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On prediction of individual sequences


Author Info

  • Nicolo Cesa Bianchi
  • Gábor Lugosi



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, 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 Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 324.

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Date of creation: Jul 1998
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Handle: RePEc:upf:upfgen:324

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Related research

Keywords: Universal prediction; prediction with experts; absolute loss; empirical processes; covering numbers; finite-state machines;

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Cited by:
  1. A. Borodin & R. El-Yaniv & V. Gogan, 2011. "Can We Learn to Beat the Best Stock," Papers 1107.0036,
  2. Gabor Lugosi & Shie Mannor & Gilles Stoltz, 2008. "Strategies for prediction under imperfect monitoring," Post-Print hal-00124679, HAL.
  3. Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.


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