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Revisiting linear machine learning through the perspective of inverse problems. / Liu, Shuang; Kabanikhin, Sergey; Strijhak, Sergei et al.

In: Journal of Inverse and Ill-Posed Problems, 28.03.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Liu, S, Kabanikhin, S, Strijhak, S, Wang, YA & Zhang, Y 2025, 'Revisiting linear machine learning through the perspective of inverse problems', Journal of Inverse and Ill-Posed Problems. https://doi.org/10.1515/jiip-2025-0010

APA

Liu, S., Kabanikhin, S., Strijhak, S., Wang, Y. A., & Zhang, Y. (2025). Revisiting linear machine learning through the perspective of inverse problems. Journal of Inverse and Ill-Posed Problems. https://doi.org/10.1515/jiip-2025-0010

Vancouver

Liu S, Kabanikhin S, Strijhak S, Wang YA, Zhang Y. Revisiting linear machine learning through the perspective of inverse problems. Journal of Inverse and Ill-Posed Problems. 2025 Mar 28. doi: 10.1515/jiip-2025-0010

Author

Liu, Shuang ; Kabanikhin, Sergey ; Strijhak, Sergei et al. / Revisiting linear machine learning through the perspective of inverse problems. In: Journal of Inverse and Ill-Posed Problems. 2025.

BibTeX

@article{8b14f0b21bc04356becab61300c5fbd9,
title = "Revisiting linear machine learning through the perspective of inverse problems",
abstract = "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.",
keywords = "Machine learning, linear inverse and ill-posed problems, linear neural network, regularization",
author = "Shuang Liu and Sergey Kabanikhin and Sergei Strijhak and Wang, {Ying Ao} and Ye Zhang",
note = "Funding source: National Key Research and Development Program of China Award Identifier / Grant number: 2022YFC3310300",
year = "2025",
month = mar,
day = "28",
doi = "10.1515/jiip-2025-0010",
language = "English",
journal = "Journal of Inverse and Ill-Posed Problems",
issn = "0928-0219",
publisher = "Walter de Gruyter GmbH",

}

RIS

TY - JOUR

T1 - Revisiting linear machine learning through the perspective of inverse problems

AU - Liu, Shuang

AU - Kabanikhin, Sergey

AU - Strijhak, Sergei

AU - Wang, Ying Ao

AU - Zhang, Ye

N1 - Funding source: National Key Research and Development Program of China Award Identifier / Grant number: 2022YFC3310300

PY - 2025/3/28

Y1 - 2025/3/28

N2 - 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.

AB - 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.

KW - Machine learning

KW - linear inverse and ill-posed problems

KW - linear neural network

KW - regularization

UR - https://www.mendeley.com/catalogue/1abb48ac-5627-3b25-9af4-7436d13a8a9c/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001642247&origin=inward&txGid=16463e7a8425cdeeb8907866ad0feef8

U2 - 10.1515/jiip-2025-0010

DO - 10.1515/jiip-2025-0010

M3 - Article

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

ER -

ID: 65167992