Parameters Estimation of RBF-AR Model Based on EM and Variable Projection Algorithm

Abstract

The radial basis function network-based on state-dependent autoregressive (RBF-AR) model is widely used in the modeling and prediction of nonlinear time series. The parameters estimation of RBF-AR model is a typical separable nonlinear least squares problem. Variable Projection (VP) algorithm is an efficient algorithm to solve this problem. However, The actual solution may be a ill-conditioned problems, and the classical VP algorithm may have a over-fitting phenomenon. which makes the estimated linear parameters too large, resulting in poor generalization performance of the model. Aiming at this kind of problem, this paper uses expectation maximization (EM) algorithm to automatically select the appropriate regularization parameters, and combines with the high efficiency of VP algorithm to estimate parameters, proposes an effective algorithm for solving the separable nonlinear least squares problem — EM-VP algorithm. The numerical experiments show that the EM-VP algorithm can select the appropriate regularization parameters, so that the estimated model has better generalization performance.