Regression with input-dependent noise: A Gaussian process treatment

Paul W. Goldberg, Christopher K. I. Williams, Christopher M. Bishop, Michael I. Jordan (Editor), Michael J. Kearns (Editor), Sara A. Solla (Editor)

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)493-499
    Number of pages7
    JournalAdvances in Neural Information Processing Systems
    Publication statusPublished - 1997

    Bibliographical note

    Copyright of Massachusetts Institute of Technology Press


    • Gaussian processes
    • regression functions
    • posterior distribution
    • synthetic data set
    • true variance


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