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 ) } , i = 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 ) . We show that, for suitable finite N , the resulting model will be reliable, that is it will explain any other unseen output, up to a given and arbitrary high probability.