English, Article, Journal or magazine article edition: Worst-case Bounds for the Logarithmic Loss of Predictors Nicolò Cesa Bianchi; Gábor Lugosi

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Bookmark: http://trove.nla.gov.au/version/111840
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Worst-case Bounds for the Logarithmic Loss of Predictors
Author
  • Nicolò Cesa Bianchi
  • Gábor Lugosi
Physical Description
  • preprint
Notes
  • We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes of predictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.
  • Universal prediction, universal coding, empirical processes, on-line learning, metric entropy
  • RePEc:upf:upfgen:418
Language
  • English
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