A Hybrid Connectionist for Multiple Regression

We present a hybrid system for generating multiple linear regression lines for the solution of a function approximation problem. The system consists of three components: (1) a neural network which is trained to fit the data samples; (2) a simple algorithm for splitting the input space of the data into subregions and (3) the traditional multiple regression technique for finding the coefficients of the regression lines. While neural networks work particularly well for nonlinear function approximation, their outputs are difficult to explain to a human user. Our proposed system predicts the network outputs as linear functions of the input attributes. In order to maintain the predictive accuracy of the networks, the system divides the space of the input data into several subspaces. In each of these subspaces, a linear equation is generated for predicting the target values for all samples that belong to the subspace. We illustrate the effectiveness of the system using two data sets, one is an artificial data set, while the other is a real world data set for predicting the fuel consumption of automobiles.