Editing Ridge regression (section)

==History==
Tikhonov regularization was invented independently in many different contexts.
It became widely known through its application to integral equations in the works of [[Andrey Nikolayevich Tikhonov|Andrey Tikhonov]]<ref>{{Cite journal| last=Tikhonov | first=Andrey Nikolayevich | author-link=Andrey Nikolayevich Tikhonov | year=1943 | title=Об устойчивости обратных задач |trans-title=On the stability of inverse problems | journal=[[Doklady Akademii Nauk SSSR]] | volume=39 | issue=5 | pages=195–198|url=http://a-server.math.nsc.ru/IPP/BASE_WORK/tihon_en.html| archive-url=https://web.archive.org/web/20050227163812/http://a-server.math.nsc.ru/IPP/BASE_WORK/tihon_en.html | archive-date=2005-02-27 }}</ref><ref>{{Cite journal| last=Tikhonov | first=A. N. | year=1963 | title=О решении некорректно поставленных задач и методе регуляризации | journal=Doklady Akademii Nauk SSSR | volume=151 | pages=501–504}}. Translated in {{Cite journal| journal=Soviet Mathematics | volume=4 | pages=1035–1038 | title=Solution of incorrectly formulated problems and the regularization method }}</ref><ref>{{Cite book| last=Tikhonov | first=A. N. |author2=V. Y. Arsenin  | year=1977 | title=Solution of Ill-posed Problems | publisher=Winston & Sons | location=Washington | isbn=0-470-99124-0}}</ref><ref>{{cite book |last1=Tikhonov |first1=Andrey Nikolayevich |last2=Goncharsky |first2=A. |last3=Stepanov |first3=V. V. |last4=Yagola |first4=Anatolij Grigorevic |title=Numerical Methods for the Solution of Ill-Posed Problems |date=30 June 1995 |publisher=Springer Netherlands |location=Netherlands |isbn=0-7923-3583-X |url=https://www.springer.com/us/book/9780792335832 |access-date=9 August 2018 |ref=TikhonovSpringer1995Numerical}}</ref><ref>{{cite book |last1=Tikhonov |first1=Andrey Nikolaevich |last2=Leonov |first2=Aleksandr S. |last3=Yagola |first3=Anatolij Grigorevic |title=Nonlinear ill-posed problems |date=1998 |publisher=Chapman & Hall |location=London |isbn=0-412-78660-5 |url=https://www.springer.com/us/book/9789401751698 |access-date=9 August 2018 |ref=TikhonovChapmanHall1998Nonlinear}}</ref> and David L. Phillips.<ref>{{Cite journal | last1 = Phillips | first1 = D. L. | doi = 10.1145/321105.321114 | title = A Technique for the Numerical Solution of Certain Integral Equations of the First Kind | journal = Journal of the ACM | volume = 9 | pages = 84–97 | year = 1962 | s2cid = 35368397 | doi-access = free }}</ref> Some authors use the term '''Tikhonov–Phillips regularization'''.
The finite-dimensional case was expounded by [[Arthur E. Hoerl]], who took a statistical approach,<ref>{{cite journal |last1=Hoerl |first1=Arthur E. |title=Application of Ridge Analysis to Regression Problems |journal=Chemical Engineering Progress |date=1962 |volume=58 |issue=3 |pages=54–59 |ref=AEHoerl1962V58I3}}</ref> and by Manus Foster, who interpreted this method as a [[Kriging|Wiener–Kolmogorov (Kriging)]] filter.<ref>{{Cite journal | last1 = Foster | first1 = M. | title = An Application of the Wiener-Kolmogorov Smoothing Theory to Matrix Inversion | doi = 10.1137/0109031 | journal = Journal of the Society for Industrial and Applied Mathematics | volume = 9 | issue = 3 | pages = 387–392 | year = 1961 }}</ref> Following Hoerl, it is known in the statistical literature as ridge regression,<ref>{{cite journal | last = Hoerl | first = A. E. |author2=R. W. Kennard | year = 1970 | title=Ridge regression: Biased estimation for nonorthogonal problems | journal=Technometrics | volume=12 | issue=1 | pages = 55–67 | doi=10.1080/00401706.1970.10488634}}</ref> named after ridge analysis ("ridge" refers to the path from the constrained maximum).<ref>{{Cite journal |last=Hoerl |first=Roger W. |date=2020-10-01 |title=Ridge Regression: A Historical Context |url=https://www.tandfonline.com/doi/full/10.1080/00401706.2020.1742207 |journal=Technometrics |language=en |volume=62 |issue=4 |pages=420–425 |doi=10.1080/00401706.2020.1742207 |issn=0040-1706|url-access=subscription }}</ref>