Identification of Reliable Predictor Models for Unknown Systems: a Data-Consistency Approach based on Learning Theory

In this paper we present preliminary results for a new framework in identification of predictor models for unknown systems, which builds on recent developments of statistical learning theory. The three key elements of our approach are: the unknown mechanism that generates the observed data (referred to as the remote data generation mechanism - DGM), a selected family of models, with which we want to describe the observed data (the data descriptor model - DDM), and a consistency criterion, which serves to assess whether a given observation is compatible with the selected model. The identification procedure will then select a model within the assumed family, according to some given optimality objective (for instance, accurate prediction), and which is consistent with the observations. To the optimal model, we attach a certificate of reliability, that is a statement of probability that the computed model will be consistent with future unknown data.