A Note on Generalised Information Criteria for Structured Sparse Models

We propose a generalised information criteria ( gic) that accounts for sparsity pattern in the model. We obtain both asymptotic and nonasymptotic results for model selection. Moreover, we show that the gic is useful for selecting the regularisation parameter in regularised estimation in high-dimensional scenarios. The results are illustrated in two examples: group LASSO in the context of generalised linear regressions and low-rank matrix regression.