Open Access
December 1999 On prediction of individual sequences
Nicolò Cesa-Bianchi, Gábor Lugosi
Ann. Statist. 27(6): 1865-1895 (December 1999). DOI: 10.1214/aos/1017939242


Sequential randomized prediction of an arbitrary binary sequence is investigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss (or regret), that is, to make almost as few mistakes as the best “expert” in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) expert, we completely characterize the minimax regret in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimax regret in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax regret for the class of autoregressive linear predictors and for the class of Markov experts.


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Nicolò Cesa-Bianchi. Gábor Lugosi. "On prediction of individual sequences." Ann. Statist. 27 (6) 1865 - 1895, December 1999.


Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0961.62081
MathSciNet: MR1765620
Digital Object Identifier: 10.1214/aos/1017939242

Primary: 62C20
Secondary: 60G20

Keywords: absolute loss , covering numbers , Empirical processes , finite-state machines , prediction with experts , universal prediction

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 6 • December 1999
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