Zhang Nan, Nanshan Muye, Cao Jiguo
School of Data Science, Fudan University, Shanghai, China.
Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, Canada.
Stat Comput. 2022;32(5):69. doi: 10.1007/s11222-022-10117-y. Epub 2022 Aug 23.
Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where observations are allowed to be non-Gaussian. The new method is unified with existing collocation methods by considering the likelihood, ODE fidelity and sparse regularization simultaneously. We design a block coordinate descent algorithm for optimizing the non-convex and non-differentiable objective function. The global convergence of the algorithm is established. The simulation study and two applications demonstrate the superior performance of the proposed method in estimation and improved performance of identifying the sparse structure.
常微分方程（ODEs）在实际应用中被广泛用于刻画复杂系统的动态特性。在本文中，我们针对广义稀疏加性常微分方程提出了一种新颖的联合估计方法，该方法允许观测值为非高斯分布。通过同时考虑似然性、常微分方程保真度和稀疏正则化，新方法与现有的配置方法实现了统一。我们设计了一种块坐标下降算法来优化非凸且不可微的目标函数，并证明了该算法的全局收敛性。仿真研究和两个应用实例展示了所提方法在估计方面的卓越性能以及在识别稀疏结构方面的改进效果。
