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報告題目：The normalized expectation-maximization (N-EM) algorithm  (正則化的EM算法)

主講人：田國梁教授（南方科技大學(xué)）

時間：2021年11月18日（周四）10:00 a.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會議室      

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

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. [This is a joint work with Xuanyu LIU, Kam Chuen YUEN and Chi ZHANG]

主講人簡介：

田國梁博士曾在美國馬里蘭大學(xué)從事醫(yī)學(xué)統(tǒng)計(jì)研究六年, 在香港大學(xué)統(tǒng)計(jì)與精算學(xué)系任副教授八年, 從2016年6月至今在南方科技大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系任教授,、博士生導(dǎo)師,、副系主任,。他目前的研究方向?yàn)?0, 1) 區(qū)間上連續(xù)數(shù)據(jù)以及成份數(shù)據(jù)的統(tǒng)計(jì)分析,、多元零膨脹計(jì)次數(shù)據(jù)分析, 在國外發(fā)表140篇SCI論文,、出版3本英文專著,、在科學(xué)出版社出版英文教材1本,。他是四個國際統(tǒng)計(jì)期刊的副主編。主持國自科面上項(xiàng)目二項(xiàng),、參加國自科重點(diǎn)項(xiàng)目并主持深圳市穩(wěn)定支持面上項(xiàng)目各一項(xiàng),。