Sparse regression and support recovery with L-2-Boosting algorithms

作者：Champion Magali; Cierco Ayrolles Christine; Gadat Sebastien^*; Vignes Matthieu

来源：Journal of Statistical Planning and Inference, 2014, 155: 19-41.

DOI：10.1016/j.jspi.2014.07.006

• Boosting
• Regression
• Sparsity
• High-dimension

This paper focuses on the analysis of L-2-Boosting algorithms for linear regressions. Consistency results were obtained for high-dimensional models when the number of predictors grows exponentially with the sample size n. 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 L-2-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.

• 出版日期2014-12