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Proof of the optimality of the empirical star J.-Y. Audibert
 

Summary: Proof of the optimality of the empirical star
algorithm
J.-Y. Audibert
Abstract
This note contains the proof of the assertion made in page 5 of the NIPS
paper "Progressive mixture rules are deviation suboptimal". Specifically, it
proves that the empirical star algorithm is deviation optimal for the model
selection type aggregation problem.
CONTENTS
1. CONTEXT . . . . . . . . . . . . . . . . . . . . 1
2. THE EMPIRICAL STAR ALGORITHM. . . . . . . . . . . 2
3. THE MAIN RESULT . . . . . . . . . . . . . . . . . 2
4. AN INTERMEDIATE RESULT ON EMPIRICAL RISK MINI-
MIZATION ON A SEGMENT . . . . . . . . . . . . . . 3
5. PROOF OF THE MAIN RESULT . . . . . . . . . . . . . 5
6. EXTENSIONS . . . . . . . . . . . . . . . . . . . 8
1. CONTEXT
Let (X, B) be a measurable space. Let g1, . . . , gd be uniformly bounded
measurable functions from X to the set of real numbers R equipped with its
Borel algebra A. Let P be an unknown distribution on (X×R, BA) such

  

Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure

 

Collections: Computer Technologies and Information Sciences