报告一题目:The normalized expectation-maximization (N-EM) algorithm (正则化的EM算法)

报告摘要：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]

报告时间：2021年12月22日14：30-15：20

报告地点：腾讯会议（581 312 792）

主办单位：统计学院

报告二题目:Squared normal model and its generalization for the analysis of skewed positive data (用平方正态模型及其推广来分析斜的且非负的数据)

报告摘要：To model skewed positive data with high kurtosis, this paper proposes, in the first time, a new squared normal (SQN) distribution, which is constructed by squaring the normal random variable with non-zero mean and non-unit variance. The SQN distribution can be regarded as an extension of the chi-squared distribution, which cannot be applied to directly modeling real-life data. Some distributional properties, parameter estimation methods and hypothesis testing are investigated for the SQN distribution itself and the corresponding regression model. Furthermore, a generalization to a squared skew-normal (SSN) distribution is proposed by incorporating an additional skew parameter, improving the flexibility of the model. Finally, simulation experiments are conducted and a real data set is analyzed to demonstrate the proposed methodologies. [This is a joint work with Chi ZHANG, Xuanyu LIU and Kam Chuen YUEN]

报告时间：2021年12月22日15：30-16：20

报告地点：腾讯会议（581 312 792）

主办单位：统计学院

专家简介：田国梁教授，曾在美国马里兰大学从事医学统计研究六年, 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, 在国外发表140篇SCI论文、出版3本英文专著、在科学出版社出版英文教材1本。他是四个国际统计期刊的副主编。主持国自然面上项目二项、参加国自然重点项目并主持深圳市稳定支持面上项目各一项。