The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 1 (2014), 211-224.
Optimal learning with Q-aggregation
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.
Ann. Statist., Volume 42, Number 1 (2014), 211-224.
First available in Project Euclid: 18 February 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 68Q32: Computational learning theory [See also 68T05]
Secondary: 62G08: Nonparametric regression 62G05: Estimation
Lecué, Guillaume; Rigollet, Philippe. Optimal learning with Q -aggregation. Ann. Statist. 42 (2014), no. 1, 211--224. doi:10.1214/13-AOS1190. https://projecteuclid.org/euclid.aos/1392733186