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# 20th European Young Statisticians Meeting

14-18 August 2017
Uppsala University
Europe/Stockholm timezone

## Information criteria for structured sparse variable selection

17 Aug 2017, 14:30
30m
Ångströmslaboratoriet (Uppsala University)

Speaker

### Speaker

Mr Bastien Marquis (Université Libre de Bruxelles)

### Description

In contrast to the low dimensional case, variable selection under the assumption of sparsity in high dimensional models is strongly influenced by the effects of false positives. The effects of false positives are tempered by combining the variable selection with a shrinkage estimator, such as in the lasso, where the selection is realized by minimizing the sum of squared residuals regularized by an $\ell_1$ norm of the selected variables. Optimal variable selection is then equivalent to finding the best balance between closeness of fit and regularity, i.e., to optimization of the regularization parameter with respect to an information criterion such as Mallows's Cp or AIC. For use in this optimization procedure, the lasso regularization is found to be too tolerant towards false positives, leading to a considerable overestimation of the model size. Using an $\ell_0$ regularization instead requires careful consideration of the false positives, as they have a major impact on the optimal regularization parameter. As the framework of the classical linear model has been analysed in previous work, the current paper concentrates on structured models and, more specifically, on grouped variables. Although the imposed structure in the selected models can be understood to somehow reduce the effect of false positives, we observe a qualitatively similar behavior as in the unstructured linear model.

### Primary author

Mr Bastien Marquis (Université Libre de Bruxelles)

### Co-author

Mr Maarten Jansen (Université Libre de Bruxelles)

 Paper