Bayesian Network Structural Learning Using Adaptive Genetic Algorithm with Varying Population Size

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.

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.

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

Frailty remains a challenge in the aging research area with a number of gaps in knowledge still to be filled. New approaches to its study have been proposed, including the one discussed in this article. We tested frailty as through the use of graphical probabilistic models (bayesian networks) with empirical data. Data from the Mexican Health and Aging Study (main data 2012, mortality 2015) was used. Frailty was operationalized with a 35-deficit frailty index (FI). Analyzed nodes were the deficits, plus death and the total score of the FI. The edges, or ties, linking those nodes (set E) were obtained through structural learning, and an undirected discrete graph G (V, E) associated with a discrete graphical probabilistic model (Markov network) was derived. Structural learning was possible through hill-climbing (hc) and PC algorithms. Analyses were performed for the whole population and tertiles of the total FI score. The number of connections within nodes increased according to the tertile level of the total FI score. Groups of interconnected deficits increased as the FI score raised. Almost all deficits related to mobility were interconnected and death was not the most connected node. Frailty behaves as a nonlinear system under the looks of a complex network. Further research should aim to identify the nature of the interactions observed. This could contribute to the development of a conceptual framework that would allow specific interventions to mitigate the consequences of frailty in older adults to be developed.

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.

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 this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.

Stroke is a major chronic non-communicable disease with high incidence, high mortality, and high recurrence. To comprehensively digest its risk factors and take some relevant measures to lower its prevalence is of great significance. This study aimed to employ Bayesian Network (BN) model with Max-Min Hill-Climbing (MMHC) algorithm to explore the risk factors for stroke. From April 2019 to November 2019, Shanxi Provincial People's Hospital conducted opportunistic screening for stroke in ten rural areas in Shanxi Province. First, we employed propensity score matching (PSM) for class balancing for stroke. Afterwards, we used Chi-square testing and Logistic regression model to conduct a preliminary analysis of risk factors for stroke. Statistically significant variables were incorporated into BN model construction. BN structure learning was achieved using MMHC algorithm, and its parameter learning was achieved with Maximum Likelihood Estimation. After PSM, 748 non-stroke cases and 748 stroke cases were included in this study. BN was built with 10 nodes and 12 directed edges. The results suggested that age, fasting plasma glucose, systolic blood pressure, and family history of stroke constitute direct risk factors for stroke, whereas sex, educational levels, high density lipoprotein cholesterol, diastolic blood pressure, and urinary albumin-to-creatinine ratio represent indirect risk factors for stroke. BN model with MMHC algorithm not only allows for a complicated network relationship between risk factors and stroke, but also could achieve stroke risk prediction through Bayesian reasoning, outshining traditional Logistic regression model. This study suggests that BN model boasts great prospects in risk factor detection for stroke.

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.

Learning Bayesian network structure with immune algorithm

Bayesian networks have become a popular knowledge representation scheme for probabilistic knowledge. One of the main challenges in Bayesian networks structure learning is the development of inductive learning techniques that scale up to large and possibly physically distributed data sets. We consider an approach to learning the structure of BN from distributed data. This is based on the collective learning strategy, where a local structure is obtained at each site and the global structure is obtained by cross learning and combining. Local learning is used to identify the local structure of local nodes and local links of cross nodes from local sample data sets. Cross learning can find the entire cross-links of cross nodes. Combined together, the local BNs and BN learnt from cross learning and removes any extra local links. We use the collective learning algorithm in distributed flood decision supporting system. The result shows that the Bayesian network structure is the same compare the collective learning algorithm from distributed data sets with learning from concentrated data sets. And meanwhile the collective learning algorithm is more efficient than transmitting all samples to a central site.

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.

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.

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.

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.