Revisiting linear machine learning through the perspective of inverse problems | Sciact - Система учета научной деятельности ИМ СО РАН

Revisiting linear machine learning through the perspective of inverse problems Научная публикация

Журнал

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Вых. Данные

Год: 2025, Том: 33, Номер: 2, Страницы: 281-303 Страниц : 23 DOI: 10.1515/jiip-2025-0010

Ключевые слова

Machine learning; linear neural network; linear inverse and ill-posed problems; regularization

Авторы

Liu Shuang ¹ , Kabanikhin Sergey ² , Strijhak Sergei ³ , Wang Ying-Ao ⁴ , Zhang Ye ⁵

Организации

1	Novosibirsk State University , Novosibirsk , Russian Federation
2	Sobolev Institute of Mathematics, Siberian Branch , Russian Academy of Sciences , Novosibirsk , Russian Federation
3	Ivannikov Institute for System Programming of the Russian Academy of Sciences , Moscow , Russian Federation
4	School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 100081 , P. R. China
5	MSU-BIT-SMBU Joint Research Center of Applied Mathematics , Shenzhen MSU-BIT University , Shenzhen 518172 , P. R. China

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2024-0001

In this paper, we revisit Linear Neural Networks (LNNs) with single-output neurons performing linear operations. The study focuses on constructing an optimal regularized weight matrix Q from training pairs { G , H } , reformulating the LNNs framework as matrix equations, and addressing it as a linear inverse problem. The ill-posedness of linear machine learning problems is analyzed through the lens of inverse problems. Furthermore, classical and modern regularization techniques from both the machine learning and inverse problems communities are reviewed. The effectiveness of LNNs is demonstrated through a real-world application in blood test classification, highlighting their practical value in solving real-life problems.

Liu S. , Kabanikhin S. , Strijhak S. , Wang Y-A. , Zhang Y.
Revisiting linear machine learning through the perspective of inverse problems
Journal of Inverse and Ill-Posed Problems. 2025. V.33. N2. P.281-303. DOI: 10.1515/jiip-2025-0010 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	2 февр. 2025 г.
Принята к публикации:	14 февр. 2025 г.
Опубликована online:	28 мар. 2025 г.
Опубликована в печати:	1 апр. 2025 г.

Web of science:	WOS:001454281300001
Scopus:	2-s2.0-105001642247
РИНЦ:	81901697
OpenAlex:	W4408919045

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