Bayesian Network Structure Learning from Attribute Uncertain Data

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.

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.

Bayesian network model selection techniques may be used to learn and elucidate conditional relationships between features in pattern recognition tasks. The learned Bayesian network may then be used to infer unknown node-states, which may correspond to semantic tasks. One such application of this framework is scene categorization. In this paper, we employ low-level classification based on color and texture, semantic features, such as sky and grass detection, along with indoor vs. outdoor ground truth information, to create a feature set for Bayesian network structure learning. Indoor vs. outdoor inference may then be performed on a set of features derived from a testing set where node states are unknown. Experimental results show that this technique provides classification rates of 97% correct, which is a significant improvement over previous work, where a Bayesian network was constructed based on expert opinion.

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.

Estimation of conditional dependencies over a joint multivariate probability distribution is a difficult task for big data, e.g. –omics datasets, and it becomes quickly intractable when the number of variables involved grows large. For instance, structure learning in Bayesian networks has super-exponential complexity. Dimension reduction techniques such as principal component analysis can be useful but often transform the original space and can still pose problems with scalability. This substantially limits characterization of joint probability: in general, only pairwise or k-level correlations can be analyzed efficiently. We introduce the Multivariate Independence Set Search via Progressive Addition for Conditional Markov Acyclic Networks (MISS-PACMAN), which operates a greedy selection of jointly independent feature sets from a larger set of covariates, given a variable ordering. The method is non-parametric and can be used with any kernel function. MISS-PACMAN is therefore suitable for heterogeneous big data, as it combines flexibility and scalability. In our tests on both simulated and real-world data, using random forests as kernel, MISS-PACMAN was able to select independence feature sets linearly with the number of features. Further, by combining multiple independence sets, MISS-PACMAN well-approximates the underlying conditional structure of data variables (according to the generating Bayesian network), and compares favorably with other network structure discovery algorithms, such as the Peter-Clark and the fast incremental association Markov blanket.

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.

Several hardness results are presented for the parent assignment problem: Given m observations of n attributes x 1, ..., x n , find the best parents for x n , that is, a subset of the preceding attributes so as to minimize a fixed cost function. This attribute or feature selection task plays an important role, e.g., in structure learning in Bayesian networks, yet little is known about its computational complexity. In this paper we prove that, under the commonly adopted full-multinomial likelihood model, the MDL, BIC, or AIC cost cannot be approximated in polynomial time to a ratio less than 2 unless there exists a polynomial-time algorithm for determining whether a directed graph with n nodes has a dominating set of size logn, a LOGSNP-complete problem for which no polynomial-time algorithm is known; as we also show, it is unlikely that these penalized maximum likelihood costs can be approximated to within any constant ratio. For the NML (normalized maximum likelihood) cost we prove an NP-completeness result. These results both justify the application of existing methods and motivate research on heuristic and super-polynomial-time algorithms.KeywordsPolynomial TimeBayesian NetworkDirected GraphPositive InstanceParent AssignmentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A new structure learning approach for Bayesian networks based on asexual reproduction optimization (ARO) is proposed in this paper. ARO can be considered an evolutionary-based algorithm that mathematically models the budding mechanism of asexual reproduction. In ARO, a parent produces a bud through a reproduction operator; thereafter, the parent and its bud compete to survive according to a performance index obtained from the underlying objective function of the optimization problem: This leads to the fitter individual. The convergence measure of ARO is analyzed. The proposed method is applied to real-world and benchmark applications, while its effectiveness is demonstrated through computer simulations. Results of simulations show that ARO outperforms genetic algorithm (GA) because ARO results in a good structure and fast convergence rate in comparison with GA.

Bayesian Network is a knowledge representation formalism that has been proven to be valuable in gene regulatory network reconstruction. However, it is showed that the structure learning of Bayesian networks is an NP-hard problem. Several heuristic searching techniques have been used to find better network structures. Among these algorithms, K2 algorithm has been found to be the most successful. However, the performance of K2 algorithm is greatly affected by a prior ordering of input nodes. If using inappropriate orderings, the accuracy of the learned structures will be relatively low. This paper represents a new structure learning method to reconstruct gene networks from the observational gene expression data. The proposed method is based on Binary Particle Swarm Optimization and K2 algorithm. It firstly identifies nodes ordering from the experimental data by using Binary Particle Swarm Optimization algorithm. Then, the nodes ordering information is used as an input of K2 algorithm so as to improve the performance and efficiency of the K2 algorithm in determining the network structure. Our method is evaluated using two benchmark network datasets with known structures. Experimental studies show that the proposed method can identify networks more efficiently and accurately than comparable methods reported in the literature.

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.

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

Learning Bayesian network structure with immune algorithm

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...

This paper addresses exact learning of Bayesian network structure from data and expert's knowledge based on score functions that are decomposable. First, it describes useful properties that strongly reduce the time and memory costs of many known methods such as hill-climbing, dynamic programming and sampling variable orderings. Secondly, a branch and bound algorithm is presented that integrates parameter and structural constraints with data in a way to guarantee global optimality with respect to the score function. It is an any-time procedure because, if stopped, it provides the best current solution and an estimation about how far it is from the global solution. We show empirically the advantages of the properties and the constraints, and the applicability of the algorithm to large data sets (up to one hundred variables) that cannot be handled by other current methods (limited to around 30 variables).