极大似然最大熵概率密度估计及其优化解法

发布时间：2018-04-08 23:08

本文选题：概率密度估计　切入点：可靠性　出处：《南京航空航天大学学报》2017年01期

【摘要】：针对经典最大熵概率密度估计中拉格朗日乘子计算目前存在高度非线性、计算精度不高或有时难以收敛等问题,提出了一种"最大似然+逐次优化"的方法。基于最大似然估计法,推导建立了简化的拉格朗日优化函数;在此基础上,基于样本原点矩约束,提出了逐次寻优算法。根据优化过程不稳定,重新推导了拉格朗日乘子的线性变换公式,避免矩阵求逆运算引起的奇异现象。针对几种常见的概率分布类型及可靠性问题,采用极大似然最大熵概率密度估计法与经典型最大熵概率密度估计法分别计算概率密度及可靠度的对比表明:极大似然最大熵概率密度估计法的优化函数非线性程度低,形式简单,而且"极大似然最大熵概率密度估计+逐次优化法计算"精度高,收敛性好。
[Abstract]:Aiming at the problems of Lagrangian multiplier calculation in the classical maximum entropy probability density estimation, such as high nonlinearity, low accuracy or difficulty in convergence, a method of "maximum likelihood successive optimization" is proposed.Based on the maximum likelihood estimation method, a simplified Lagrange optimization function is derived, and a sequential optimization algorithm is proposed based on the origin moment constraint of the sample.According to the instability of the optimization process, the linear transformation formula of Lagrange multiplier is rederived to avoid the singularity caused by matrix inversion.Aiming at several common probability distribution types and reliability problems,The comparison between the maximum likelihood entropy probability density estimation method and the classical maximum entropy probability density estimation method shows that the maximum likelihood maximum entropy probability density estimation method has low nonlinear degree of optimization function.The form is simple and the "maximum likelihood entropy probability density estimation successive optimization method" has high accuracy and good convergence.
【作者单位】：南京航空航天大学能源与动力学院;
【基金】：国家自然科学基金(51205190)资助项目
【分类号】：O212.1

【相似文献】