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Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach
Wu, Leqin1; Qiu, Xing2; Yuan, Ya-xiang3; Wu, Hulin4
2019-04-03
Source PublicationJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN0162-1459
Volume114Issue:526Pages:657-667
AbstractOrdinary 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.
KeywordComplex system Eigenvalue updating algorithm High dimension Matrix-based variable selection Ordinary differential equation Separable least squares
DOI10.1080/01621459.2017.1423074
Language英语
Funding ProjectNIH[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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000472559400013
PublisherAMER STATISTICAL ASSOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34944
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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