Construction of Bayesian network structures from data: A brief survey and an efficient algorithm

The type of constraint-based methods is one of the most important approaches to learn Bayesian network (BN) structures from observational data with conditional independence (CI) tests. In this paper, we find that existing constraint-based methods often perform many redundant CI tests, which significantly reduces the learning efficiency of those algorithms. To tackle this issue, we propose a novel framework to accelerate BN structure learning by reducing redundant CI tests without sacrificing accuracy. Specifically, we first design a CI test cache table to store CI tests. If a CI test has been computed before, the result of the CI test is obtained from the table instead of computing the CI test again. If not, the CI test is computed and stored in the table. Then based on the table, we propose two CI test cache table based PC (CTPC) learning frameworks for reducing redundant CI tests for BN structure learning. Finally, we instantiate the proposed frameworks with existing well-established local and global BN structure learning algorithms. Using twelve benchmark BNs, the extensive experiments have demonstrated that the proposed frameworks can significantly accelerate existing BN structure learning algorithms without sacrificing accuracy.

A Conditional Probability Model to Predict the Mortality in Patients With Breast Cancer: A Bayesian Network Analysis

When the number of samples is large, the scale of the Bayesian network (BN) structure search space increases exponentially with the number of nodes, resulting in a sharp increase in the difficulty of learning the BN structure. Aiming at this problem, this paper proposes a fault diagnosis model construction method combining association rules and a BN network. The Euclidean distance under the Symbolic Aggregation Approximation (SAX) algorithm is utilized to compute and average the distance between the standard and faulty samples and filter the candidate nodes by the average value, which in turn reduces the search sample space. The method of combining Association Rules algorithm with traditional BN structure learning results is used to solve the problem of wrong edges in structure learning. Finally, the maximum likelihood estimation method is used for parameter learning to complete the construction of the diagnostic network. The experimental results show that the running time of the Bayesian Network based on the Association Rules (AR-BN) model proposed in this paper is short and that the Hamming distance with the original structure is small, so this model can effectively reduce the search space and solve the problem of wrong edges, and it also has a good performance in fault diagnosis.

This study aims to comprehensively identify risks to food safety and halal status in food manufacturing processes. The research was conducted through risk identification, data collection, Bayesian Network (BN) structure, decision analysis, and mitigation programs. The results showed that there were 19 integrated risks to food safety and halal. Twelve risks were due to food safety and seven risks were due to halal status. Overall, risks identified were described through the BN structure, which consists of four levels, as a basis for determining risk opportunity values. The results of BN decision analysis show that the highest integrated risk to food safety and halal each level. The risk of chickens dying when stunning is the highest risks in level 1 and cleaning and chilling department in level 2. The partially integrated risks for level 3 and total integrated risks in level 4 has a chance of contamination. Due is the results, the analysis and decision analysis is to reject or rework.

Bayesian network (BN) is a probabilistic graphical model which describes the joint probability distribution over a set of random variables. Finding an optimal network structure based on an available training dataset is one of the most important challenges in the field of BNs. Since the problem of searching the optimal BN structure belongs to the class of NP-hard problems, typically greedy algorithms are used to solve it. In this paper two novel learning automata-based algorithms are proposed to solve the BNs’ structure learning problem. In both, there is a learning automaton corresponding with each possible edge to determine the appearance and the direction of that edge in the constructed network; therefore, we have a game of learning automata, at each stage of the proposed algorithms. Two special cases of the game of the learning automata have been discussed, namely, the game with a common payoff and the competitive game. In the former, all the automata in the game receive a unique payoff from the environment, but in the latter, each automaton receives its own payoff. As the algorithms proceed, the learning processes focus on the BN structures with higher scores. The use of learning automata has led to design the algorithms with a guided search scheme, which can avoid getting stuck in local maxima. Experimental results show that the proposed algorithms are capable of finding the optimal structure of BN in an acceptable execution time; and compared with other search-based methods, they outperform them.

Prediction models are built with various machine learning algorithms to identify defects prior to release to facilitate software testing, and save testing costs. Naive Bayes classifier is one of the best performing classification techniques in defect prediction. It assumes conditional independence of features and for defect prediction problem some of the features are not actually conditionally independent. The interesting problem is to relax these conditional independence assumptions and to check whether there is any improvement in performance of classifiers. We have built Bayesian Network structures using different classes of algorithms namely score-based, constraint-based and hybrid algorithms. We propose an approach to augment these Bayesian Network structures with class node. Bayesian Network classifiers along with Random Forests, Logistic Regression and Naive Bayes classifiers are then evaluated using measures like AUC and H-measure. We observe that RSMAX2 and Grow-Shrink classifiers (after augmentation) perform consistently better in defect prediction.

In order to solve the problems that the intelligence algorithm falls into the local optimum easily and has a slow convergence in Bayesian networks (BN) structure learning, an algorithm based on adaptive selection operator with simulated annealing is proposed. This chapter conducts the adaptive selection rule in combination with conditional independence tests of BN nodes to guide the generation of neighbor. In order to better compare the adaptive effect, an algorithm based on selection operator with simulated annealing (SOSA) is proposed; at the same time 15 data sets in the three typical networks are accessed as learning samples. The results of the Bayesian Dirichlet (BD) score, Hamming distance (HD), and evolution time of the network after learning show that it has the quicker convergence and it searches the optimal solution more easily compared with simulated annealing (SA) and SOSA.

