Robust Structure Learning of Bayesian Network by Identifying Significant Dependencies

The University of California at Irvine (UCI), in a 29-page audit of its Willed Body Program that took more than a year and a half to complete, has faulted its former director, Christopher S Brown. The audit uncovered lack of supervision, poor record keeping, failure to return remains to families in accordance with their wishes, and financial irregularities. The last included supplying 7 cadaver spines to a research group in Phoenix, Arizona, for $5,125. The payment was made to a company, University Health Services, not affiliated with UCI and owned by Jeffrey Frazier, a business associate of Brown's. The audit also found overcharges of several hundred dollars by Harry's Transportation, a company owned by Brown and Frazier for carrying cadavers. Donated cadavers were used, without UCI's permission, in a private anatomy class run in UCI's Willed Body morgue by Frazier's company Replica, which charged $175 per student. Brown charged families who desired a return of their cremated donors' ashes a $600 fee. Three families paid to have ashes returned, but there is no record that UCI received the money. Poor record keeping prevented the UCI auditors from accounting for 320 of the 441 cadavers donated to the Willed Body Program from January 1, 1995, through August 11, 1999. As the result of alleged misplaced bodies, about 20 lawsuits have been filed by survivors against UCI, Brown, and Frazier. UCI fired Brown in September 1999. No charges have been brought against him, but the Orange County District Attorney's office is investigating the allegations. Corrective measures taken by UCI include replacing Brown, a former funeral director, with a more experienced mortician as program director and written policies and procedures. Thomas C Cesario, UCI College of Medicine Dean, has appointed Peter Lawrence, a professor of surgery, to oversee the program, in conjunction with an advisory committee of faculty members. Willed Body programs based at US medical schools collect about 15,000 bodies annually. The demand far outstrips the supply, according to Philip Guyett, former manager of the Willed Body Program at Western University of Health Sciences in Pomona, California. After the audit began last year, Cesario said, The people who will their body to medical science and education have made one of the most noble gifts possible, and it is absolutely essential that our Willed Body Program operate not only in accordance with the highest professional standards, but also with the highest standards of respect for these donors and their families.

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

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.

The paper first introduces the concept of organizational factors in the socio-technical system and the basic theory of Bayesian Network and then discusses the algorithm of structure learning of Bayesian network. A new algorithm base on dependency analysis is proposed to effectively reduce the number of detecting condition independence. It uses heuristic cutset searching algorithm and orients all the edges in the network before removing superfluous edges. Experiment results indicate that it outperforms the traditional algorithm. Finally, organizational factors Bayesian network is constructed by using the algorithm which is helpful for the nuclear pant to discover the critical factors influencing human reliability in nuclear power plant.

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.

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.

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.

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.

The Bayesian network, a powerful tool for predicting and diagnosing uncertain phenomena, is used in various fields including artificial intelligence, business administration, and medical science. We use a statistical approach, and present a simple algorithm for learning Bayesian network structure from data. First we obtain from data the original correlation graph and the correlation graphs when one or two variables are fixed. Then we construct a Bayesian network that would produce the most similar correlation graphs. Simulation results are given to demonstrate that the algorithm determines the network structure with a high accuracy.

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.

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.

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