最大熵分位值估计及其对偶型优化解法
发布时间：2019-04-23 15:45
【摘要】：针对经典最大熵分位值估计中拉格朗日系数计算目前存在高度非线性、计算结果精度不高或有时难以收敛等问题,提出了一种对偶型-逐次寻优的方法.基于拉格朗日对偶法,推导建立了含有拉格朗日系数优化函数的对偶表达式;在此基础上,基于样本的概率权重矩约束,提出了逐次寻优算法.针对几种常见的概率分布类型和一种较为复杂的概率分布类型,采用对偶型最大熵方法和经典最大熵方法对其概率累积函数和分位值进行计算对比分析表明:对偶型最大熵分位值估计不仅具有非线性程度低、形式简单,而且对偶型-逐次寻优的方法具有比较高的计算精度,优化迭代的收敛性好等特点.
[Abstract]:In order to solve the problems of high nonlinearity in Lagrangian coefficient calculation in classical maximum entropy estimation, the accuracy of calculation results is not high or sometimes it is difficult to converge. A dual-order optimization method is proposed in this paper. Based on the Lagrangian dual method, the dual expression with Lagrangian coefficient optimization function is derived, and based on the constraint of probability weight moment of samples, a successive optimization algorithm is proposed. For several common types of probability distribution and a more complex type of probability distribution, The dual maximum entropy method and the classical maximum entropy method are used to calculate and compare the probability cumulative function and the quantitive value. The results show that the dual maximum entropy estimation is not only of low nonlinearity, but also simple in form. Moreover, the dual-successive optimization method has the characteristics of high calculation precision and good convergence of optimization iteration.
【作者单位】： 南京航空航天大学能源与动力学院;
【分类号】：TB114.3
本文编号：2463598
[Abstract]:In order to solve the problems of high nonlinearity in Lagrangian coefficient calculation in classical maximum entropy estimation, the accuracy of calculation results is not high or sometimes it is difficult to converge. A dual-order optimization method is proposed in this paper. Based on the Lagrangian dual method, the dual expression with Lagrangian coefficient optimization function is derived, and based on the constraint of probability weight moment of samples, a successive optimization algorithm is proposed. For several common types of probability distribution and a more complex type of probability distribution, The dual maximum entropy method and the classical maximum entropy method are used to calculate and compare the probability cumulative function and the quantitive value. The results show that the dual maximum entropy estimation is not only of low nonlinearity, but also simple in form. Moreover, the dual-successive optimization method has the characteristics of high calculation precision and good convergence of optimization iteration.
【作者单位】： 南京航空航天大学能源与动力学院;
【分类号】：TB114.3
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