A cost-sensitive constrained Lasso
|Author/s||Blanquero Bravo, Rafael
Carrizosa Priego, Emilio José
Ramírez Cobo, Josefa
Sillero Denamiel, María Remedios
|Department||Universidad de Sevilla. Departamento de Estadística e Investigación Operativa|
|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 ...
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.
|Citation||Blanquero Bravo, R., Carrizosa Priego, E.J., Ramírez Cobo, J. y Sillero Denamiel, M.R. (2020). A cost-sensitive constrained Lasso. Advances in Data Analysis and Classification, 15 (1), 121-158.|