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Fundamental Limitations in Sequential Prediction and Recursive Algorithms: $\mathcal{L}_{p}$ Bounds via an Entropic Analysis (1912.02628v2)
Published 3 Dec 2019 in cs.LG, cs.IT, eess.SP, math.IT, math.ST, stat.ML, and stat.TH
Abstract: In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the data and/or noises involved, and the derived lower bounds may all be quantified in a conditional entropy characterization. We also study the conditions to achieve the generic bounds from an innovations' viewpoint.
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