We focus on the problem of linear regression estimation in high dimension, when the parameter β is ”sparse” (most of its coordinates are 0) and ”blocky” (β i and β i + 1 are likely to be equal). Recently, some authors defined estimators taking into account this information, such as the Fused-LASSO [19] or the S-LASSO among others. However, there are no theoretical results about the obtained estimators in the general design matrix case. Here, we propose an alternative point of view, based on the Iterative Feature Selection method. We propose an iterative algorithm that takes into account the fact that β is sparse and blocky, with no prior knowledge on the position of the blocks. Moreover, we give a theoretical result that ensures that every step of our algorithm actually improves the statistical performance of the obtained estimator. We provide some simulations, where our method outperforms LASSO-type methods in the cases where the parameter is sparse and blocky. Moreover, we give an application to real data (CGH arrays), that shows that our estimator can be used on large datasets.
ALQUIER, P. (2010). An Algorithm for Iterative Selection of Blocks of Features. Dans: 21st International Conference on Algorithmic Learning Theory (ALT’10). Caberra: Springer Berlin Heidelberg, pp. 35-49.