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Permanent link (DOI): https://doi.org/10.7939/R35T46

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Statistical analysis of L1-penalized linear estimation with applications Open Access

Descriptions

Other title
Subject/Keyword
linear estimation
linear regression
machine learning
Lasso
excess risk
reinforcement learning
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Ávila Pires, Bernardo
Supervisor and department
Csaba Szepesvári (Computing Science)
Examining committee member and department
Dale Schuurmans (Computing Science)
Byron Schmuland (Mathematical and Statistical Sciences)
Department
Department of Computing Science
Specialization

Date accepted
2011-10-02T15:13:27Z
Graduation date
2012-06
Degree
Master of Science
Degree level
Master's
Abstract
We study linear estimation based on perturbed data when performance is measured by a matrix norm of the expected residual error, in particular, the case in which there are many unknowns, but the “best” estimator is sparse, or has small L1-norm. We propose a Lasso-like procedure that finds the minimizer of an L1-penalized squared norm of the residual. For linear regression we show O(sqrt(1/n)) uniform bounds for the difference between the residual error norm of our estimator and that of the “best” estimator. These also hold for on-policy value function approximation in reinforcement learning. In the off-policy case, we show O(sqrt((ln n)/n)) bounds for the expected difference. Our analysis has a unique feature: it is the same for both regression and reinforcement learning. We took care to separate the deterministic and probabilistic arguments, so as to analyze a range of seemingly different linear estimation problems in a unified way.
Language
English
DOI
doi:10.7939/R35T46
Rights
License granted by Bernardo Pires (bpires@ualberta.ca) on 2011-09-30T08:23:06Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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