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

• 成果类型: Article
• 署名作者: Wu, Leqin; Qiu, Xing; Yuan, Ya-xiang; Wu, Hulin
• 署名单位: Jinan University; University of Rochester; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Texas System; University of Texas Health Science Center Houston
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1423074
• 发表日期: 2019
• 页码: 657-667
• 关键词: time-varying coefficients; saccharomyces-cerevisiae; bayesian-approach; dynamic-models; kinetochore; inference; algorithm; networks; genes; error

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.