Regression with input-dependent noise: A Gaussian process treatment


Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.

Divisions: Aston University (General)
Additional Information: Copyright of Massachusetts Institute of Technology Press
Uncontrolled Keywords: Gaussian processes,regression functions,posterior distribution,synthetic data set,true variance
Publication ISSN: 1049-5258
Last Modified: 27 Dec 2023 08:04
Date Deposited: 18 Sep 2009 16:03
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://mitpress ... type=2&tid=8363 (Publisher URL)
PURE Output Type: Article
Published Date: 1997
Authors: Goldberg, Paul W.
Williams, Christopher K. I.
Bishop, Christopher M.



Version: Published Version

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