Model selection with lasso-zero: adding straw to the haystack to better find needles

Code

• github.com/pascalinedescloux/lasso-zero
  OfficialIn papernone★ 0

Abstract

The high-dimensional linear model y = X ^0 + is considered and the focus is put on the problem of recovering the support S^0 of the sparse vector ^0. We introduce Lasso-Zero, a new _1-based estimator whose novelty resides in an "overfit, then threshold" paradigm and the use of noise dictionaries concatenated to X for overfitting the response. To select the threshold, we employ the quantile universal threshold based on a pivotal statistic that requires neither knowledge nor preliminary estimation of the noise level. Numerical simulations show that Lasso-Zero performs well in terms of support recovery and provides an excellent trade-off between high true positive rate and low false discovery rate compared to competitors. Our methodology is supported by theoretical results showing that when no noise dictionary is used, Lasso-Zero recovers the signs of ^0 under weaker conditions on X and S^0 than the Lasso and achieves sign consistency for correlated Gaussian designs. The use of noise dictionary improves the procedure for low signals.

Tasks

Reproductions