Online model-selection and learning for nonlinear estimation based on multikernel adaptive filtering

We study a use of Gaussian kernels with a wide range of scales for nonlinear function estimation. The estimation task can then be split into two sub-tasks: (i) model selection and (ii) learning (parameter estimation) under the selected model. We propose a fully-adaptive and all-in-one scheme that jointly carries out the two sub-tasks based on the multikernel adaptive filtering framework. The task is cast as an asymptotic minimization problem of an instantaneous fidelity function penalized by two types of block l1-norm regularizers. Those regularizers enhance the sparsity of the solution in two different block structures, leading to effi- cient model selection and dictionary refinement. The adaptive generalized forward-backward splitting method is derived to deal with the asymptotic minimization problem. Numerical examples show that the scheme achieves the model selection and learning simultaneously, and demonstrate its strik- ing advantages over the multiple kernel learning (MKL) method called SimpleMKL.