@techreport{c47c2f5bb21c4da38bafe3cc61f721e7,
title = "Bayesian Classification with Gaussian processes",
abstract = "We consider the problem of assigning an input vector bfx to one of m classes by predicting P(c|bfx) for c = 1, ldots, m. For a two-class problem, the probability of class 1 given bfx is estimated by s(y(bfx)), where s(y) = 1/(1 + e-y). A Gaussian process prior is placed on y(bfx), and is combined with the training data to obtain predictions for new bfx 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 multi-class problems (m >2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.",
keywords = "assigning, input vector, probability, Gaussian process, training data, predictions, Bayesian treatment prior, uncertainty, Laplace, approximation, multi-class problems, softmax function",
author = "Williams, \{Christopher K. I.\} and David Barber",
note = "Copyright {\textcopyright} 1997, Christopher K. I. Williams and David Barber. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/).",
year = "1997",
month = dec,
day = "13",
language = "English",
series = "NCRG",
publisher = "Aston University",
number = "97/015",
type = "WorkingPaper",
institution = "Aston University",
}