NEW MODELS FOR NONLINEAR REGRESSION AND FOR HANDLING MISSING DATA

Abstract

This work is one step towards better data mining. To be more specific, it ad­ dresses the problem of nonlinear regression in case of complete and missing data. We first introduced the Penalized likelihood regression model. This concept vies to achieve a compromise between goodness of fit (as typified by the likelihood function) and smoothness of the data. Attempts to con­ sider the general multidimensional case have been limited. In our work, we propose a new multidimensional penalized likelihood regression method. The approach is based on proposing a roughness term based on the dis­ crepancy between the function values among the K-nearest-neighbors. The proposed formulation yields a simple solution in terms of a system of linear equations. We show that the proposed model is fairly versatile in that it exhibits nice features in handling user defined function constraints and data imperfections. Experimental results confirm that it is competitive with the Gaussian process regression method (one of the best methods out there), and exhibits significant speed advantage.