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On the Prediction Performance of the Lasso


  • Arnak S. Dalalyan

    () (CREST-ENSAE)

  • Mohamed Hebiri

    () (Université Paris Est)

  • Johannes Lederer

    () (Cornell University)


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

Suggested Citation

  • Arnak S. Dalalyan & Mohamed Hebiri & Johannes Lederer, 2014. "On the Prediction Performance of the Lasso," Working Papers 2014-05, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2014-05

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    Cited by:

    1. Pierre Bellec & Alexandre Tsybakov, 2015. "Sharp oracle bounds for monotone and convex regression through aggregation," Working Papers 2015-04, Center for Research in Economics and Statistics.
    2. Gold, David & Lederer, Johannes & Tao, Jing, 2020. "Inference for high-dimensional instrumental variables regression," Journal of Econometrics, Elsevier, vol. 217(1), pages 79-111.

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    multiple linear regression; sparse recovery; total variation penalty; oracle inequalities;

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