On prediction of individual sequences
AbstractSequential 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, i.e., 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) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimax relative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 324.
Date of creation: Jul 1998
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Web page: http://www.econ.upf.edu/
Universal prediction; prediction with experts; absolute loss; empirical processes; covering numbers; finite-state machines;
Find related papers by JEL classification:
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-1998-11-20 (All new papers)
- NEP-ECM-1998-11-23 (Econometrics)
- NEP-EXP-1998-11-20 (Experimental Economics)
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- Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.
- Gabor Lugosi & Shie Mannor & Gilles Stoltz, 2008. "Strategies for prediction under imperfect monitoring," Post-Print hal-00124679, HAL.
- A. Borodin & R. El-Yaniv & V. Gogan, 2011. "Can We Learn to Beat the Best Stock," Papers 1107.0036, arXiv.org.
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