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Submitted to the Annals of Statistics ROBUST LINEAR LEAST SQUARES REGRESSION
 

Summary: Submitted to the Annals of Statistics
ROBUST LINEAR LEAST SQUARES REGRESSION
By Jean-Yves Audibert,, and Olivier Catoni,§
We consider the problem of robustly predicting as well as the
best linear combination of d given functions in least squares regres-
sion, and variants of this problem including constraints on the pa-
rameters of the linear combination. For the ridge estimator and the
ordinary least squares estimator, and their variants, we provide new
risk bounds of order d/n without logarithmic factor unlike some stan-
dard results, where n is the size of the training data. We also provide
a new estimator with better deviations in presence of heavy-tailed
noise. It is based on truncating differences of losses in a min-max
framework and satisfies a d/n risk bound both in expectation and in
deviations. The key common surprising factor of these results is the
absence of exponential moment condition on the output distribution
while achieving exponential deviations. All risk bounds are obtained
through a PAC-Bayesian analysis on truncated differences of losses.
Experimental results strongly back up our truncated min-max esti-
mator.
CONTENTS

  

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

 

Collections: Computer Technologies and Information Sciences