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Optimal Learning with Q-aggregation

Author(s): Lecué, Guillaume; Rigollet, Philippe

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Abstract: We consider a general supervised learning problem with strongly convex and Lipschitz loss and study the problem of model selection aggregation. In particular, given a finite dictionary functions (learners) together with the prior, we generalize the results obtained by Dai, Rigollet and Zhang [Ann. Statist. 40 (2012) 1878–1905] for Gaussian regression with squared loss and fixed design to this learning setup. Specifically, we prove that the Q-aggregation procedure outputs an estimator that satisfies optimal oracle inequalities both in expectation and with high probability. Our proof techniques somewhat depart from traditional proofs by making most of the standard arguments on the Laplace transform of the empirical process to be controlled.
Publication Date: Feb-2014
Citation: Lecué, Guillaume, Rigollet, Philippe. (2014). Optimal learning with Q-aggregation. The Annals of Statistics, 42 (1), 211 - 224. doi:10.1214/13-AOS1190
DOI: doi:10.1214/13-AOS1190
ISSN: 0090-5364
Pages: 211 - 224
Type of Material: Journal Article
Journal/Proceeding Title: The Annals of Statistics
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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