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Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling

Author

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  • Hulin Wu
  • Tao Lu
  • Hongqi Xue
  • Hua Liang

Abstract

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group least absolute shrinkage and selection operator (LASSO) techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Suggested Citation

  • Hulin Wu & Tao Lu & Hongqi Xue & Hua Liang, 2014. "Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 700-716, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:700-716
    DOI: 10.1080/01621459.2013.859617
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    Cited by:

    1. Sang, Peijun & Wang, Liangliang & Cao, Jiguo, 2019. "Weighted empirical likelihood inference for dynamical correlations," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 194-206.
    2. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Yunlong Nie & LiangLiang Wang & Jiguo Cao, 2017. "Estimating time‐varying directed gene regulation networks," Biometrics, The International Biometric Society, vol. 73(4), pages 1231-1242, December.
    4. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
    5. Mu Niu & Benn Macdonald & Simon Rogers & Maurizio Filippone & Dirk Husmeier, 2018. "Statistical inference in mechanistic models: time warping for improved gradient matching," Computational Statistics, Springer, vol. 33(2), pages 1091-1123, June.
    6. Zhang, Tingting & Sun, Yinge & Li, Huazhang & Yan, Guofen & Tanabe, Seiji & Miao, Ruizhong & Wang, Yaotian & Caffo, Brian S. & Quigg, Mark S., 2020. "Bayesian inference of a directional brain network model for intracranial EEG data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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