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Poster

Bilevel learning of the Group Lasso structure

Jordan Frecon · Saverio Salzo · Massimiliano Pontil

Room 210 #92

Keywords: [ Model Selection and Structure Learning ] [ Structured Prediction ] [ Multitask and Transfer Learning ] [ Regression ] [ Non-Convex Optimization ]


Abstract:

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.

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