Efficient computation of smoothing splines via adaptive basis sampling

Handle URI:
http://hdl.handle.net/10754/598102
Title:
Efficient computation of smoothing splines via adaptive basis sampling
Authors:
Ma, Ping; Huang, Jianhua Z.; Zhang, Nan
Abstract:
© 2015 Biometrika Trust. Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O(n<sup>3</sup>). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. Using simulation studies and a large-scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a sampling method that does not use the values of response variables.
Citation:
Ma P, Huang JZ, Zhang N (2015) Efficient computation of smoothing splines via adaptive basis sampling. Biometrika 102: 631–645. Available: http://dx.doi.org/10.1093/biomet/asv009.
Publisher:
Oxford University Press (OUP)
Journal:
Biometrika
Issue Date:
24-Jun-2015
DOI:
10.1093/biomet/asv009
Type:
Article
ISSN:
0006-3444; 1464-3510
Sponsors:
The first author thanks Chong Gu for many helpful discussions. Ma’s work was partially supportedby the National Science Foundation and the U.S. Department of Energy. Huang’s workwas partially supported by the National Science Foundation and King Abdullah University ofScience and Technology.
Appears in Collections:
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Full metadata record

DC FieldValue Language
dc.contributor.authorMa, Pingen
dc.contributor.authorHuang, Jianhua Z.en
dc.contributor.authorZhang, Nanen
dc.date.accessioned2016-02-25T13:12:43Zen
dc.date.available2016-02-25T13:12:43Zen
dc.date.issued2015-06-24en
dc.identifier.citationMa P, Huang JZ, Zhang N (2015) Efficient computation of smoothing splines via adaptive basis sampling. Biometrika 102: 631–645. Available: http://dx.doi.org/10.1093/biomet/asv009.en
dc.identifier.issn0006-3444en
dc.identifier.issn1464-3510en
dc.identifier.doi10.1093/biomet/asv009en
dc.identifier.urihttp://hdl.handle.net/10754/598102en
dc.description.abstract© 2015 Biometrika Trust. Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O(n<sup>3</sup>). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. Using simulation studies and a large-scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a sampling method that does not use the values of response variables.en
dc.description.sponsorshipThe first author thanks Chong Gu for many helpful discussions. Ma’s work was partially supportedby the National Science Foundation and the U.S. Department of Energy. Huang’s workwas partially supported by the National Science Foundation and King Abdullah University ofScience and Technology.en
dc.publisherOxford University Press (OUP)en
dc.subjectBayesian confidence intervalen
dc.subjectCore-mantle boundaryen
dc.subjectNonparametric regressionen
dc.subjectPenalized least squaresen
dc.subjectReproducing kernel Hilbert spaceen
dc.subjectSamplingen
dc.titleEfficient computation of smoothing splines via adaptive basis samplingen
dc.typeArticleen
dc.identifier.journalBiometrikaen
dc.contributor.institutionThe University of Georgia, Athens, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
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