Variable Selection According to Goodness of Fit in Nonparametric Nonlinear System Identification

Abstract

To achieve a parsimonious model, it is necessary to rank the importance of input variables according to some measures. The problem is nontrivial in the setting of nonlinear and nonparametric system identification. Difficulties lie in the lack of structural information of the unknown system, unknown underlying probabilistic distributions, and unknown nonlinear correlations of variables. In this article, we present a way to rank variables according to goodness of fit (GoF). Asymptotic results are established, and numerical algorithms are proposed. The problem is cast in a reproducing kernel Hilbert space (RKHS) that allows us to deal with nonparametric nature of the unknown system, to avoid making strong conditions on the unknown distributions, to link GoFs to computable conditional covariance operators on RKHS, and to develop computationally friendly numerical algorithms. Numerical simulations support the theoretical developments.