暨南经院学术系列活动之
统计学系列 Seminar 第89期
主题：The normalized expectation-maximization (N-EM) algorithm (正则化的EM算法)
主讲人：田国梁教授（南方科技大学）
主持人：姜云卢（威尼斯欢迎你welcome）
会议时间：2021 年 11 月 12 日（周五）下午16:00-17:00
会议地点：威尼斯欢迎你welcome（中惠楼）102会议室
摘要
Although the expectation-maximization (EM) algorithm is a powerful optimization tool in statistics, it can only be applied to missing/incomplete data problems or to problems with a latent-variable structure. It is well known that the introduction of latent variables (or the data augmentation) is an art; i.e., it could only be done case by case. In this paper, we propose a new algorithm, a so-called normalized EM (N-EM) algorithm, for a class of log-likelihood functions with integrals. As an extension of the original EM algorithm, the N-EM algorithm inherits all advantages of EM-type algorithms and consists of three steps: normalization step (N-step), expectation step (E-step) and maximization step (M-step), where the N-step is to construct a normalized density function (ndf), the E-step is to compute a well-established surrogate Q-function and the M-step is to maximize the Q-function as in the original EM algorithm. The ascent property, the best choice of the ndf, and those N-EM algorithms with a difficult M-step are also explored. By multiple real applications, we have shown that the N-EM algorithm can solve some problems which cannot be addressed by the EM algorithm. Next, for problems to which the EM can be applied (often case by case), the N-EM algorithm can be employed in a unified framework. Numerical experiments are performed and convergence properties are also established.
★主讲人简介★
田国梁博士曾在美国马里兰大学从事医学统计研究6年、在香港大学统计与精算学系任副教授八年, 从2016年6月至今在南方科技大学统计与数据科学系任教授、博士生导师、副系主任。他目前的研究方向为(0, 1) 区间上连续数据以及成份数据的统计分析、多元零膨胀计次数据分析, 在SCI收录期刊发表论文140篇、出版英文专著3本、出版英文教材1本。他是四个统计学国际期刊的副主编。主持国家自然科学基金面上项目2项、参与国家自然科学基金重点项目1项、主持深圳市稳定支持面上项目1项。
