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L0-constrained regression using mixed integer linear programming

Lookup NU author(s): Dr Mark Willis, Dr Moritz von Stosch

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Abstract

In this work, sparse regression using a penalized least absolute deviations objective function is considered. Regression model sparsity is promoted using a L₀ - pseudo norm penalty (the cardinality of the model parameter vector). Implemented using mixed integer linear programming (MILP) it is demonstrated that the use of the L₀ - norm (without approximation) enables efficient and accurate solutions to sparse regression problems of practical size. For model development with a large number of potential model parameters (or features) methods to relax the MILP are also developed; using nonlinear function approximations to the L₀- norm, penalty terms are linearized and solved using sequential linear programming. Experimental results (using both simulated and real data) demonstrate that these algorithms are also computationally efficient producing accurate and parsimonious model structures. Applications considered are the development of a calibration model for prediction with Near Infrared (NIR) data and the development of a model for the prediction of chemical toxicity - a quantitative structure activity relationship (QSAR).

Publication metadata

Author(s): Willis MJ, von-Stosch M

Publication type: Article

Publication status: Published

Journal: Chemometrics and intelligent laboratory systems

Year: 2017

Volume: 165

Pages: 29-37

Print publication date: 15/06/2017

Online publication date: 12/04/2017

Acceptance date: 02/12/2016

Date deposited: 25/04/2017

ISSN (print): 0169-7439

ISSN (electronic): 1873-3239

Publisher: Elsevier

URL: http://dx.doi.org/10.1016/j.chemolab.2016.12.016

DOI: 10.1016/j.chemolab.2016.12.016

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