Probability
653 $a Quadrature's
690 $a 0364
690 $a 0463
710 2 $a The George Washington University. $b Systems Engineering. $e degree granting institution. $3 990046
720 1 $a van Dorp, Johan Rene $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-10B.
790 $a 0075
791 $a Ph.D.
792 $a 2024
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31144897