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dc.contributor.authorWintenberger, Olivier
dc.contributor.authorAlquier, Pierre
dc.subjectPAC-Bayesian boundsen
dc.subjectMixing processesen
dc.subjectFast rates Sparsityen
dc.subjectOracle inequalitiesen
dc.subjectTime series predictionen
dc.subjectStatistical learning theoryen
dc.titleFast rates in learning with dependent observationsen
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.contributor.editoruniversityotherLaboratoire de Probabilités et Modèles Aléatoires (LPMA) CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot;France
dc.description.abstractenIn this paper we tackle the problem of fast rates in time series forecasting from a statistical learning perspective. In a serie of papers (e.g. Meir 2000, Modha and Masry 1998, Alquier and Wintenberger 2012) it is shown that the main tools used in learning theory with iid observations can be extended to the prediction of time series. The main message of these papers is that, given a family of predictors, we are able to build a new predictor that predicts the series as well as the best predictor in the family, up to a remainder of order $1/\sqrt{n}$. It is known that this rate cannot be improved in general. In this paper, we show that in the particular case of the least square loss, and under a strong assumption on the time series (phi-mixing) the remainder is actually of order $1/n$. Thus, the optimal rate for iid variables, see e.g. Tsybakov 2003, and individual sequences, see \cite{lugosi} is, for the first time, achieved for uniformly mixing processes. We also show that our method is optimal for aggregating sparse linear combinations of predictors.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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