Bayesian Inference of Noise Levels in Regression

Christopher M. Bishop, C. S. Qazaz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood for training such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

Original languageEnglish
Title of host publicationProceedings 1996 International Conference on Artificial Neural Networks, ICANN'96, Bochum, Germany
PublisherSpringer
Pages59-64
Number of pages5
Publication statusPublished - 1 Jan 1997

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