Bartlett, Peter L. & Mendelson, Shahar (2006) Empirical minimization. Probability Theory and Related Fields, 135(3), pp. 311-334.
We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand’s concentration inequality for empirical processes.
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|Item Type:||Journal Article|
|Keywords:||Empirical processes, Empirical minimization, Isomorphic coordinate projections, Error bounds|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2006 Springer|
|Deposited On:||18 Aug 2011 11:10|
|Last Modified:||01 Mar 2012 00:34|
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