STRONG UNIVERSAL CONSISTENCY OF NEURAL-NETWORK CLASSIFIERS

In statistical pattern recognition a classifier is called universally consistent if its error probability converges to the Bayes-risk as the size of the training data grows, for all possible distributions of th e random variable pair of the observation vector and its class. It is proven that if a one layered neural network with properly chosen numbe r of nodes is trained to minimize the empirical risk on the training d ata, then it results in a universally consistent classifier. It is sho wn that the exponent in the rate of convergence does not depend on the dimension if certain smoothness conditions on the distribution are sa tisfied. That is, this class of universally consistent classifiers doe s not suffer from the ''curse of dimensionality.'' A training algorith m is also presented that finds the optimal set of parameters in polyno mial time if the number of nodes and the space dimension is fixed and the amount of training data grows.