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

doi:10.1080/01621459.2017.1423074

	Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach
	Wu, Leqin 1; Qiu, Xing 2; Yuan, Ya-xiang3 ; Wu, Hulin 4
	2019-04-03
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	114 期号:526 页码:657-667
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.
关键词	Complex system Eigenvalue updating algorithm High dimension Matrix-based variable selection Ordinary differential equation Separable least squares
DOI	10.1080/01621459.2017.1423074
语种	英语
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
WOS类目	Statistics & Probability
WOS记录号	WOS:000472559400013
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34944
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 Rochester, Dept Biostat & Computat Biol, Rochester, NY USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 4.Univ Texas Hlth Sci Ctr Houston, Dept Biostat, Houston, TX 77030 USA
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.