Generalized ordered linear regression with regularization

Bulletin of the Polish Academy of Sciences. Technical Sciences

J.M. ??skiCorresponding authorInstitute of Electronics, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹  N. HenzelInstitute of Medical Technology and Equipment, 118A Roosevelt St., 41-800 Zabrze, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar² 

[1] Institute of Electronics, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland;Institute of Medical Technology and Equipment, 118A Roosevelt St., 41-800 Zabrze, Poland

关键词: Keywords : linear regression;    IRLS;    OWA;    conjugate gradient optimization;    robust methods.;   

DOI  :  10.2478/v10175-012-0061-2

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

Linear regression analysis has become a fundamental tool in experimental sciences. We propose a new method for parameter estimation in linear models. The ’Generalized Ordered Linear Regression with Regularization’ (GOLRR) uses various loss functions (including the ǫ-insensitive ones), ordered weighted averaging of the residuals, and regularization. The algorithm consists in solving a sequence of weighted quadratic minimization problems where the weights used for the next iteration depend not only on the values but also on the order of the model residuals obtained for the current iteration. Such regression problem may be transformed into the iterative reweighted least squares scenario. The conjugate gradient algorithm is used to minimize the proposed criterion function. Finally, numerical examples are given to demonstrate the validity of the method proposed.

【 授权许可】

Unknown