Sparse regression and support recovery with L2L2-Boosting algorithms

• We investigate the prediction consistency and support recovery of L2 Boosting.
• We extend these results to a high dimensional statistical framework.
• We investigate the behaviour of such algorithms in a multivariate settings.

This paper focuses on the analysis of L2L2-Boosting algorithms for linear regressions. Consistency results were obtained for high-dimensional models when the number of predictors grows exponentially with the sample size nn. We propose a new result for Weak Greedy Algorithms that deals with the support recovery, provided that reasonable assumptions on the regression parameter are fulfilled. For the sake of clarity, we also present some results in the deterministic case. Finally, we propose two multi-task versions of L2L2-Boosting for which we can extend these stability results, provided that assumptions on the restricted isometry of the representation and on the sparsity of the model are fulfilled. The interest of these two algorithms is demonstrated on various datasets.