Low-rank approximations in statistics

Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Usevich, Konstantin 2025. Low-rank approximations in statistics. Lovric, Miodrag, ed. International Encyclopedia of Statistical Science, Springer, pp. 1398-1400. (10.1007/978-3-662-69359-9_338)

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Abstract

Low-rank approximations are one of the great success stories in statistics over the last decade. They now constitute the dominant paradigm for improving the amenability of large-scale problems, primarily to reduce the dimension of the problem in hand. They are also used in ill-posed problems, where restricting the rank acts as a kind of regularization to assist in obtaining a stable and tractable solution. The most classic result in the field of low-rank approximations is the truncated singular value decomposition (SVD) described in Theorem 1, which offers an optimal way to find a rank r approximation of a given matrix X.

Item Type:	Book Section
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer
ISBN:	9783662693582
Date of First Compliant Deposit:	27 June 2025
Date of Acceptance:	27 May 2025
Last Modified:	02 Jul 2025 13:50
URI:	https://orca.cardiff.ac.uk/id/eprint/179365

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