Research On Parameter Learning Algorithms For Monotonic Bayesian Networks

With the increasing attention and application of Artificial Intelligence technology,Bayesian networks,as a classical Machine Learning algorithm,has been widely used in uncertain modeling and probabilistic reasoning because of its advantages of accurate probabilistic reasoning and clear semantic expression.Parameter learning of Bayesian networks is an important issue and challenge in Bayesian networks research and application.Accurate learning of network parameters has an important impact on the accuracy and interpretability of Bayesian networks model.In many applications in the real world,the sample data that people can collect is limited.Therefore,how to improve the accuracy of network parameter learning is an important research topic for limited training sample data.At the same time,some scholars have shown that monotony exists widely in various fields of life.In many problems,there is a certain monotonic relationship between attributes and attributes,attributes and decision-making.This paper focuses on the parameter learning of Bayesian networks with limited training sample data.Based on the monotonic relationship between Bayesian networks nodes and the monotonicity of Bayesian networks,the main research work and innovations are as follows:(1)In this paper,we propose a pure data-driven monotonic Bayesian networks parameter learning method.Firstly,the method automatically discriminates the monotonic relationship between network nodes by monotonicity metrics.Then,based on the monotonic definition of Bayesian networks,the monotonic inequality constraints of the network node conditional probability table are constructed,and the Bayesian networks parameter learning is transformed into a constrained optimization problem.Finally,the problem is solved by different methods.Experiments on the open standard Bayesian networks libraries and real classification datasets demonstrate the effectiveness of the proposed method on the limited training sample data.(2)For the samples obtained in reality with missing data,an improved EM algorithm with monotonic constraints is proposed.The improved EM algorithm converts the maximal expected likelihood function into a constrained optimization problem by adding parameter monotonicity inequality constraints based on the Bayesian networks monotonicity definition in the M step of each iteration.The improved EM algorithm makes the network parameters obtained in the M step satisfy the monotonic relationship between the network nodes,and reduces the dependence of the EM algorithm on the training sample data volume.Experimental results on datasets with different missing rates show that the improved EM algorithm improves the accuracy of parameter learning.