一种基于信息几何的支持向量回归模型选择新标准

A New Model Selection Criterion for Support Vector Regression Based on Information Geometry

针对现有模型选择标准无法对支持向量回归(SVR)模型选择过程给出明确几何意义的弱点,提出了一种基于信息几何理论的模型选择新标准.它将模型空间看成是一个流形,将模型复杂度等价于其所能覆盖的概率分布个数,模型拟合度则视为样本的真实分布与模型分布之间的分散度,由此直观地解释了SVR的求解过程,并明确了模型选择的几何意义.

Since the entire extent model selection criterions for Support Vector Regression （SVR） were short of clear understanding of geometric significances, a new model selection criterion based on the theory of information geometry was proposed in this paper. The new criterion regarded the model space as a manifold and computed the complexity by counting the number of the distinguishable probability distributions that a model can generate and estimated the fitness by using the divergence between the true distribution and model distribution. Therefore, it explained the SVR intuitionally and gave the process of model selection with a clear geometric significance.