Learning noisy functions via interval models

This paper considers the problem of identification of an interval model for an unknown static function using a finite batch of stochastic input–output data {u(i),y(i)}{u(i),y(i)}, i=1,…,Ni=1,…,N. The criterion used for identification is that the width of the interval output of the model should be minimized, while containing a given fraction of the observed outputs y(i)y(i). We show that, for suitable finite NN, the resulting model will be reliable, that is it will explain any other unseen output, up to a given and arbitrary high probability.