Bayes分类误差逼近算法

APPROXIMATION ALGORITHM FOR BAYES CLASSIFICATION ERROR

本文提出在正态分布条件下面向不同分布多类问题的Bayes分类误差逼近算法.本算法是基于上界逼近的迭代算法.Bayes错误概率上界的描述通过对最小错误概率的积分域进行分割,对不同积分域采用统计不等式及Taylor展开等方法实现.构造的迭代算法搜索最佳的逼近参数,减小错误概率上界的近似误差,使得上界充分逼近真实的错误概率.该算法由三重迭代组成.通过分层搜索得到错误概率上界最小的参数组.通过分析和实例表明这一迭代算法使得上界型Bayes分类误差成为简便、实用的分析手段.

A new recursive algorithm based on approximation of upper bound for Bayes classification error normal multidistribution and multiclass problem oriented is presented. The upper bound of error probability can be close to Bayes error by dividing the integral domain applied inequality and Taylor formula. This algorithm is threefold with the parameter number of integral domain ' n ' , ' s ' and length of integral domain ' a ' respectively. The optimal set of these parameters can be searched hierarchically to minimize the upper bound of error probability. The theoretical analysis and experimental results show that the performance of proposed algorithm is superior to Chernoff bound and make the upper bound of error probability become a convenient and practical method.