Research On Optimization Algorithm Based On Probabilistic Graph Model

Now as blowout general information explosion era, a large amount of data and complex network system filled in around us, find an effective analysis method, set up a feasible mathematical model, found a kind of new way of thinking, for us to handle complex data. Analysis of existing data, find and discover the rules behind the data,through the data to explore the nature of things has important significance.So graph model also arises at the historic moment, the graph model is the product of the organic combination of probability theory and graph theory. It can not only show the structural information of the problem in graph theory, but also to maintain the related properties of statistics has a good applicability. This greatly reduced the we calculate the problem complexity, improve the efficiency of our work,so that people can put the application of probability theory in machine learning, causal inference, artificial intelligence and other fields.Around the basic knowledge of graph model, introduced on Markov network and Bayesian network parameters of maximum likelihood estimation are studied, get the parameters in two cases of maximum likelihood representation, to Markov network of joint distribution and marginal distribution are studied. The idea of using variable elimination, a precise algorithm; but when the problem size is large and the computation of the algorithm will become large, no polynomial time algorithm,through the introduction of the concept of information communication, given the the a approximation algorithm. By introducing the concept of prime blocks, the structure decomposition algorithm of graph model is studied, and an effective algorithm to reduce the dimension of the graph model is presented, which can reduce the complexity of the problem.