Grouping strategies and thresholding for high dimensional linear models: Discussion

Guillaume Obozinski (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

This is a discussion of the article entitled Grouping strategies and thresholding for high dimensional linear models by M. Mougeot, D. Picard and K. Tribouley and published in the Journal of Statistical Planning and Inference (2013). http://dx.doi.org/10.1016/j.jspi.2013.03.001. We first discuss how to define and measure intra and inter-group correlations, what their respective roles in the problem are and relate this to the quantities considered in the paper. We then compare the strategy of grouping either most correlated or most uncorrelated variables together. An alternative grouping algorithm based on the ideas in the paper and using hierarchical clustering and bin packing is proposed. Finally, we discuss if the construction proposed could be beneficial to the group Lasso.

Keywords: Sparsity; group Lasso; between-group coherence; intra-group coherence; correlation; RIP; restricted eigenvalue condition; mutual incoherence

Domains: Statistics Theory [stat.TH]

Guillaume Obozinski. Grouping strategies and thresholding for high dimensional linear models: Discussion. Journal of Statistical Planning and Inference, 2013, 143 (9), pp.1441-1446. ⟨10.1016/j.jspi.2013.03.003⟩. ⟨hal-00833808⟩