Joint Learning of Model Parameters and Coefficients for Online Nonlinear Estimation

Abstract

We propose a novel online algorithm for efficient nonlinear estimation. Target nonlinear functions are approximated with “unfixed” Gaussians of which the parameters are regarded as (a part of) variables. The Gaussian parameters (scales and centers), as well as the coefficients, are updated to suppress the instantaneous squared errors regularized by the $\ell _{1}$ norm of the coefficients to enhance the model efficiency. Another point for enhancing the model efficiency is the multiscale screening method, which is a hierarchical dictionary growing scheme to initialize Gaussian scales with multiple choices. To reduce the computational complexity, a certain selection strategy is presented for growing the dictionary and updating the Gaussian parameters. Computer experiments show that the proposed algorithm enjoys high adaptation-capability and produces efficient estimates.