On the Prediction Performance of the Lasso

Arnak Dalalyan, Mohamed Hebiri (mohamed.hebiri@univ-mlv.fr) and Johannes Lederer (johanneslederer@cornell.edu)
Additional contact information
Mohamed Hebiri: Université Paris Est
Johannes Lederer: Cornell University

No 2014-05, Working Papers from Center for Research in Economics and Statistics

Abstract: Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context of multiple linear regression. We show, in particular, that the incorporation of a simple correlation measure into the tuning parameter leads to a nearly optimal prediction performance of the Lasso even for highly correlated covariates. However, we also reveal that for moderately correlated covariates, the prediction performance of the Lasso can be mediocre irrespective of the choice of the tuning parameter. For the illustration of our approach with an important application, we deduce nearly optimal rates for the least-squares estimator with total variation penalty

Keywords: multiple linear regression; sparse recovery; total variation penalty; oracle inequalities (search for similar items in EconPapers)
Pages: 30
Date: 2014-02
New Economics Papers: this item is included in nep-ecm and nep-for
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Citations: View citations in EconPapers (6)

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Related works:
Working Paper: On the prediction performance of the Lasso (2017)
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