证据框架与自由能框架  

Evidence Framework and Free Energy Framework

作　　者：陆晓峰[1] 郑南宁[1] 袁泽剑[1] 

机构地区：[1]西安交通大学电子与信息工程学院,西安710049

出　　处：《西安交通大学学报》2003年第2期167-170,174,共5页Journal of Xi'an Jiaotong University

基　　金：中国创新研究群体科学基金资助项目(60024301)；国家自然科学基金资助项目(60175006)．

摘　　要：在指出证据框架和自由能最小化方法等贝叶斯推理方法的局限性的前提下,通过对比证据框架的方法,提出了自由能框架的概念,将通常难以求解的自由能最小化过程分解成参数自由能最小化、超参数自由能最小化、模型参数自由能最小化等层次,在每个层次上调节参数、超参数和模型参数,使其后验分布与其真实分布之间的Kullback Leibler距最小,以使可变自由能逼近真实自由能.同时,保持其他层次上的参数、超参数和模型参数固定不变,以简化贝叶斯前馈神经网络的参数估计.应用自由能框架,对通常较难求解的贝叶斯支持向量回归机器的参数与超参数进行估计,推导出相应的计算公式,并验证了该方法的可行性与有效性.Some existing Bayesian inference methods, such as the evidence framework method and the free energy minimization method, have inherent limitations. A new concept named free energy framework is proposed by contrast with the evidence framework. The free energy minimization is often difficult to treat, so it is divided into several levels in the free energy framework, i.e. parameter free energy minimization, hyper parameter free energy minimization and model free energy minimization. At each level, the parameters, hyper parameters and model parameters are adjusted to minimize the KullbackLeibler divergence between their posteriors and real distributions so that the variable free energy can approach the real free energy. Simultaneousty, the parameters, hyper parameters and model parameters at the other levels keep unchanged to simplify the parameters estimation of Bayesian feed forward networks. An application of free energy framework on support vector regression machine parameters estimation is presented, and the corresponding formulas for selecting parameters and hyper parameters are derived to verify the feasibility and validity of this method.

关 键 词：支持向量机 自由能最小化 证据框架 自由能框架 贝叶斯推理 神经网络 参数估计 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]