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Abstract:
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 the posterior distribution of the noise rate
can be sampled using Gibbs sampling. Our results on a synthetic
data set give a posterior variance that well-approximates the true
variance. We also show that the predictive likelihood of a test
data set approximates the true likelihood better under this model
than under a uniform noise model.
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