Some theoretical results concerning the convergence of compositions of regularized linear functions

Tong Zhang

Some theoretical results concerning the convergence of compositions of regularized linear functions

Tong Zhang^*

^*Corresponding author for this work

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

2 Citations (Scopus)

Abstract

Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. Ini this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linear functions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers with similar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods from the asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999
Publisher	Neural information processing systems foundation
Pages	370-378
Number of pages	9
ISBN (Print)	0262194503, 9780262194501
Publication status	Published - 2000
Externally published	Yes
Event	13th Annual Neural Information Processing Systems Conference, NIPS 1999 - Denver, CO, United States Duration: 29 Nov 1999 → 4 Dec 1999

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Conference

Conference	13th Annual Neural Information Processing Systems Conference, NIPS 1999
Country/Territory	United States
City	Denver, CO
Period	29/11/99 → 4/12/99

Cite this

@inproceedings{718ffd5a88774489b58356e7af3947bc,

title = "Some theoretical results concerning the convergence of compositions of regularized linear functions",

abstract = "Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. Ini this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linear functions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers with similar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods from the asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms.",

author = "Tong Zhang",

year = "2000",

language = "English",

isbn = "0262194503",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

pages = "370--378",

booktitle = "Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999",

note = "13th Annual Neural Information Processing Systems Conference, NIPS 1999 ; Conference date: 29-11-1999 Through 04-12-1999",

}

Zhang, T 2000, Some theoretical results concerning the convergence of compositions of regularized linear functions. in Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999. Advances in Neural Information Processing Systems, Neural information processing systems foundation, pp. 370-378, 13th Annual Neural Information Processing Systems Conference, NIPS 1999, Denver, CO, United States, 29/11/99.

Some theoretical results concerning the convergence of compositions of regularized linear functions. / Zhang, Tong.
Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999. Neural information processing systems foundation, 2000. p. 370-378 (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

TY - GEN

T1 - Some theoretical results concerning the convergence of compositions of regularized linear functions

AU - Zhang, Tong

PY - 2000

Y1 - 2000

N2 - Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. Ini this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linear functions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers with similar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods from the asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms.

AB - Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. Ini this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linear functions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers with similar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods from the asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms.

UR - http://www.scopus.com/inward/record.url?scp=0006557529&partnerID=8YFLogxK

M3 - Conference Paper published in a book

AN - SCOPUS:0006557529

SN - 0262194503

SN - 9780262194501

T3 - Advances in Neural Information Processing Systems

SP - 370

EP - 378

BT - Advances in Neural Information Processing Systems 12 - Proceedings of the 1999 Conference, NIPS 1999

PB - Neural information processing systems foundation

T2 - 13th Annual Neural Information Processing Systems Conference, NIPS 1999

Y2 - 29 November 1999 through 4 December 1999

ER -

Some theoretical results concerning the convergence of compositions of regularized linear functions

Abstract

Publication series

Conference

Other files and links

Fingerprint

Cite this