Local variable selection and dimension determination of nonlinear non-parametric systems

In this paper, we consider the variable selection problem for a nonlinear non-parametric system. The approach proposed selects a variable by detecting if the corresponding partial derivative is zero or not at the point of interest. The algorithm is shown to have not only the parameter but also the set convergence. This is critical because the variable selection problem is binary, a variable is either selected or not selected. The approach allows the unknown non-parametric nonlinear system to have different local dimensions at different points of interest.