Abstract
Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot exploit the sparsity. On the other hand, in gene regulatory network inference problems, the parameters to be estimated often exhibit sparse structure. In this paper, a regularized expectation-maximization (rEM) algorithm for sparse parameter estimation in nonlinear dynamic systems is proposed that is based on the maximum a posteriori (MAP) estimation and can incorporate the sparse prior. The expectation step involves the forward Gaussian approximation filtering and the backward Gaussian approximation smoothing. The maximization step employs a re-weighted iterative thresholding method. The proposed algorithm is then applied to gene regulatory network inference. Results based on both synthetic and real data show the effectiveness of the proposed algorithm.
Highlights
The dynamic system is a widely used modeling tool that finds applications in many engineering disciplines
We focus on the sparse parameter estimation problem instead of the sparse state estimation problem
We show the inference results of the parameter and the state estimation provided by the unscented Kalman filter (UKF) based on the model using the inferred parameters
Summary
The dynamic system is a widely used modeling tool that finds applications in many engineering disciplines. The expectation-maximization (EM) algorithm has been applied to solve the sparse state estimate problem in dynamic systems [8,9,10,11,12]. We consider a general nonlinear dynamic system, where both the state equation and the measurement equation are parameterized by some unknown parameters which are assumed to be sparse. We propose a regularized expectation-maximization (rEM) algorithm for sparse parameter estimation in nonlinear dynamic systems. To illustrate the proposed sparse parameter estimation method in dynamic systems, we consider the gene-regulatory network inference based on gene expression data. We discuss the procedures for computing the densities p(xk, xk−1|Y K , θ ) and p(xk|Y K , θ ), the integrals, and the minimization in (8)
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