10月13日 南方科技大学田国梁教授学术报告

发布时间:2017-09-29浏览次数:45

报 告 人:田国梁 教授(南方科技大学)

报告题目:An assembly and decomposition (AD) approach for constructing separable minorizing functions in a class of MM algorithms (在一类MM算法中, 建立可分离的受控函数的一个新的组装与分解方法)

报告时间:2017年10月13日(周五)下午16:30

报告地点:静远楼1506报告厅

报告人简介:

    田国梁,现任南方科技大学数学系统计学正教授、博士生导师。田教授于1988年获得武汉大学统计学硕士学位、于1998年获得中国科学院应用数学研究所统计学博士学位。从1998至2002年, 他分别在北京大学概率统计系和美国田纳西州孟斐斯市的 St. Jude 儿童研究医院生物统计系从事博士后研究, 2002年至2008年他在美国马里兰大学Greenbaum 癌症中心任 Senior Bio-statistician。2008年至2016年他在香港大学统计及精算学系任副教授、博士生导师。田教授是国际统计学会 (ISI) 当选会员, 他担任 Computational Statistics & Data Analysis, Statistics and Its Interface 等四个国际统计学杂志的副主编。他主要的研究领域是生物统计, 社会统计和计算统计。目前的研究方向包括多元零膨胀计数数据分析、不完全分类数据分析和敏感性问题抽样调查。到目前为止,他在国际顶尖生物统计学期刊 Statistical Methods in Medical Research, Statistics in Medicine, Biometrics 发表论文13篇, 在其他统计学期刊发表论文80余篇。他在美国著名出版社 John Wiley & Sons 和 Chapman & Hall/CRC 出版英文专著3部, 且在中国的科学出版社出版中文专著1部和英文教科书1本。2017年度他的研究课题<<MM算法中的几类问题之研究及其应用>>获得国家自然科学基金面上项目的5A资助。

报告摘要:

    The minorization-maximization (MM) principle provides an important and useful tool for optimization problems and has a broad range of applications in statistics because of its conceptual simplicity, ease of implementation and numerical stability. A key step in developing an MM algorithm is to construct an appropriate minorizing function. This is quite challenging to many practitioners as it has to be donecase by case and its success often involves and heavily depends on a clever and specific use ofJensen's inequality or a similar kind. To address this problem, in this paper, we propose a new assembly and decomposition (AD) approach which successfully constructs separable minorizing functions in a general class of MM algorithms. The AD approach constructs a minorizing function by employing two novel techniques which we refer to as the assembly technique (or A-technique) and the decomposition technique (or D-technique), respectively.  The A-technique first introduces the notions of assemblies and complemental assembly, consisting of several families of concave functions that have arisen in numerous applications. The D-technique then cleverly decomposes the high-dimensional objective function into a sum of one-dimensional functions to construct minorizing functions as guided and facilitated by the A-technique. We demonstrate the utility of the proposed approach in diverse applications which result in novel algorithms with theoretical and numerical advantages.  Extensive numerical studies are provided to assess its finite-sample performance. Further extensions of the AD techniques are also discussed.