The Bayesian Network Story

2017 ◽  
Author(s):  
Richard Neapolitan ◽  
Xia Jiang
Keyword(s):  
Artificial Intelligence ◽  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Bayes Theorem ◽  
Standard Application

Bayesian networks are now among the leading architectures for reasoning with uncertainty in artificial intelligence. This chapter concerns their story, namely what they are, how and why they came into being, how we obtain them, and what they actually represent. First, it is shown that a standard application of Bayes’ Theorem constitutes inference in a two-node Bayesian network. Then more complex Bayesian networks are presented. Next the genesis of Bayesian networks and their relationship to causality is presented. A technique for learning Bayesian networks from data follows. Finally, a discussion of the philosophy of the probability distribution represented by a Bayesian network is provided.

scholarly journals Uniqueness of the Level Two Bayesian Network Representing a Probability Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Linda Smail
Keyword(s):  
Artificial Intelligence ◽  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Probabilistic Models ◽  
Probability Distributions ◽  
Random Variables ◽  
Inference Problem ◽  
Computation Algorithm

Bayesian Networks are graphic probabilistic models through which we can acquire, capitalize on, and exploit knowledge. they are becoming an important tool for research and applications in artificial intelligence and many other fields in the last decade. This paper presents Bayesian networks and discusses the inference problem in such models. It proposes a statement of the problem and the proposed method to compute probability distributions. It also uses D-separation for simplifying the computation of probabilities in Bayesian networks. Given a Bayesian network over a family of random variables, this paper presents a result on the computation of the probability distribution of a subset of using separately a computation algorithm and D-separation properties. It also shows the uniqueness of the obtained result.

Learning Bayesian Networks

2011 ◽  
pp. 315-321
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

scholarly journals Hybrid Optimization Algorithm for Bayesian Network Structure Learning

Information ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 294 ◽  
Author(s):  
Xingping Sun ◽  
Chang Chen ◽  
Lu Wang ◽  
Hongwei Kang ◽  
Yong Shen ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Structure Learning ◽  
Expert Knowledge ◽  
Hybrid Optimization ◽  
Experimental Simulation ◽  
Bayesian Network Structure ◽  
Bayesian Network Structure Learning

Since the beginning of the 21st century, research on artificial intelligence has made great progress. Bayesian networks have gradually become one of the hotspots and important achievements in artificial intelligence research. Establishing an effective Bayesian network structure is the foundation and core of the learning and application of Bayesian networks. In Bayesian network structure learning, the traditional method of utilizing expert knowledge to construct the network structure is gradually replaced by the data learning structure method. However, as a result of the large amount of possible network structures, the search space is too large. The method of Bayesian network learning through training data usually has the problems of low precision or high complexity, which make the structure of learning differ greatly from that of reality, which has a great influence on the reasoning and practical application of Bayesian networks. In order to solve this problem, a hybrid optimization artificial bee colony algorithm is discretized and applied to structure learning. A hybrid optimization technique for the Bayesian network structure learning method is proposed. Experimental simulation results show that the proposed hybrid optimization structure learning algorithm has better structure and better convergence.

Learning Bayesian Networks

2011 ◽  
pp. 674-677
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

Learning Bayesian Networks

2011 ◽  
pp. 1124-1128
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

Application of Bayesian Network in Safety Evaluation of Metro Construction

2013 ◽  
Vol 838-841 ◽  
pp. 1463-1468
Author(s):  
Xiang Ke Liu ◽  
Zhi Shen Wang ◽  
Hai Liang Wang ◽  
Jun Tao Wang
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Posterior Probability ◽  
Fault Tree ◽  
Fault Tree Analysis ◽  
Safety Evaluation ◽  
Tree Analysis ◽  
Tunnel Blasting ◽  
Better Than

The paper introduced the Bayesian networks briefly and discussed the algorithm of transforming fault tree into Bayesian networks at first, then regarded the structures impaired caused by tunnel blasting construction as a example, introduced the built and calculated method of the Bayesian networks by matlab. Then assumed the probabilities of essential events, calculated the probability of top event and the posterior probability of each essential events by the Bayesian networks. After that the paper contrast the characteristics of fault tree analysis and the Bayesian networks, Identified that the Bayesian networks is better than fault tree analysis in safety evaluation in some case, and provided a valid way to assess risk in metro construction.

