A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization
type: Item
instance of: scholarly article
title: A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization
zbMATH Open document ID: 1208.41007
author: Pakize Taylan
author: Fatma Yerlikaya Özkurt
author: Gerhard-Wilhelm Weber
published in: Top
publication date: 2011-01-28T00:00:00Z
review text: Multivariate approximation and data mining using optimization and regularization methods are discussed in this article. High dimensional approximation problems are solved by a Tikhonov regularization ansatz with a penalized residual sum of squares. The ensuing problem is then solved by modern continuous optimization methods such as interior point methods. At first, the multivariate adaptive regression spline method is introduced and next the aforementioned ansatz with the penalized residual sum of squares used. The optimization methods are then discussed and numerical examples are given.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5842732
zbMATH Keywords: regression
zbMATH Keywords: statistical learning
zbMATH Keywords: MARS
zbMATH Keywords: clustering
zbMATH Keywords: curvature
zbMATH Keywords: penalty methods
zbMATH Keywords: classification
zbMATH Keywords: continuous optimization
zbMATH Keywords: conic quadratic programming
zbMATH Keywords: well-structured convex problems
zbMATH Keywords: interior point methods
describes a project that uses: Regularization tools
describes a project that uses: UCI-ml
describes a project that uses: UTV
MaRDI profile type: Publication
full work available at URL: s11750-010-0155-7
OpenAlex ID: W2078100786
cites work: Q4654008
cites work: Q3327527
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DOI: 10.1007/S11750-010-0155-7
description: scientific article; zbMATH DE number 5842732