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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.
In this paper, Bayesian classification error approximation algorithm for different distributions of many kinds of problems under normal distribution conditions is proposed. The algorithm is an iterative algorithm based on the upper bound. The upper bound of Bayes error probability is described by segmenting the integral field of the minimum error probability, The methods of statistical inequality and Taylor expansion are applied to different integration domains. The constructed iterative algorithm searches for the best approximation parameters and reduces the approximate error of the upper bound of the error probability so that the upper bound sufficiently approximates the true error probability. The algorithm consists of three iterations Which is composed of the parameters of the group with the lowest error probability upper bound by hierarchical search.The analysis and examples show that this iterative algorithm makes the upper bound Bayes classification error a simple and practical analytical method.