IDENTIFICATION OF RELIABLE PREDICTOR MODELS FOR UNKNOWN SYSTEMS: A DATA-CONSISTENCY APPROACH BASED ON LEARNING THEORY
Giuseppe Calafiore* M.C. Campi** Laurent El Ghaoui***
* Dipartimento di Automatica e Informatica, Politecnico di Torino, Italy. e-mail: calafiore@polito.it
** Dipartimento di Elettronica per lAutomazione, Università di Brescia, Italy. e-mail: campi@ing.unibs.it
*** Department of Electrical Engineering and Computer Science, UC Berkeley, CA. e-mail: elghaoui@eecs.berkeley.edu

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.
Keywords: Identification, Set-valued maps, VC theory, Convex optimization
Session slot T-Mo-A02: A learning approach to identification and control/Area code 3a : Modelling, Identification and Signal Processing

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