BAYESIAN NETWORK REVISION WITH PROBABILISTIC CONSTRAINTS

2012 ◽  
Vol 20 (03) ◽  
pp. 317-337 ◽  
Author(s):  
YUN PENG ◽  
ZHONGLI DING ◽  
SHENYONG ZHANG ◽  
RONG PAN
Keyword(s):  
Bayesian Network ◽  
Network Structure ◽  
Knowledge Integration ◽  
Computational Cost ◽  
Probabilistic Constraints ◽  
Iterative Proportional Fitting ◽  
Specific Knowledge ◽  
Fitting Procedure ◽  
Integration Problem ◽  
The Given

This paper deals with an important probabilistic knowledge integration problem: revising a Bayesian network (BN) to satisfy a set of probability constraints representing new or more specific knowledge. We propose to solve this problem by adopting IPFP (iterative proportional fitting procedure) to BN. The resulting algorithm E-IPFP integrates the constraints by only changing the conditional probability tables (CPT) of the given BN while preserving the network structure; and the probability distribution of the revised BN is as close as possible to that of the original BN. Two variations of E-IPFP are also proposed: 1) E-IPFP-SMOOTH which deals with the situation where the probabilistic constraints are inconsistent with each other or with the network structure of the given BN; and 2) D-IPFP which reduces the computational cost by decomposing a global E-IPFP into a set of smaller local E-IPFP problems.

BAYESIAN NETWORK REASONING WITH UNCERTAIN EVIDENCES

2010 ◽  
Vol 18 (05) ◽  
pp. 539-564 ◽  
Author(s):  
YUN PENG ◽  
SHENYONG ZHANG ◽  
RONG PAN
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Efficient Algorithms ◽  
Iterative Proportional Fitting ◽  
Jeffrey’S Rule ◽  
Fitting Procedure ◽  
Uncertain Evidence ◽  
Hard Evidence

This paper investigates the problem of belief update in Bayesian networks (BN) with uncertain evidence. Two types of uncertain evidences are identified: virtual evidence (reflecting the uncertainty one has about a reported observation) and soft evidence (reflecting the uncertainty of an event one observes). Each of the two types of evidence has its own characteristics and obeys a belief update rule that is different from hard evidence, and different from each other. The particular emphasis is on belief update with multiple uncertain evidences. Efficient algorithms for BN reasoning with consistent and inconsistent uncertain evidences are developed, and their convergences analyzed. These algorithms can be seen as combining the techniques of traditional BN reasoning, Pearl's virtual evidence method, Jeffrey's rule, and the iterative proportional fitting procedure.

A Multistep Iterative Proportional Fitting Procedure to Estimate Cohortwise Interregional Migration Tables Where Only Inconsistent Marginals are Known

1992 ◽  
Vol 24 (11) ◽  
pp. 1531-1547 ◽  
Author(s):  
S Saito
Keyword(s):  
Published Data ◽  
Interregional Migration ◽  
Detailed Data ◽  
Iterative Proportional Fitting ◽  
Actual Application ◽  
Fitting Procedure ◽  
Universal Applicability ◽  
The Given ◽  
Marginal Tables ◽  
Different Sources

The interregional cohort survival model developed by Rogers is an excellent one that includes all of the three population processes: birth-death, aging, and interregional migration. Rogers's model, however, has been rarely implemented because it requires detailed data concerning cohortwise (that is by age and sex) interregional migration tables which are not usually available as published data. The most usual case is that only marginal tables that are from different sources can be obtained. However, in this case, those marginal tables necessarily show inconsistency in the sense that they do not have identical common submarginals. This inconsistency prevents the standard iterative proportional fitting (IPF) procedure from converging to the estimate of the complete migration table which conforms to the given observed marginals. Thus to implement Rogers's model some method is needed to estimate the complete migration table where only inconsistent marginals are available. In this paper a multistep IPF procedure is proposed for that purpose and an actual application of the proposed method is shown. The multistep IPF procedure has universal applicability to a wide class of general problems concerned with the estimation of a joint table under inconsistent marginals.

