Integer constraints for enhancing interpretability in linear regression
One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/362095 |
| Acceso en línea: | https://hdl.handle.net/2117/362095 https://dx.doi.org/10.2436/20.8080.02.95 |
| Access Level: | acceso abierto |
| Palabra clave: | linear regression multicollinearity sparsity cardinality constraint mixed integer non linear programming Programació (Matemàtica) Estadística matemàtica Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming Classificació AMS::62 Statistics::62J Linear inference, regression Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Sumario: | One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated features. In this paper we aim to enhance interpretability in linear regression in presence of multicollinearity by: (i) forcing the sign of the estimated coefficients to be consistent with the sign of the correlations between predictors, and (ii) avoiding spurious coefficients so that only significant features are represented in the model. This will be addressed by modelling constraints and adding them to an optimization problem expressing some estimation procedure such as ordinary least squares or the lasso. The so-obtained constrained regression models will become Mixed Integer Quadratic Problems. The numerical experiments carried out on real and simulated datasets show that tightening the search space of some standard linear regression models by adding the constraints modelling (i) and/or (ii) help to improve the sparsity and interpretability of the solutions with competitive predictive quality. |
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