Bayesian classification with Gaussian processes

Christopher K. I. Williams, David Barber

    Research output: Contribution to journalArticle

    Abstract

    We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c=1,...,m. For a two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y)=1/(1+e-y). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a Bayesian treatment, integrating over uncertainty in y and in the parameters that control the Gaussian process prior the necessary integration over y is carried out using Laplace's approximation. The method is generalized to multiclass problems (m>2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.
    Original languageEnglish
    Pages (from-to)1342 -1351
    Number of pages10
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Volume20
    Issue number12
    DOIs
    Publication statusPublished - 12 Dec 1998

    Bibliographical note

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    Keywords

    • assigning
    • input vector
    • probability
    • Gaussian process
    • training data
    • predictions
    • Bayesian treatment prior
    • uncertainty
    • Laplace
    • approximation
    • multi-class problems
    • softmax function

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