A learning theory approach to the construction of predictor models

Abstract. This paper presents new results for the identification of predictive models for unknown dynamical systems. The three key elements of the proposed approach are: i) an unknown mechanism that generates the observed data; ii) a family of models, among which we select our predictor, on the basis of past observations; iii) an optimality criterion that we want to minimize. A major departure from standard identification theory is taken in that we consider interval models for prediction, that is models that return output intervals, as opposed to output values. Moreover, we introduce a consistency criterion (the model is required to be consistent with obser-vations) which act as a constraint in the optimization procedure. In this framework, the model has not to be interpreted as a faithful description of reality, but rather as an instrument to perform prediction. To the optimal model, we attach a certificate of reliability, that is a statement of the probability that the computed model will actually be consistent with future unknown data. 1. Introduction. I