Complexity reduction in probabilistic neural networks

Abstract

Probability density estimation using the probabilistic neural network or the kernel method is considered. In its basic form this method can be computationally prohibitive, as all training data need to be stored and each individual training vector gives rise to a new term of the estimate. Given an original training sample of size N in a d-dimensional space, a simple binned kernel estimate with O(Nd/d+4) terms can be shown to attain an estimation accuracy only marginally inferior to the standard kernel method. This can be taken to indicate the order of complexity reduction generally achievable when a radial basis function style expansion is used in place of the probabilistic neural network.