A mixed-integer programming approach to GRNN parameter estimation

A mixed-integer programming formulation for sparse general regression neural networks (GRNNs) is presented, along with a method for estimating GRNN parameters based on techniques drawn from support vector machines (SVMs) and evolutionary computation. GRNNs have been widely used for regression estimation, learning a function from a set of input/output examples, but they utilise the full set of training examples to evaluate the interpolation function. Sparse GRNNs choose a subset of the training examples, analogous to the support vectors chosen by SVMs. Experimental comparisons are made with non-sparse GRNNs and with sparse GRNNs whose centres are randomly chosen or are chosen using vector quantisation of the input domain. It is shown that the mixed-integer programming approach leads to lower prediction errors compared with previous approaches, especially when using a small fraction of the training examples.