scholarly journals Constraint-Based Bayesian Network Structure Learning using Uncertain Experts’ Knowledge

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Christophe Gonzales ◽  
Axel Journe ◽  
Ahmed Mabrouk
Keyword(s):  
Bayesian Network ◽  
Network Structure ◽  
Structure Learning ◽  
Learning Algorithm ◽  
Learning Algorithms ◽  
Specific Knowledge ◽  
Bayesian Network Structure ◽  
Bayesian Network Structure Learning ◽  
Mathematical Foundations

Exploiting experts' knowledge can significantly increase the quality of the Bayesian network (BN) structures produced by learning algorithms. However, in practice, experts may not be 100% confident about the opinions they provide. Worst, the latter can also be conflicting. Including such specific knowledge in learning algorithms is therefore complex. In the literature, there exist a few score-based algorithms that can exploit both data and the knowledge about the existence/absence of arcs in the BN. But, as far as we know, no constraint-based learning algorithm is capable of exploiting such knowledge. In this paper, we fill this gap by introducing the mathematical foundations for new independence tests including this kind of information. We provide a new constraint-based algorithm relying on these tests as well as experiments that highlight the robustness of our method and its benefits compared to other constraint-based learning algorithms.

scholarly journals An Algorithm Based on Loop Cutting Contribution Function for Loop Cutset Problem in Bayesian Network

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 462
Author(s):  
Jie Wei ◽  
Yufeng Nie ◽  
Wenxian Xie
Keyword(s):  
Bayesian Inference ◽  
Bayesian Network ◽  
Network Structure ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Global Perspective ◽  
Node Pair ◽  
Bayesian Network Structure ◽  
Network Structure Analysis ◽  
Contribution Index

The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop cutting contribution index. Compared with the existing algorithms, the algorithm uses the loop cutting contribution index of nodes and node-pairs to analyze nodes from a global perspective, and select loop cutset candidates with node-pair as the unit. The algorithm uses the parameter μ to control the range of node pairs, and the parameter ω to control the selection conditions of the node pairs, so that the algorithm can adjust the parameters according to the size of the Bayesian networks, which ensures computational efficiency. The numerical experiments show that the calculation efficiency of the algorithm is significantly improved when it is consistent with the accuracy of the existing algorithm; the experiments also studied the influence of parameter settings on calculation efficiency using trend analysis and two-way analysis of variance. The loop cutset solving algorithm based on the loop cutting contribution index uses the node-pair as the unit to solve the loop cutset, which helps to improve the efficiency of Bayesian inference and Bayesian network structure analysis.

Bidirectional heuristic search to find the optimal Bayesian network structure

2021 ◽  
Vol 426 ◽  
pp. 35-46
Author(s):  
Xiangyuan Tan ◽  
Xiaoguang Gao ◽  
Zidong Wang ◽  
Chuchao He
Keyword(s):  
Bayesian Network ◽  
Network Structure ◽  
Heuristic Search ◽  
Bayesian Network Structure

scholarly journals Bayesian Network Structure and Predictability of Autistic Traits

2020 ◽  
pp. 003329412097815
Author(s):  
Giovanni Briganti ◽  
Donald R. Williams ◽  
Joris Mulder ◽  
Paul Linkowski
Keyword(s):  
Sex Differences ◽  
Network Analysis ◽  
Bayesian Network ◽  
Network Structure ◽  
Network Connectivity ◽  
Autistic Traits ◽  
Data Set ◽  
Conditional Dependence ◽  
Bayesian Network Structure ◽  
Male Subjects

The aim of this work is to explore the construct of autistic traits through the lens of network analysis with recently introduced Bayesian methods. A conditional dependence network structure was estimated from a data set composed of 649 university students that completed an autistic traits questionnaire. The connectedness of the network is also explored, as well as sex differences among female and male subjects in regard to network connectivity. The strongest connections in the network are found between items that measure similar autistic traits. Traits related to social skills are the most interconnected items in the network. Sex differences are found between female and male subjects. The Bayesian network analysis offers new insight on the connectivity of autistic traits as well as confirms several findings in the autism literature.

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