[Ml-stat-talks] Guillaume Lecue, Friday, 1:30pm

Philippe Rigollet rigollet at Princeton.EDU
Tue May 22 09:53:07 EDT 2012

=== ORFE - Wilks Statistics Seminar Announcement ===

DATE:  Friday, May 25, 2012

TIME:  1:30pm

LOCATION:  Sherrerd Hall 101

SPEAKER:  Guillaume Lecue, CNRS - Laboratory for analysis, topology and probability, LATP, Marseille, FR

TITLE:   Some Oracle Inequalities for Empirical Risk Minimization (ERM), Regularized ERM and Penalized ERM
Procedures with Applications

ABSTRACT:   We show  that empirical risk minimization procedures, regularized and penalized empirical risk
minimization procedures satisfy some general non-exact oracle inequalities in an unbounded framework, under
the assumption that the model/class has a subexponential envelope function. The main novelty is that those
inequalities can yield fast rates even in situations in which exact oracle inequalities only hold with slower rates.

We apply these results to show that procedures based on $\ell_1$ and nuclear norms regularization functions
satisfy oracle inequalities with a residual term that decreases like $1/n$  for every  $L_q$-loss functions ($q\geq2$),
while only assuming that the tail behaviour of the input and output variables are well behaved. In particular, no RIP
type of assumption or ``incoherence condition'' are needed to obtain fast residual terms in those setups.

Joint work with Shahar Mendelson.
Philippe Rigollet

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