General bounds on Bayes errors for regression with Gaussian processes

Manfred Opper; Francesco Vivarelli

General bounds on Bayes errors for regression with Gaussian processes

Manfred Opper, Francesco Vivarelli

Aston University

Research output: Chapter in Book/Published conference output › Conference publication

Abstract

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 1999
Pages	302-308
Number of pages	7
Publication status	Published - 1999
Event	12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United Kingdom Duration: 30 Nov 1998 → 5 Dec 1998

Conference

Conference	12th Annual Conference on Neural Information Processing Systems, NIPS 1998
Country/Territory	United Kingdom
City	Denver, CO
Period	30/11/98 → 5/12/98

Bibliographical note

Copyright of the Massachusetts Institute of Technology Press (MIT)

Keywords

convexity
Bayesian prediction errors
regression
Gaussian processes
covariance kernel
asymptotically

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Cite this

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title = "General bounds on Bayes errors for regression with Gaussian processes",

abstract = "Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.",

keywords = "convexity, Bayesian prediction errors, regression, Gaussian processes, covariance kernel, asymptotically",

author = "Manfred Opper and Francesco Vivarelli",

note = "Copyright of the Massachusetts Institute of Technology Press (MIT); 12th Annual Conference on Neural Information Processing Systems, NIPS 1998 ; Conference date: 30-11-1998 Through 05-12-1998",

year = "1999",

language = "English",

isbn = "978-026211245-1",

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booktitle = "Advances in Neural Information Processing Systems 1999",

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T1 - General bounds on Bayes errors for regression with Gaussian processes

AU - Opper, Manfred

AU - Vivarelli, Francesco

N1 - Copyright of the Massachusetts Institute of Technology Press (MIT)

PY - 1999

Y1 - 1999

N2 - Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

AB - Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

KW - convexity

KW - Bayesian prediction errors

KW - regression

KW - Gaussian processes

KW - covariance kernel

KW - asymptotically

UR - http://www.scopus.com/inward/record.url?scp=0343244538&partnerID=8YFLogxK

UR - http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=4746

M3 - Conference publication

SN - 978-026211245-1

SP - 302

EP - 308

BT - Advances in Neural Information Processing Systems 1999

T2 - 12th Annual Conference on Neural Information Processing Systems, NIPS 1998

Y2 - 30 November 1998 through 5 December 1998

ER -

General bounds on Bayes errors for regression with Gaussian processes

Abstract

Conference

Bibliographical note

Keywords

Access to Document

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Cite this