Escalator-related injuries have become an important issue in daily metro operation. To reduce the probability and severity of escalator-related injuries, this study conducted a probability and severity analysis of escalator-related injuries by using a Bayesian network to identify the risk factors that affect the escalator safety in metro stations. The Bayesian network structure was constructed based on expert knowledge and Dempster–Shafer evidence theory, and further modified based on conditional-independence test. Then, 950 escalator-related injuries were used to estimate the posterior probabilities of the Bayesian network with expectation–maximization (EM) algorithm. The results of probability analysis indicate that the most influential factor in four passenger behaviors is failing to stand firm (p = 0.48), followed by carrying out other tasks (p = 0.32), not holding the handrail (p = 0.23), and another passenger’s movement (p = 0.20). Women (p = 0.64) and elderly people (aged 66 years and above, p = 0.48) are more likely to be involved in escalator-related injuries. Riding an escalator with company (p = 0.63) has a relatively high likelihood of resulting in escalator-related injuries. The results from the severity analysis show that head and neck injuries seem to be more serious and are more likely to require an ambulance for treatment. Passengers who suffer from entrapment injury tend to claim for compensation. Severe injuries, as expected, significantly increase the probability of a claim for compensation. These findings could provide valuable references for metro operation corporations to understand the characteristics of escalator-related injuries and develop effective injury prevention measures.

Bayesian network is an important model for reasoning in an uncertain environment. A reliable node rank is required by K2 algorithm to learn Bayesian network structure better. To provide a high-quality node rank tailored for K2 algorithm, we propose a node priority-based sorting algorithm. Given observable data only, our algorithm can be employed to learn a node rank without expert knowledge. Specifically, MCMC algorithm is first utilized to yield some Bayesian network structures that can sufficiently fit the observed data. We then define the priority of each node in these network structures. Node rank is finally obtained through weighted scoring based on the priority. The empirical results show that our sorting algorithm performs significantly better than commonly used methods, e.g., randomly sorting and MCMC algorithm, on an Asia network-learning dataset.

Efficient Bayesian network modeling of systems

It is often necessary to optimize the Bayesian network structure. Based on the junction tree, Bayesian network had been decomposed into a number of sub-networks. For different situations of adding edges, deleting edges and reversing edges in Bayesian network, it takes disparate approach. The changes in sub-networks were detected by the scoring function. And the conditional independence test of sub networks corresponding to adjacent cliques of junction tree is used to determine the inter-networks changes. At last utilizing all the change of within or between sub-networks, the optimization of Bayesian network structure is selected. The effectiveness of this method has been to verify by the simulation results.

When the amount of available data is small with respect to the problem size, many Bayesian networks can account for the data in a similar way. In these cases model averaging offers a framework which allows us to make better predictions than model selection. Selective model averaging directly uses a subset of these networks with high probability mass to reason over the probability of the structural features (arcs) which can appear in the problem domain network model. In this paper, instead of using this subset of networks to reason about the domain network structure, we propose to use the probability distribution over the structural features induced by these networks, in order to learn a new Bayesian network whose variables are the structural features which can appear in the problem domain network. This network can be considered as a higher level model or meta model, because it can be seen as an approximation of the whole space of Bayesian networks defined over the problem domain variables. This meta-model (Bayesian network) can be used to reason about the probability of structural features, as selective model averaging, but also as a decision support tool to be used by an expert in the problem domain.

We present an improved method for learning Bayesian network (BN) structures. The new approach incorporate the idea of simulated annealing algorithm (SA) into the selection operator of genetic algorithm(GA). The BN structure with the highest score is given high priority in selection, as well as the structure with lower score could also be given opportunity to be selected. That is high score prior genetic-simulated annealing algorithm to Bayesian network structure learning(GSA_BNSL).This strategy will reserve optimal gene while avoiding the premature caused by the misleading from high score individual in the population. Experiments on comparison of several BN learning algorithms are carried out using typical data set of data mining. The result indicates that the GSA_BNSL is able to obtain an optimized BN structure with higher accuracy rate.

In this paper, we introduce PEBL, a Python library and application for learning Bayesian network structure from data and prior knowledge that provides features unmatched by alternative software pac...

Due to environmental fluctuations, the operating performance of complex industrial processes may deteriorate and affect economic benefits. In order to obtain maximal economic benefits, operating performance assessment is a novel focus. Therefore, this paper proposes a whole framework from operating performance assessment to nonoptimal cause identification based on partial-least-squares-based Granger causality analysis (PLS-GC) and Bayesian networks (BNs). The proposed method has three main contributions. First, a multiblock operating performance assessment model is established to correspondingly extract economic-related information and dynamic information. Then, a Bayesian network structure is established by PLS-GC that excludes the strong coupling of variables and simplifies the network structure. Lastly, nonoptimal root cause and and nonoptimal transmission path are identified by Bayesian inference. The effectiveness of the proposed method was verified on Benchmark Simulation Model 1.