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Bilevel learning of the Group Lasso structure
Jordan Frecon · Saverio Salzo · Massimiliano Pontil

Thu Dec 06 02:00 PM -- 04:00 PM (PST) @ Room 210 #92

Regression with group-sparsity penalty plays a central role in high-dimensional prediction problems. Most of existing methods require the group structure to be known a priori. In practice, this may be a too strong assumption, potentially hampering the effectiveness of the regularization method. To circumvent this issue, we present a method to estimate the group structure by means of a continuous bilevel optimization problem where the data is split into training and validation sets. Our approach relies on an approximation scheme where the lower level problem is replaced by a smooth dual forward-backward algorithm with Bregman distances. We provide guarantees regarding the convergence of the approximate procedure to the exact problem and demonstrate the well behaviour of the proposed method on synthetic experiments. Finally, a preliminary application to genes expression data is tackled with the purpose of unveiling functional groups.

Author Information

Jordan Frecon (Istituto Italiano di Tecnologia)
Saverio Salzo (Istituto Italiano di Tecnologia)
Massimiliano Pontil (IIT & UCL)

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