روش به روز کردن پارامتر شبکه های بیزی براساس برآوردهای محتمل حداکثری Bayesian network’s parameter update method based on maximum likelihood estimates

I. INTRODUCTION After a BN’s topological structure is constructed, valuing its probability parameters is called as parameter learning. Bayesian arithmetic, Maximum Likelihood Estimates (MLE) and Adaptive Probabilistic Networks(APN) are the most familiar parameter learning algorithm. Bayesian algorithm [1] calculates all the possible value of the parameters in the given topological structure and seek the parameters’ value with maximum posterior probability on the condition of topological structure and dataset are both known. MLE is put forward by Spiegelhalter [2], and it is considered as the especial example of Bayesian arithmetic. When parameters’ prior information is neglected entirely, Bayesian arithmetic is converted into MLE. Russell [3]1995 has brought forward a parameter learning method based gradient degression, namely APN. This method takes the samples in the date set as evidence and propagate the evidence to all the topological structure. In order to obtain the parameters of the DAG with maximal probability contained in the dataset, it updates the parameters adopting the method of gradient degression. This paper, probability parameters updating method for Bayesain network with fixed structure and initial probability parameters is discussed, when new data set is available. It should reserve the original probability parameters as much as possible and also reflect the probability distribution contained in data set furthest. An outline of the remainder of the paper is as follows. In Section 2, we discuss the principle of parameters updating method based on MLE. In Section 3, BN’s parameters updating algorithm for complete data set is discussed. In Section 4, we discuss parameter updating algorithm for incomplete data set. In Section 5, a case study is put forward to show how the algorithm works. Finally, in Section 6, we make a summarizer for this paper. II. PROBABILITY PARAMETER UPDATING PRINCIPLE The update of BN parameters needs to meet two requirements: One is to improve the parameters to fit the new data set, and the other is to keep the probability parameter information contained in the original network as much as possible. Therefore, there is a need to strike a balance between these two requirements. The BN is known as BN VE ( , ) , and 1 { ,…, ,…, } VV V V i n is the set of all nodes in the network, and E is the set of all the arcs in the network. Suppose the set of probability parameters of the conditional probability of each node in the network is T T { } ijk . The updating of BN parameters is based on the new data set D , updating the probability parameter T to T T { } ijk , so that T T { } ijk can be consistent with the original network parameters as much as possible while reflecting the potential probability distribution in the new data set.