A Scilab toolbox of nonlinear regression models using a linear solver

Abstract

This work describes a toolbox of nonlinear regression models developed on an open-source platform of Scilab. The models are formed from radial basis function (RBF) neural network structures. For a fast calculation of the models, we adopt a linear solver in implementations. A specific effort is made on applications of linear priors, which presents a unique feature different from other existing regression toolboxes. In this work, we define linear priors to be a class of prior information that exhibits a linear relation to the attributes of interests, such as variables, free parameters, or their functions of the models. Two approaches of incorporating linear priors are implemented in the models, namely, Lagrange Multiplier (LM) and Direct Elimination (DE). Several numerical examples are demonstrated in the toolbox for the educational purpose on learning nonlinear regression models. From the numerical examples, users can understand the importance of utilizing linear priors in models. The linear priors include the hard constraints on interpolation points and soft constraints on ranking list.