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In regression models with functional covariates, it is of paramount importance to estimate coefficient functions in an interpretable way.We develop a method able to produce estimated functions which are exactly zero in a subset of positive Lebesgue measure of their domain.We achieve this by combining the B-splines basis with the Overlap Group Lasso penalty, a generalization of the ℓ2 penalty which allows groups to have common elements. The resulting optimization problem is efficiently solved using the Alternating Direction Method of Multipliers (ADMM) algorithm. The advantage of the proposed method over classical approaches is supported by simulations and a real data analysis.

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Locally Sparse Estimation for Functional Linear Models with Scalar Response

  • 会议论文

  • 发表日期：

    2025年

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  • Marco Stefanucci,
  • Mauro Bernardi,
  • Antonio Canale

摘要

In regression models with functional covariates, it is of paramount importance to estimate coefficient functions in an interpretable way.We develop a method able to produce estimated functions which are exactly zero in a subset of positive Lebesgue measure of their domain.We achieve this by combining the B-splines basis with the Overlap Group Lasso penalty, a generalization of the ℓ2 penalty which allows groups to have common elements. The resulting optimization problem is efficiently solved using the Alternating Direction Method of Multipliers (ADMM) algorithm. The advantage of the proposed method over classical approaches is supported by simulations and a real data analysis.