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PAC-Bayesian aggregation of affine estimators

By Lucie Montuelle and Erwan Le Pennec

Abstract

Aggregating estimators using exponential weights depending on their risk performs well in expectation, but sadly not in probability. Considering exponential weights of a penalized risk is a way to overcome this issue. We focus on the fixed design regression framework with sub-Gaussian noise and provide penalties allowing to obtain oracle inequalities in deviation for the aggregation of affine estimators. Sharp oracle inequalities are provided by a condition using the regression function's norm. MSC 2010 subject classifications: Primary 62G08; secondary 62J02

Topics: Exponentially weighted aggregation, Regression, Oracle inequality, Deviation, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]
Publisher: HAL CCSD
Year: 2016
OAI identifier: oai:HAL:hal-01070805v2
Provided by: Hal-Diderot

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