一种基于广义KL距离和几何曲率的模型选择准则  

A New Model Selection Criterion Based on Kullback-Leibler Information Divergence and Geometric Curvature

作　　者：杨坚[1] 罗四维[1] 刘蕴辉[1] 

机构地区：[1]北京交通大学计算机与信息技术学院计算机研究所,北京100044

出　　处：《电子学报》2005年第12期2272-2277,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60373029);博士点基金(No.20020004020)

摘　　要：模型选择的目标就是识别产生给定数据的模型，通常模型的好坏由模型的泛化能力来度量，而泛化能力包含模型对给定数据的拟合度和模型自身复杂度两个方面，本文从信息几何的观点使用定义在流形上的广义KL距离来度量模型的拟合度；另一方面从微分几何的观点用曲率的概念来度量模型的内在复杂度；因此，拟合度和复杂度的表示都具有在参数变换下保持不变的特点，通过理论分析，我们证明了用于表示模型预测能力的未来残差与模型固有曲率的关系，由此提出一种新的基于广义KL距离和曲率的模型选择准则KILCIC．该准则不仅考虑了样本大小、参数个数和函数形式等影响复杂度的因素，而且具有非常清晰直观的几何意义，实验结果表明该方法的有效性．The goal of model selection is to identify the model that generated the data. Goodness of a model is measttred using generalizability, which takes two opposite aspects： goodness of fit and model complexity into account, we use generalized KL-divergence defined on the manifold to measure the goodness of fit, and use the conception of curvature from the point of view of differential geometry to explore the intrinsic model complexity that is flee of reparametrization; through theoretical analysis, we proved the future residual that is qualified to measure the generalizability can be expressed by using the intrinsic curvature army of model,from which we propose a new model selection criterion KL-divergence and curvature information criterion with very clear and intuitive geometric understanding of model selection. Experimental results reveal its validity.

关 键 词：模型选择 广义Kullback-Leibler距离 曲率立体阵 解轨迹 未来残差 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]