A Tree-Based Solution to Nonlinear Regression Problem

In this paper, we offer and examine a new algorithm for sequential nonlinear regression problem. In this architecture, we use piecewise adaptive linear functions to find the nonlinear regression model sequentially. For more accurate and faster convergence, we combine a large class of piecewise linear functions. These piecewise linear functions are constructed by composing different adaptive linear functions, which are represented by the nodes of a lexicographical tree. With this tree structure, computational complexity of the algorithm is significantly reduced. To show the performance of the proposed algorithm, we present a simulation which is performed by using a well-known real data set.