Section: New Results

Axis 2: Multi-Layer Group-Lasso

Participants : Alain Celisse, Guillemette Marot.

Multi-Layer Group-Lasso (MLGL) is a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high-dimensional data. A sparsity assumption is made that is, only a few variables are assumed to be relevant for predicting the response variable. In this context, the performance of classical Lasso-based approaches strongly deteriorate as the redundancy strengthens. The proposed approach combines variable aggregation and selection in order to improve interpretability and performance. First, a hierarchical clustering procedure provides at each level a partition of the variables into groups. Then, the set of groups of variables from the different levels of the hierarchy is given as input to group-Lasso, with weights adapted to the structure of the hierarchy. At this step, group-Lasso outputs sets of candidate groups of variables for each value of regularization parameter. The versatility offered by MLGL to choose groups at different levels of the hierarchy a priori induces a high computational complexity. MLGL however exploits the structure of the hierarchy and the weights used in group-lasso to greatly reduce the final time cost. The final choice of the regularization parameter – and therefore the final choice of groups – is made by a multiple hierarchical testing procedures. A paper associated to the R package MLGL has been submitted [45].