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Article: Adaptive iterative Hessian sketch via A-optimal subsampling
Title | Adaptive iterative Hessian sketch via A-optimal subsampling |
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Authors | |
Keywords | Hessian sketch Subsampling Optimal design Preconditioner Exact line search |
Issue Date | 2020 |
Publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174 |
Citation | Statistics and Computing, 2020, v. 30 n. 4, p. 1075-1090 How to Cite? |
Abstract | Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (J Mach Learn Res 17(1):1842–1879, 2016) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorithm under the unconstrained least squares problem setting and then propose a deterministic approach for improving IHS via A-optimal subsampling. Our contributions are threefold: (1) a good initial estimator based on the A-optimal design is suggested; (2) a novel ridged preconditioner is developed for repeated sketching; and (3) an exact line search method is proposed for determining the optimal step length adaptively. Extensive experimental results demonstrate that our proposed A-optimal IHS algorithm outperforms the existing accelerated IHS methods. |
Persistent Identifier | http://hdl.handle.net/10722/288176 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 0.923 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhang, A | - |
dc.contributor.author | ZHANG, H | - |
dc.contributor.author | Yin, G | - |
dc.date.accessioned | 2020-10-05T12:08:59Z | - |
dc.date.available | 2020-10-05T12:08:59Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Statistics and Computing, 2020, v. 30 n. 4, p. 1075-1090 | - |
dc.identifier.issn | 0960-3174 | - |
dc.identifier.uri | http://hdl.handle.net/10722/288176 | - |
dc.description.abstract | Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (J Mach Learn Res 17(1):1842–1879, 2016) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorithm under the unconstrained least squares problem setting and then propose a deterministic approach for improving IHS via A-optimal subsampling. Our contributions are threefold: (1) a good initial estimator based on the A-optimal design is suggested; (2) a novel ridged preconditioner is developed for repeated sketching; and (3) an exact line search method is proposed for determining the optimal step length adaptively. Extensive experimental results demonstrate that our proposed A-optimal IHS algorithm outperforms the existing accelerated IHS methods. | - |
dc.language | eng | - |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174 | - |
dc.relation.ispartof | Statistics and Computing | - |
dc.rights | This is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI] | - |
dc.subject | Hessian sketch | - |
dc.subject | Subsampling | - |
dc.subject | Optimal design | - |
dc.subject | Preconditioner | - |
dc.subject | Exact line search | - |
dc.title | Adaptive iterative Hessian sketch via A-optimal subsampling | - |
dc.type | Article | - |
dc.identifier.email | Zhang, A: ajzhang@hku.hk | - |
dc.identifier.email | Yin, G: gyin@hku.hk | - |
dc.identifier.authority | Zhang, A=rp02179 | - |
dc.identifier.authority | Yin, G=rp00831 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11222-020-09936-8 | - |
dc.identifier.scopus | eid_2-s2.0-85081925874 | - |
dc.identifier.hkuros | 315646 | - |
dc.identifier.volume | 30 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 1075 | - |
dc.identifier.epage | 1090 | - |
dc.identifier.isi | WOS:000538281900019 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0960-3174 | - |