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Comparison of Newton’s and Broyden’s Method as Nonlinear Solver in the Implementation of MFV-robustified Linear Regression

文献类型： 会议论文

第一作者： Ferenc Tolner

作者： Ferenc Tolner 1 ; Balázs Barta 2 ; Gy?rgy Eigner 3 ;

作者机构： 1.Pannon Business Network Association, Szombathely, Hungary|Doctoral School of Applied Informatics and Applied Mathematics, óbuda University, Budapest, Hungary

2.Pannon Business Network Association, Szombathely, Hungary

3.University Research and Innovation Center, Physiological Controls Research Center and óbuda University|Biomatics and Applied Artificial Intelligence Institution, John von Neumann Faculty of Informatics, óbuda University

关键词： Economics;Earth;Nonlinear equations;Linear regression;Machine learning;Minimization;Iterative methods

会议名称： IEEE International Conference on Systems, Man, and Cybernetics

主办单位：

页码： 1518-1523

摘要： Linear regression is one of the fundamental tasks of mathematical statistics and machine learning related disciplines. Several techniques have been elaborated, however the most common one is still the application of the least squares technique. In this paper we present an alternative, ”robustified” approach for linear regression that instead of relying on the minimization of the L2-norm, minimizes the P-norm that was introduced by Steiner et. al. in connection with earth sciences and Most Frequent Value (MFV) calculations. Although the proposed alternative serves with a rather robust and outlier-resistant regression, a nonlinear equation system has to be solved in an iterative way. The present study serves with a comparison between the Newton’s and Broyden’s method solving the nonlinear system in the iterative procedure in case of a test example and in case of real life economic data regarding unconditional economic $beta$ convergence of the EU countries and regions.

分类号： tp13-53

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