Variable selection with Multi-Layer Group Lasso

International audienceThe MLGL (Multi-Layer Group-Lasso) R package implements a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high0dimensional 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 deteriorates as the redundancy strengthens.The proposed approach combines variables 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 procedure