On adaptivity of online model selection method based on multikernel adaptive filtering

We investigate adaptivity of the online model selection method which has been proposed recently within the multikernel adaptive filtering framework. Specifically, we consider a situation in which the nonlinear system under study changes during adaptation and an appropriate kernel also does accordingly. Our time-varying cost functions involve three regularizers: the ℓ₁ norm and two block ℓ₁ norms which promote sparsity both in the kernel and data groups. The block ℓ₁ regularizers are approximated by their Moreau envelopes, and the adaptive proximal forward-backward splitting (APFBS) method is applied to the approximated cost function. Numerical examples show that the proposed algorithm can adaptively estimate a reasonable model.