Robust piecewise linear L1-regression via nonsmooth DC optimization. (4th July 2022)

• Record Type: Journal Article
• Authors: Bagirov, Adil M.; Taheri, Sona; Karmitsa, Napsu; Sultanova, Nargiz; Asadi, Soodabeh
• Is Part Of: Optimization methods and software. Volume 37:Number 4(2022)
• Page Start: 1289
• Page End: 1309
• Publication Date: 2022-07-04
• Subjects: Regression analysis -- least absolute deviation regression -- outliers -- nonsmooth optimization -- nonconvex optimization -- DC optimization; 65K05 -- 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1855171
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: Piecewise linear L 1 -regression problem is formulated as an unconstrained difference of convex (DC) optimization problem and an algorithm for solving this problem is developed. Auxiliary problems are introduced to design an adaptive approach to generate a suitable piecewise linear regression model and starting points for solving the underlying DC optimization problems. The performance of the proposed algorithm as both approximation and prediction tool is evaluated using synthetic and real-world data sets containing outliers. It is also compared with mainstream machine learning regression algorithms using various performance measures. Results demonstrate that the new algorithm is robust to outliers and in general, provides better predictions than the other alternative regression algorithms for most data sets used in the numerical experiments.