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.

摘要

分段线性 ${\mathrm{大号}}_{\mathrm{1个}}$回归问题被公式化为无约束凸（DC）优化问题，并开发了解决该问题的算法。引入了辅助问题来设计一种自适应方法，以生成合适的分段线性回归模型和用于解决基本DC优化问题的起点。使用包含离群值的合成数据和真实数据集，评估了该算法作为逼近和预测工具的性能。它也与使用各种性能指标的主流机器学习回归算法进行了比较。结果表明，对于数值实验中使用的大多数数据集，新算法对异常值均具有鲁棒性，并且与其他替代回归算法相比，通常可以提供更好的预测。