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Regularization in Finite-Sample System Identification

Csáji, Balázs Csanád (2018) Regularization in Finite-Sample System Identification. In: 20th European Conference on Mathematics for Industry, June 18-22, 2018, Budapest, Hungary.

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Abstract

Finite-sample system identification (FSID) methods infer properties of stochastic dynamical systems under minimal distributional assumptions; typically they build confidence regions with rigorous non-asymptotic guarantees. Similarly to bootstrap and Monte Carlo approaches, they generate alternative samples based on some mild regularities of the random elements of the system. An arch-typical example of such regularities is the case, when the noise sequence has a jointly symmetric distribution about zero. Sign-Perturbed Sums and, its generalizations, Data Perturbation (DP) methods are recently developed FSID algorithms that can construct exact confidence regions for finite samples. They have a number of additional favorable properties, e.g., the confidence sets of SPS for linear regression problems are star convex with the least-squares estimate as a star center, as well as they are strongly consistent, meaning that the regions shrink around the true parameter, and asymptotically cannot contain false parameters (w.p.1). Regularization is an important tool in regression which helps, for example, to handle ill-posed and ill-conditioned problems, reduce over-fitting, enforce sparsity, and in general to control the shape and smoothness of the regression function. The talk will address ways to incorporate regularization techniques to FSID constructions, from standard approaches like Tikhonov regularization (ridge regression), LASSO (least absolute shrinkage and selection operator), and elastic nets to regularization with suitably chosen Hilbert space norms, which also have important applications in machine learning.

Item Type: Conference or Workshop Item (Lecture)
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Dr. Balázs Csanád Csáji
Date Deposited: 05 Oct 2018 07:22
Last Modified: 05 Oct 2018 07:22
URI: http://real.mtak.hu/id/eprint/86590

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