Incrementally Solving Nonlinear Regression Tasks Using IBHM Algorithm

This paper considers the black-box approximation problem where the goal is to create a regression model using only empirical data without incorporating knowledge about the character of nonlinearity of the approximated function. This paper reports on ongoing work on a nonlinear regression methodology called IBHM which builds a model being a combination of weighted nonlinear components. The construction process is iterative and is based on correlation analysis. Due to its iterative nature, the methodology does not require a priori assumptions about the final model structure which greatly simplifies its usage. Correlation based learning becomes ineffective when the dynamics of the approximated function is too high. In this paper we introduce weighted correlation coefficients into the learning process. These coefficients work as a kind of a local filter and help overcome the problem. Proof of concept experiments are discussed to show how the method solves approximation tasks. A brief discussion about complexity is also conducted.