比例风险模型下参数极大似然估计的自适应优化算法及其改进算法  

AUTO-ADAPTED OPTIMIZATION ALGORITHMS AND ITS IMPROVED ALGORITHM FOR PARAMETER MAXIMUM LIKELIHOOD ESTIMATION UNDER THE PROPORTIONAL HAZARDS MODEL

作　　者：林文强 LIN Wen-qiang(School of Mathematics and Statistics Wuhan University,Wuhan,430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2020年第3期363-378,共16页Journal of Mathematics

摘　　要：自适应优化算法可避免很多常用数值算法遭遇的困难,例如:高维矩阵求逆问题,初值选取的问题和算法的收敛问题等等.因此,自适应优化算法得到了迅速的发展和广泛的应用,本文研究了比例风险模型下的自适应优化算法.首先利用三种自适应优化算法-Adam算法、RMSprop算法、Adagrad算法求解比例风险模型下的参数估计数值解问题,获得了自适应算法的计算优良性.然后,推广了比例风险模型下的Adam算法的研究,发展了一种改进的Adam算法,进一步提高了算法的计算速度并展现了其计算优势.The adaptive optimization algorithm can avoid the difficulties encountered by many commonly used numerical algorithms,such as high-dimensional matrix inversion problem,initial value selection problem and algorithm convergence problem.Therefore,the adaptive optimization algorithm was rapidly developed and widely applied.This paper studies the adaptive optimization algorithm under the proportional risk model.First,three adaptive optimization algorithms,Adam algorithm,RMSprop algorithm and Adagrad algorithm,are used to solve the numerical solution of parameter estimation under the proportional risk model,and the computational superiority of the adaptive algorithm is obtained.Then,the research on the Adam algorithm under the proportional risk model is extended and an improvement is developed.The Adam algorithm further improves the computational speed of the algorithm and demonstrates its computational advantages.

关 键 词：Adam算法 RMSprop算法 Adagrad算法 比例风险模型 

分 类 号：O212.2[理学—概率论与数理统计]