A Joint Estimation Approach to Sparse Additive Ordinary Differential Equations

TL;DR

This paper introduces a joint estimation method for sparse additive ODEs that handles non-Gaussian data, unifies likelihood and regularization, and demonstrates superior estimation and structure identification performance.

Contribution

It proposes a novel unified estimation approach for generalized sparse additive ODEs with non-Gaussian observations, including a convergent optimization algorithm.

Findings

Superior estimation accuracy demonstrated in simulations

Effective sparse structure identification in applications

Algorithm with proven global convergence

Abstract

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.