Skip navigation
Skip navigation

Regression with the Optimised Combination Technique

Garcke, Jochen

Description

We consider the sparse grid combination technique for regression, which we regard as a problem of function reconstruction in some given function space. We use a regularised least squares approach, discretised by sparse grids and solved using the so-called combination technique, where a certain sequence of conventional grids is employed. The sparse grid solution is then obtained by addition of the partial solutions with combination coefficients dependent on the involved grids. This approach...[Show more]

dc.contributor.authorGarcke, Jochen
dc.coverage.spatialPittsburgh USA
dc.date.accessioned2015-12-07T22:47:19Z
dc.date.createdJune 25-29 2006
dc.identifier.isbn1595933832
dc.identifier.urihttp://hdl.handle.net/1885/26024
dc.description.abstractWe consider the sparse grid combination technique for regression, which we regard as a problem of function reconstruction in some given function space. We use a regularised least squares approach, discretised by sparse grids and solved using the so-called combination technique, where a certain sequence of conventional grids is employed. The sparse grid solution is then obtained by addition of the partial solutions with combination coefficients dependent on the involved grids. This approach shows instabilities in certain situations and is not guaranteed to converge with higher discretisation levels. In this article we apply the recently introduced optimised combination technique, which repairs these instabilities. Now the combination coefficients also depend on the function to be reconstructed, resulting in a non-linear approximation method which achieves very competitive results. We show that the computational complexity of the improved method still scales only linear in regard to the number of data.
dc.publisherAssociation for Computing Machinery Inc (ACM)
dc.relation.ispartofseriesInternational Conference on Machine Learning (ICML 2006)
dc.sourceProceedings of 23rd International Conference of Machine Learning
dc.source.urihttp://shop.omnipress.com/icml/toc.pdf
dc.subjectKeywords: Computational complexity; Data acquisition; Function evaluation; Least squares approximations; Nonlinear analysis; Combination coefficients; Combination technique; Function space; Optimized combination technique; Sparse Grid combination technique; Regress
dc.titleRegression with the Optimised Combination Technique
dc.typeConference paper
local.description.notesImported from ARIES
local.description.refereedYes
dc.date.issued2006
local.identifier.absfor010301 - Numerical Analysis
local.identifier.ariespublicationu3488905xPUB42
local.type.statusPublished Version
local.contributor.affiliationGarcke, Jochen, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage321
local.bibliographicCitation.lastpage328
local.identifier.doi10.1145/1143844.1143885
dc.date.updated2015-12-07T11:50:31Z
local.identifier.scopusID2-s2.0-34250774501
CollectionsANU Research Publications

Download

File Description SizeFormat Image
01_Garcke_Regression_with_the_Optimised_2006.pdf256.03 kBAdobe PDFThumbnail
02_Garcke_Regression_with_the_Optimised_2006.pdf289.24 kBAdobe PDFThumbnail


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  19 May 2020/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator