Research and application of structure learning algorithm for Bayesian networks from distributed data

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.

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.

Learning Bayesian network structure with immune algorithm

In this work we applied Variable Mesh Optimization population metaheuristc (VMO) for Bayesian network (BN)structure learning as score-and-search method. Our idea was to represent each node of the Mesh as a Bayesian network through a set of arcs. Then new BNs are created using among sets (union and difference) operations. For this process, three types of BNs are identified, local optima (BNs with the best score in each neighborhood), global optima (BN with the best score among local optima), and frontier solutions (more and less different in structure BNs). Finally the clearing process is applied to select the most representative BNs in the Mesh (score and structure). For determining the global score, each BN is used as a Bayesian classifier and classification accuracy is obtained using cross validation over dataset. The Proposal is compared with other classifiers using UCI repository data set. Results show that our proposal obtains the best score, that proves to be a very competitive algorithm for supervised classification.

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.

A hybrid algorithm for Bayesian network structure learning with application to multi-label learning

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.

In recent years there has been a growing interest in Bayesian Network learning from uncertain data. While many researchers focus on Bayesian Network learning from data with tuple uncertainty, Bayesian Network structure learning from data with attribute uncertainty gets little attention. In this paper we make a clear definition of attribute uncertain data and Bayesian Network Learning problem from such data. We propose a structure learning method named DTAU based on information theory. The algorithm assumes that the structure of a Bayesian network is a tree. It avoids enumerating all possible worlds. The dependency tree is computed with polynomial time complexity. We conduct experiments to demonstrate the effectiveness and efficiency of our method. The experiments show the clustering results on uncertain dataset by our dependency tree are acceptable.KeywordsuncertaintyBayesian Network structuredependency

A new algorithm, PCB (Partial Correlation-Based) algorithm, is presented for Bayesian network structure learning. The algorithm combines ideas from local learning with partial correlation techniques in an effective way. It reconstructs the skeleton of a Bayesian network based on partial correlation and then performs greedy hill-climbing search to orient the edges. Specifically, we make three contributions. Firstly, we give the proof that in a SEM (simultaneous equation model) with uncorrelated errors, when datasets are generated by SEM no matter what distribution disturbances subject to, we can use partial correlation as the criterion of CI test. Second, we have done a series of experiments to find the best threshold value of partial correlation. Finally, we show how partial relation can be used in Bayesian network structure learning under SEM. The effectiveness of the method is compared with current state of the art methods on 8 networks. Simulation shows that PCB algorithm outperforms existing algorithms in both accuracy and run time.

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.

Bayesian networks are useful analytical models for designing the structure of knowledge in machine learning. Bayesian networks can represent probabilistic dependency relationships among the variables. One strategy of Bayesian Networks structure learning is the score and search technique. The authors present the Elephant Swarm Water Search Algorithm (ESWSA) as a novel approach to Bayesian network structure learning. In the algorithm; Deleting, Reversing, Inserting, and Moving are used to make the ESWSA for reaching the optimal structure solution. Mainly, water search strategy of elephants during drought periods is used in the ESWSA algorithm. The proposed method is compared with simulated annealing and greedy search using BDe score function. The authors have also investigated the confusion matrix performances of these techniques utilizing various benchmark data sets. As presented by the results of the evaluations, the proposed algorithm has better performance than the other algorithms and produces better scores and accuracy values.

