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Sparse modelling or model selection with categorical data is challenging evenfor a moderate number of variables, because one parameter is roughly needed toencode one category or level. The Group Lasso is a well known efficientalgorithm for selection continuous or categorical variables, but all estimatesrelated to a selected factor usually differ. Therefore, a fitted model may notbe sparse, which makes the model interpretation difficult. To obtain a sparsesolution of the Group Lasso we propose the following two-step procedure: first,we reduce data dimensionality using the Group Lasso; then to choose the finalmodel we use an information criterion on a small family of models prepared byclustering levels of individual factors. We investigate selection correctnessof the algorithm in a sparse high-dimensional scenario. We also test our methodon synthetic as well as real datasets and show that it performs better than thestate of the art algorithms with respect to the prediction accuracy or modeldimension.

Improving Group Lasso for high-dimensional categorical data