Adaptive recovery of signals by convex optimization

author: Dmitry Ostrovsky, Grenoble University
published: Aug. 20, 2015,   recorded: July 2015,   views: 1651


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We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. It addresses two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. We illustrate some potential applications of the proposed approach.

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