Heavy-Tailed Linear Regression and <i>K</i>-Means
Most standard machine learning algorithms are formulated with the implicit assumption that empirical data are “well-behaved”. In this work, we consider heavy-tailed data whose underlying distribution does not necessarily possess finite moments. For such a scenario, classical linear regression techni...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Information |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2078-2489/16/3/184 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850090431206916096 |
|---|---|
| author | Mario Sayde Jihad Fahs Ibrahim Abou-Faycal |
| author_facet | Mario Sayde Jihad Fahs Ibrahim Abou-Faycal |
| author_sort | Mario Sayde |
| collection | DOAJ |
| description | Most standard machine learning algorithms are formulated with the implicit assumption that empirical data are “well-behaved”. In this work, we consider heavy-tailed data whose underlying distribution does not necessarily possess finite moments. For such a scenario, classical linear regression techniques and the standard <i>K</i>-means algorithm fail. We formulate and validate heavy-tailed versions of these machine learning methods for both scalar and multidimensional settings. The new algorithms are based on recently defined appropriate location and power parameters. Additionally, we showcase the enhanced performance of the proposed methods in comparison to some other tailored ones found in the literature. |
| format | Article |
| id | doaj-art-ca8ba38964254d9bb983eca1386b8ce4 |
| institution | DOAJ |
| issn | 2078-2489 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Information |
| spelling | doaj-art-ca8ba38964254d9bb983eca1386b8ce42025-08-20T02:42:34ZengMDPI AGInformation2078-24892025-02-0116318410.3390/info16030184Heavy-Tailed Linear Regression and <i>K</i>-MeansMario Sayde0Jihad Fahs1Ibrahim Abou-Faycal2Electrical and Computer Engineering Department, American University of Beirut, Beirut 1107 2020, LebanonElectrical and Computer Engineering Department, American University of Beirut, Beirut 1107 2020, LebanonElectrical and Computer Engineering Department, American University of Beirut, Beirut 1107 2020, LebanonMost standard machine learning algorithms are formulated with the implicit assumption that empirical data are “well-behaved”. In this work, we consider heavy-tailed data whose underlying distribution does not necessarily possess finite moments. For such a scenario, classical linear regression techniques and the standard <i>K</i>-means algorithm fail. We formulate and validate heavy-tailed versions of these machine learning methods for both scalar and multidimensional settings. The new algorithms are based on recently defined appropriate location and power parameters. Additionally, we showcase the enhanced performance of the proposed methods in comparison to some other tailored ones found in the literature.https://www.mdpi.com/2078-2489/16/3/184<i>K</i>-meanslinear regressionheavy-tailedalpha-stable?-power |
| spellingShingle | Mario Sayde Jihad Fahs Ibrahim Abou-Faycal Heavy-Tailed Linear Regression and <i>K</i>-Means Information <i>K</i>-means linear regression heavy-tailed alpha-stable ?-power |
| title | Heavy-Tailed Linear Regression and <i>K</i>-Means |
| title_full | Heavy-Tailed Linear Regression and <i>K</i>-Means |
| title_fullStr | Heavy-Tailed Linear Regression and <i>K</i>-Means |
| title_full_unstemmed | Heavy-Tailed Linear Regression and <i>K</i>-Means |
| title_short | Heavy-Tailed Linear Regression and <i>K</i>-Means |
| title_sort | heavy tailed linear regression and i k i means |
| topic | <i>K</i>-means linear regression heavy-tailed alpha-stable ?-power |
| url | https://www.mdpi.com/2078-2489/16/3/184 |
| work_keys_str_mv | AT mariosayde heavytailedlinearregressionandikimeans AT jihadfahs heavytailedlinearregressionandikimeans AT ibrahimaboufaycal heavytailedlinearregressionandikimeans |