Bundle methods for machine learning

Alexander Smola; S Vishwanathan; Quoc Le

Bundle methods for machine learning

Alexander Smola, S Vishwanathan, Quoc Le

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1=Îµ) steps to Îµ precision for general convex problems and in O(log(1=Îµ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference
Editors	Platt, John C., Koller, Daphne, Singer, Yoram and Roweis, Sam
Place of Publication	Vancouver Canada
Publisher	MIT Press
Pages	1377-1384
Edition	Peer Reviewed
ISBN (Print)	9781605603520
Publication status	Published - 2009
Event	Conference on Advances in Neural Information Processing Systems (NIPS 2007) - Vancouver Canada Duration: 1 Jan 2009 → … http://books.nips.cc/nips20.html

Conference

Conference	Conference on Advances in Neural Information Processing Systems (NIPS 2007)
Period	1/01/09 → …
Other	December 3-6 2007
Internet address	http://books.nips.cc/nips20.html

Cite this

@inproceedings{c116e0454a684327a9b4787be4d0e0ca,

title = "Bundle methods for machine learning",

abstract = "We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1={\^I}µ) steps to {\^I}µ precision for general convex problems and in O(log(1={\^I}µ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.",

author = "Alexander Smola and S Vishwanathan and Quoc Le",

year = "2009",

language = "English",

isbn = "9781605603520",

pages = "1377--1384",

editor = "{Platt, John C., Koller, Daphne, Singer, Yoram and Roweis, Sam}",

booktitle = "Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference",

publisher = "MIT Press",

edition = "Peer Reviewed",

note = "Conference on Advances in Neural Information Processing Systems (NIPS 2007) ; Conference date: 01-01-2009",

url = "http://books.nips.cc/nips20.html",

}

Bundle methods for machine learning. / Smola, Alexander; Vishwanathan, S; Le, Quoc.
Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference. ed. / Platt, John C., Koller, Daphne, Singer, Yoram and Roweis, Sam. Peer Reviewed. ed. Vancouver Canada: MIT Press, 2009. p. 1377-1384.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Bundle methods for machine learning

AU - Smola, Alexander

AU - Vishwanathan, S

AU - Le, Quoc

PY - 2009

Y1 - 2009

N2 - We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1=Îµ) steps to Îµ precision for general convex problems and in O(log(1=Îµ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.

AB - We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1=Îµ) steps to Îµ precision for general convex problems and in O(log(1=Îµ)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.

M3 - Conference contribution

SN - 9781605603520

SP - 1377

EP - 1384

BT - Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference

A2 - null, Platt, John C., Koller, Daphne, Singer, Yoram and Roweis, Sam

PB - MIT Press

CY - Vancouver Canada

T2 - Conference on Advances in Neural Information Processing Systems (NIPS 2007)

Y2 - 1 January 2009

ER -

Bundle methods for machine learning

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