A cost-sensitive constrained Lasso

Rafael Blanquero, Emilio Carrizosa, Pepa Ramírez-Cobo and M. Remedios Sillero-Denamiel ()
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Rafael Blanquero: Universidad de Sevilla
Emilio Carrizosa: Universidad de Sevilla
Pepa Ramírez-Cobo: Instituto de Matemáticas de la Universidad de Sevilla (IMUS)
M. Remedios Sillero-Denamiel: Universidad de Sevilla

Advances in Data Analysis and Classification, 2021, vol. 15, issue 1, No 7, 158 pages

Abstract: Abstract The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the accuracy prediction on certain individuals of interest is allowed. In this work we propose a novel version of the Lasso in which quadratic performance constraints are added to Lasso-based objective functions, in such a way that threshold values are set to bound the prediction errors in the different groups of interest (not necessarily disjoint). As a result, a constrained sparse regression model is defined by a nonlinear optimization problem. This cost-sensitive constrained Lasso has a direct application in heterogeneous samples where data are collected from distinct sources, as it is standard in many biomedical contexts. Both theoretical properties and empirical studies concerning the new method are explored in this paper. In addition, two illustrations of the method on biomedical and sociological contexts are considered.

Keywords: Performance constraints; Cost-sensitive learning; Sparse solutions; Sample average approximation; Heterogeneity; Lasso; 62-07 Data analysis, 62H12 Estimation in multivariate analysis, 62J07 Ridge regression; shrinkage estimators (Lasso), 62P99 Applications of statistics (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11634-020-00389-5

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