| As a product of the combination of probability theory and graph theory,graph model provides a method of combining prior knowledge into data mining process,and can qualitatively represent the probabilistic dependency of the problem domain into topological structure.Many classical multivariate probabilistic models,such as statistics,pattern recognition,machine learning and information theory,can be regarded as special cases of graph models.So far,most of the papers have studied the independence of different interpretations and some of the chain graph models under different interpretations.But at present,there are no different algorithms to explain the minimum independent graph of the chain graph.The main contribution of this paper is to give the minimum independent graph algorithm for the different models of the probability graph model in the case of a given variable order.In order to study some particular conditional independence structures which can not be solved by directed graph and undirected graph model,we combine the directed graph model with the undirected graph model,and establish a chain graph model with both directed edges and non directed edges.Based on the minimum independent graph algorithm known Bayesian networks on the graph model of independence relations,studied MVR interpretation,interpretation and interpretation of the three LWF AMP said the effective tracing algorithm under the chain graph model and independent graph algorithm,finally obtained the minimum independent graph model of different definitions below.The conditional independence of a chain graph varies with the change in the order of a given variable.The minimum independency of directed graph is studied and extended to the chain graph.A minimum independent graph is obtained by giving a variable order of chain diagram,and the algorithm to get the minimum independent graph is given.The application of the algorithm is introduced and its complexity and research prospect are discussed. |
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