Worst-case bounds for the logarithmic loss of predictors
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- dc.contributor.author Cesana Arlotti, Nicolò, 1981-ca
- dc.contributor.author Lugosi, Gáborca
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2017-07-26T10:51:02Z
- dc.date.available 2017-07-26T10:51:02Z
- dc.date.issued 1999-10-01
- dc.date.modified 2017-07-23T02:04:53Z
- dc.description.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.
- dc.format.mimetype application/pdfca
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=418
- dc.identifier.citation Machine Learning, 43, 3, (2001), pp. 247-264
- dc.identifier.uri http://hdl.handle.net/10230/934
- dc.language.iso eng
- dc.relation.ispartofseries Economics and Business Working Papers Series; 418
- dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword universal prediction
- dc.subject.keyword universal coding
- dc.subject.keyword empirical processes
- dc.subject.keyword on-line learning
- dc.subject.keyword metric entropy
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title Worst-case bounds for the logarithmic loss of predictorsca
- dc.type info:eu-repo/semantics/workingPaper