IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/418.html
   My bibliography  Save this paper

Worst-case bounds for the logarithmic loss of predictors

Author

Listed:

Abstract

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.

Suggested Citation

  • Nicolò Cesa Bianchi & Gábor Lugosi, 1999. "Worst-case bounds for the logarithmic loss of predictors," Economics Working Papers 418, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:418
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/418.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessio Sancetta, 2010. "Bootstrap model selection for possibly dependent and heterogeneous data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 515-546, June.
    2. Yuan Lo-Hua & Liu Anthony & Yeh Alec & Kaufman Aaron & Reece Andrew & Bull Peter & Franks Alex & Wang Sherrie & Illushin Dmitri & Bornn Luke, 2015. "A mixture-of-modelers approach to forecasting NCAA tournament outcomes," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 11(1), pages 13-27, March.

    More about this item

    Keywords

    Universal prediction; universal coding; empirical processes; on-line learning; metric entropy;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.