The subspace information criterion for infinite dimensional hypothesis spaces

Masashi Sugiyama, Klaus Muller

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The paper extended the range of applicability of subspace information criterion (SIC). It was showed that even if the reproducing kernels centered on training sample points do not span the whole space, SIC was an unbiased estimator of an essential part of the generalization error. The extension allowed the use of any reproducing kernel Hilbert spaces (RKHS) including infinite dimension ones.

Original languageEnglish
Pages (from-to)323-359
Number of pages37
JournalJournal of Machine Learning Research
Volume3
Issue number2
DOIs
Publication statusPublished - 2003 Feb 15
Externally publishedYes

Fingerprint

Information Criterion
Hilbert spaces
Subspace
Generalization Error
Reproducing Kernel Hilbert Space
Sample point
Reproducing Kernel
Infinite Dimensions
Unbiased estimator
Training Samples
Range of data

Keywords

  • Cross-validation
  • Finite sample statistics
  • Gaussian processes
  • Generalization error
  • Kernel regression
  • Model selection
  • Reproducing kernel Hilbert space
  • Subspace information criterion
  • Unbiased estimators

ASJC Scopus subject areas

  • Artificial Intelligence

Cite this

The subspace information criterion for infinite dimensional hypothesis spaces. / Sugiyama, Masashi; Muller, Klaus.

In: Journal of Machine Learning Research, Vol. 3, No. 2, 15.02.2003, p. 323-359.

Research output: Contribution to journalArticle

Sugiyama, Masashi ; Muller, Klaus. / The subspace information criterion for infinite dimensional hypothesis spaces. In: Journal of Machine Learning Research. 2003 ; Vol. 3, No. 2. pp. 323-359.
@article{2b070b735de3429ead59ddf22f4f857d,
title = "The subspace information criterion for infinite dimensional hypothesis spaces",
abstract = "The paper extended the range of applicability of subspace information criterion (SIC). It was showed that even if the reproducing kernels centered on training sample points do not span the whole space, SIC was an unbiased estimator of an essential part of the generalization error. The extension allowed the use of any reproducing kernel Hilbert spaces (RKHS) including infinite dimension ones.",
keywords = "Cross-validation, Finite sample statistics, Gaussian processes, Generalization error, Kernel regression, Model selection, Reproducing kernel Hilbert space, Subspace information criterion, Unbiased estimators",
author = "Masashi Sugiyama and Klaus Muller",
year = "2003",
month = "2",
day = "15",
doi = "10.1162/153244303765208412",
language = "English",
volume = "3",
pages = "323--359",
journal = "Journal of Machine Learning Research",
issn = "1532-4435",
publisher = "Microtome Publishing",
number = "2",

}

TY - JOUR

T1 - The subspace information criterion for infinite dimensional hypothesis spaces

AU - Sugiyama, Masashi

AU - Muller, Klaus

PY - 2003/2/15

Y1 - 2003/2/15

N2 - The paper extended the range of applicability of subspace information criterion (SIC). It was showed that even if the reproducing kernels centered on training sample points do not span the whole space, SIC was an unbiased estimator of an essential part of the generalization error. The extension allowed the use of any reproducing kernel Hilbert spaces (RKHS) including infinite dimension ones.

AB - The paper extended the range of applicability of subspace information criterion (SIC). It was showed that even if the reproducing kernels centered on training sample points do not span the whole space, SIC was an unbiased estimator of an essential part of the generalization error. The extension allowed the use of any reproducing kernel Hilbert spaces (RKHS) including infinite dimension ones.

KW - Cross-validation

KW - Finite sample statistics

KW - Gaussian processes

KW - Generalization error

KW - Kernel regression

KW - Model selection

KW - Reproducing kernel Hilbert space

KW - Subspace information criterion

KW - Unbiased estimators

UR - http://www.scopus.com/inward/record.url?scp=0041965965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041965965&partnerID=8YFLogxK

U2 - 10.1162/153244303765208412

DO - 10.1162/153244303765208412

M3 - Article

AN - SCOPUS:0041965965

VL - 3

SP - 323

EP - 359

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1532-4435

IS - 2

ER -