Hybrid Uncertainty Bayesian Networks Learning Model And Implementation By R

Bayesian networks can easily deal with inference problems between determinant variables,but not the random and fuzzy variables. Aiming at solving the problem of general Bayesiannetworks can’t deal with inference problems involving random and fuzzy variables, this articleproposes a new learning method called hybrid uncertainty Bayesian networks to figure out thiskind of issues which contains random and fuzzy cause and effect inference. Main researchcontents are as follows:(1) In this paper, we apply k-means cluster algorithm of fuzzy subsets partitioning todiscrete continuous variables, and then obtain the center and width of fuzzy subsets bysamples’ distribution characteristics. We use membership functions to figure the degree ofbelongingness about sample values to subsets. By this way, we firstly discrete the continuousvariables then produce a series of new samples for building a hybrid Bayesian networks.(2) This article proposes a fuzzy hybrid events filtering algorithm which can delete thosecombination events with membership degree below some threshold and helps to improve thelearning performance of hybrid Bayesian networks. Because there are lots of hybrid combinedevent after discretization for sample data, the fuzzy hybrid events filtering algorithm cansignificantly reduce space complexity and time complexity of hybrid Bayesian networks. Onthe other hand, the conditional probability tables of hybrid Bayesian networks containdeterminate variables and fuzzy variables and employs common probability and fuzzyprobability as networks’ parameters which subject to specific standardizing requirements.(3) Since the data samples of hybrid Bayesian networks are hybrid events of fuzzy subsetsin continuous variables and discrete values in discrete variables, this article employsgeneralized Max Likelihood Estimate method and Bayesian Estimate method for parameterslearning to fit this type of data samples. In this paper, we provide regular definitions for someconcepts like fuzzy subsets entropy and fuzzy subsets mutual information. By those definitions,we prove the information inequality in the condition of standardized parameters which istheoretical foundation of constraint-based algorithms for structure learning. According to theexisting Bayesian score criteria, this text imposes restrictions on the two constraint conditions of K2algorithm and the three searching operators of hill-climbing algorithm, and then obtainsthe K2algorithm and hill-climbing algorithm for structure learning of hybrid Bayesiannetworks.Based on the theory of hybrid Bayesian networks, this article utilizes R software as theprogramming platform, invokes the package named bnlearn to implement the process of hybridBayesian networks learning. The process includes data discretizing, hybrid events filtering,parameters learning, structure learning, and Bayesian networks inferring and classifying. Weconclude that hybrid Bayesian network has the advantage of dealing with the fuzzy andrandom uncertainty inference problems.