## Sparsity pattern aggregation in generalized linear models.

Series
Stochastics Seminar
Time
Thursday, September 3, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Philippe Rigollet – Princeton University
Organizer
Yuri Bakhtin
The goal of this talk is to present a new method for sparse estimation which does not use standard techniques such as $\ell_1$ penalization. First, we introduce a new setup for aggregation which bears strong links with generalized linear models and thus encompasses various response models such as Gaussian regression and binary classification. Second, by combining maximum likelihood estimators using exponential weights we derive a new procedure for sparse estimations which satisfies exact oracle inequalities with the desired remainder term. Even though the procedure is simple, its implementation is not straightforward but it can be approximated using the Metropolis algorithm which results in a stochastic greedy algorithm and performs surprisingly well in a simulated problem of sparse recovery.