Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach

doi:10.1080/01621459.2017.1423074

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach
	Wu, Leqin 1; Qiu, Xing 3; Yuan, Ya-xiang4 ; Wu, Hulin 2
刊名	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
	2019-04-03
卷号	114 期号:526 页码:657-667
关键词	Complex system Eigenvalue updating algorithm High dimension Matrix-based variable selection Ordinary differential equation Separable least squares
ISSN号	0162-1459
DOI	10.1080/01621459.2017.1423074
英文摘要	Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a "Big System" with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that the proposed matrix-based SLS method could be used to estimate the coefficient matrix more accurately and perform variable selection for a linear ODE system with thousands of dimensions and millions of parameters much better than the direct least squares method and the vector-based two-stage method that are currently available. We applied this new method to two real datasets-a yeast cell cycle gene expression dataset with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters-to illustrate the utility and numerical performance of the proposed parameter estimation and variable selection method for big systems in practice. Supplementary materials for this article are available online.
资助项目	NIH[RO1 AI087135] ; Respiratory Pathogens Research Center (NIAID)[HHSN272201200005C] ; University of Rochester CTSA award from National Center for Advancing Translational Sciences of the National Institutes of Health[UL1 TR002001] ; University of Rochester Center for AIDS Research[NIH 5 P30 AI078498-08] ; National Natural Science Foundation of China[11526096] ; National Natural Science Foundation of China[11601185]
WOS研究方向	Mathematics
语种	英语
出版者	AMER STATISTICAL ASSOC
WOS记录号	WOS:000472559400013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34943]
专题	计算数学与科学工程计算研究所
通讯作者	Wu, Hulin
作者单位	1.Jinan Univ, Dep Math, Guangzhou, Guangdong, Peoples R China 2.Univ Texas Hlth Sci Ctr Houston, Dept Biostat, Houston, TX 77030 USA 3.Univ Rochester, Dept Biostat & Computat Biol, Rochester, NY USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Wu, Leqin,Qiu, Xing,Yuan, Ya-xiang,et al. Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2019,114(526):657-667.
APA	Wu, Leqin,Qiu, Xing,Yuan, Ya-xiang,&Wu, Hulin.(2019).Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,114(526),657-667.
MLA	Wu, Leqin,et al."Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 114.526(2019):657-667.