BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Learning from MOM's principles  - Guillaume Lecué (ENSAE)
DTSTART:20171117T160000Z
DTEND:20171117T170000Z
UID:TALK93397@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:(Joint work with Matthieu Lerasle)\nWe obtain theoretical and 
 practical performances for median of means estimators. \n\nFrom a theoreti
 cal point of view\, estimation and prediction error bounds achieved by the
  MOM estimators hold with exponentially large probability -- as in the gau
 ssian framework with independent noise-- under only weak moments assumptio
 ns on the data and without assuming independence between the noise and the
  design. Moreover\, MOM procedures are  robust since a large part of the d
 ata may have nothing to do with the oracle we want to reconstruct. Our gen
 eral risk bound is of order max(minimax rate of convergence in the i.i.d. 
 setup\, (number of outliers)/number of observations)). In particular\, the
  number of outliers  may be as large as (number of data)*(minimax rate) wi
 thout affecting the statistical properties of  the MOM estimator. \n\nA re
 gularization norm may also be used together with the MOM criterium. In tha
 t case\, any norm can be used for regularization. When it has some sparsit
 y inducing power we recover sparse rates of convergence and sparse oracle 
 inequalities. For example\, the minimax rate s log(d/s)/N of recovery of a
  s-sparse vector in R^d is achieved by a median-of-means version of the LA
 SSO when the noise has q_0 moments for some q_0>2\, the design matrix C_0\
 \log(d) moments and the dataset is corrupted by s log(d/s) outliers. This 
 result holds with exponentially large probability as if the noise and the 
 design were i.i.d. Gaussian random variables. \n\nOn the practical side\, 
 MOM estimators (and their associated regularized versions) can easily be i
 mplemented. Actually\, most gradient descent algorithms used to implement 
 (non-robust) estimators like the LASSO can easily be transformed into a ro
 bust one by using a MOM approach.
LOCATION:MR12
END:VEVENT
END:VCALENDAR