It's very significant to correctly identify the hierarchical relation among attributes correctly when constructing a diagnosis test.As we know,there are various methods to identify the hierarchical relation among attributes in different cognitive diagnosis models(CDMs).Rule Space Model(RSM) is a kind of great influence CDM which was developed by Tatsuoka and her associates.In RSM,the task of attribute identification is performed after the test items have already been developed.And then an incidence Q matrix can be determined which reflects hierarchical relation.However,in Leighton,Gierl and Hunka's(2004) Attribute Hierarchy Method(AHM) the organization of attributes(attributes,number of attributes and attribute hierarchical relation) should be determined before developing the test items.In RSM and AHM the importance of correctly identifying the attributes and their hierarchical relation cannot be overstated,and the attributes and their hierarchical relations serve as the most important input variables to the models because they provide the basis for interpreting the results.The hierarchical relation among attributes describes the domain knowledge structures.Understanding the domain knowledge structures in highly specific detail provides a rational basis for proposing and evaluating potential improvements in the measurement of general proficiency.Otherwise,improvement remains largely a trial-and-error process.It has been proved that is not reliable to get the hierarchical relation by analyzing the test items,even the resulting hierarchical relations are not unique.Now,structure learning of Bayesian Networks would be introduced to study the hierarchical relation from the examinees' attribute mastery patterns.On the one hand,this paper conducted a simulation study in which Cui,Leighton and Zheng(2006)'s attribute hierarchical relation was employed,and the sample size of 5000 was used.In the simulated study,different sliping rates was considered for the purpose of testing the robustness of Bayesian structure learning.On the other hand,this paper conducted an empirical study to research the attributes which were commonly used in different numeration representation system converting,and the sample size was 189.Also the hierarchical relation generated by Bayesian structure learning and the hierarchical relation extracted by domain expert was compared.The result of simulation study and empirical study all showed the Bayesian Networks was a very useful tool in determining the hierarchical relation among attributes in the realm of education measurement and psychometrics.It is proved that the result for reference is valuable through structure learning of Bayesian Networks in simulated experiments and practical application.Meanwhile,the Bayesian Networks also can be used to test the hierarchical relation in RSM.

At present, most of the algorithms for learning Bayesian Networks (BNs) use EM algorithm to deal with incomplete data. They are of low efficiency because EM algorithm has to perform iterative process of probability reasoning to complete the incomplete data. In this paper we present an efficient BN learning algorithm, which use the combination of EMI method and a scoring function based on mutual information theory. The algorithm first uses EMI method to estimate, from incomplete data, probability distributions over local structures of BNs, then evaluates BN structures with the scoring function and searches for the best one. The detailed procedure of the algorithm is depicted in the paper. The experimental results on Asia and Alarm networks show that when achieving high accuracy, the algorithm is much more efficient than two EM based algorithms, SEM and EM-EA algorithms.

A Bayesian network (BN) is an important probabilistic model in the field of artificial intelligence and a powerful formalism used to describe uncertainty in the real world. As science and technology develop, considerable data on complex systems have been acquired by various means, which presents a significant challenge regarding how to accurately and robustly learn a network structure for a complex system. To address this challenge, many BN structure learning methods based on swarm intelligence have been developed. In this study, we perform a systematic comparison of three typical methods based on ant colony optimization, artificial bee colony algorithm, and bacterial foraging optimization. First, we analyze and summarize their main characteristics from the perspective of stochastic searching. Second, we conduct thorough experimental comparisons to examine the roles of different mechanisms in each method by means of multiaspect metrics, i.e., the K2 score, structural differences, and execution time. Next, we perform further experiments to validate the robustness of different algorithms on some benchmark data sets with noise. Finally, we present the prospects and references for researchers who are engaged in learning BN networks.

Algorithms inspired by swarm intelligence have been used for many optimization problems and their effectiveness has been proven in many fields. We propose a new swarm intelligence algorithm for structural learning of Bayesian networks, BFO-B, based on bacterial foraging optimization. In the BFO-B algorithm, each bacterium corresponds to a candidate solution that represents a Bayesian network structure, and the algorithm operates under three principal mechanisms: chemotaxis, reproduction, and elimination and dispersal. The chemotaxis mechanism uses four operators to randomly and greedily optimize each solution in a bacterial population, then the reproduction mechanism simulates survival of the fittest to exploit superior solutions and speed convergence of the optimization. Finally, an elimination and dispersal mechanism controls the exploration processes and jumps out of a local optima with a certain probability. We tested the individual contributions of four algorithm operators and compared with two state of the art swarm intelligence based algorithms and seven other well-known algorithms on many benchmark networks. The experimental results verify that the proposed BFO-B algorithm is a viable alternative to learn the structures of Bayesian networks, and is also highly competitive compared to state of the art algorithms. Reproduction selects elite individuals and realizes information transmission.Chemotaxis and elimination-and-dispersal maintain a balance between exploitation and exploration.Four operators serve as candidate directions for each bacterium to select.