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Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks
Author(s) -
Xue Hongqi,
Wu Shuang,
Wu Yichao,
Ramirez Idarraga Juan C.,
Wu Hulin
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7669
Subject(s) - ode , nonlinear system , curse of dimensionality , gene regulatory network , ordinary differential equation , computer science , mathematical optimization , smoothing , independence (probability theory) , mathematics , artificial intelligence , differential equation , biology , statistics , gene , quantum mechanics , computer vision , biochemistry , mathematical analysis , gene expression , physics
Mechanism‐driven low‐dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low‐dimensional mechanism‐based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large‐scale nonlinear networks from time‐course gene expression data remains an unresolved issue. Here, we use high‐dimensional nonlinear additive ODEs to model GRNs and propose a 4‐step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2‐stage smoothing‐based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non‐polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae .