Rudimentary结构等价性及其应用研究

Bayesian网的结构学习是Bayesian网研究的难点之一．当问题中的变量较多时,通过结构学习得到的网络结构往往不具有唯一性．文中通过对Bayesian网结构等价性的研究,提出了Rudimentary结构等价性定理,并给出了该定理的证明．该等价性定理为提高结构学习的速度和优化Bayesian网的结构提供了理论依据．实验结果表明该定理具有较好的实用价值．

Research on the Theory and Application of Rudimentary Structure Equivalence

Bayesian Network is a kind of probabilistic graphical model, which can express the conditional probability into graphical formula. Structural learning and parameter learning of Bayesian Networks are two main factors of it's application. The structural learning process maybe time consuming when the number of variables arise, and the results can be in different formulas , which are equivalence class actually. Theory of the equivalence of rudimentary structure is presented and proved, which shows that the Bayesian Networks of the same rudimentary structure are of the same description length to the database. And this theory can improve the efficiency of structure learning. Experimental results show that it is practical to the refinement of the ALARM network.