scholarly journals Modeling the City Distribution System Reliability with Bayesian Networks to Identify Influence Factors

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Hao Zhang ◽  
Liyu Zhu ◽  
Shensi Xu
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
System Reliability ◽  
Distribution System ◽  
Complex Problem ◽  
Practical Significance ◽  
Correlation Degree ◽  
Urban Distribution ◽  
Distribution System Reliability ◽  
The City

Under the increasingly uncertain economic environment, the research on the reliability of urban distribution system has great practical significance for the integration of logistics and supply chain resources. This paper summarizes the factors that affect the city logistics distribution system. Starting from the research of factors that influence the reliability of city distribution system, further construction of city distribution system reliability influence model is built based on Bayesian networks. The complex problem is simplified by using the sub-Bayesian network, and an example is analyzed. In the calculation process, we combined the traditional Bayesian algorithm and the Expectation Maximization (EM) algorithm, which made the Bayesian model able to lay a more accurate foundation. The results show that the Bayesian network can accurately reflect the dynamic relationship among the factors affecting the reliability of urban distribution system. Moreover, by changing the prior probability of the node of the cause, the correlation degree between the variables that affect the successful distribution can be calculated. The results have significant practical significance on improving the quality of distribution, the level of distribution, and the efficiency of enterprises.

scholarly journals A dynamic Bayesian network approach for prognosis computations on discrete state systems

2017 ◽  
Vol 231 (5) ◽  
pp. 516-533 ◽  
Author(s):  
Josquin Foulliaron ◽  
Laurent Bouillaut ◽  
Patrice Aknin ◽  
Anne Barros
Keyword(s):  
Complex Systems ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Multicomponent System ◽  
Dynamic Bayesian Network ◽  
Dynamic Bayesian Networks ◽  
Remaining Useful Life ◽  
Predictive Maintenance ◽  
Discrete State ◽  
Virtual Maintenance

The maintenance optimization of complex systems is a key question. One important objective is to be able to anticipate future maintenance actions required to optimize the logistic and future investments. That is why, over the past few years, the predictive maintenance approaches have been an expanding area of research. They rely on the concept of prognosis. Many papers have shown how dynamic Bayesian networks can be relevant to represent multicomponent complex systems and carry out reliability studies. The diagnosis and maintenance group from French institute of science and technology for transport, development and networks (IFSTTAR) developed a model (VirMaLab: Virtual Maintenance Laboratory) based on dynamic Bayesian networks in order to model a multicomponent system with its degradation dynamic and its diagnosis and maintenance processes. Its main purpose is to model a maintenance policy to be able to optimize the maintenance parameters due to the use of dynamic Bayesian networks. A discrete state-space system is considered, periodically observable through a diagnosis process. Such systems are common in railway or road infrastructure fields. This article presents a prognosis algorithm whose purpose is to compute the remaining useful life of the system and update this estimation each time a new diagnosis is available. Then, a representation of this algorithm is given as a dynamic Bayesian network in order to be next integrated into the Virtual Maintenance Laboratory model to include the set of predictive maintenance policies. Inference computation questions on the considered dynamic Bayesian networks will be discussed. Finally, an application on simulated data will be presented.

Application of Bayesian for the Situation Assessment of Sea-Battlefield

2013 ◽  
Vol 346 ◽  
pp. 135-139 ◽  
Author(s):  
Yong Tao Yu ◽  
Ying Ding ◽  
Zheng Xi Ding
Keyword(s):  
Decision Support ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Conditional Probability ◽  
Assessment Model ◽  
Situation Assessment ◽  
Network Characteristics ◽  
Specific Assessment

The sea-battlefield situation is dynamic and how efficient sea-battlefield situation assessment is a major problem facing operational decision support. According to research based on Bayesian networks Sea-battlefield situation assessment, first constructed sea-battlefield situation assessment Bayesian network; followed by specific assessment objectives, to simplify creating sub Bayesian assessment model; once again based on Bayesian network characteristics to determine each node probability formula; finally, according to the formula for solving the edge of the probability and the conditional probability of each node, sea-battlefield situation assessment.

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