Summary: The Gaussian Process Density Sampler
Ryan Prescott Adams and David J.C. MacKay
University of Cambridge
Cambridge CB3 0HE, U.K.
The Gaussian process is a useful prior on functions for Bayesian regression and classification.
Density estimation with a Gaussian process prior has been di#cult, however, due to the require
ments that densities be nonnegative and integrate to unity. The statistics community has explored
the use of a logistic Gaussian process for density estimation, relying on various methods of approx
imating the normalization constant (e.g. [1, 4]).
We propose the Gaussian Process Density Sampler (GPDS), a nonparametric, practical and
consistent method of constructing a Markov chain on the properties of a posterior distribution on
an unknown density, without approximation. The GPDS is composed of four parts. The first part
is a GPbased prior on density functions. We develop an exchangeable procedure for generating
exact samples in data space from a common density drawn from this prior. Second, we show
that this prior allows practical inference of specific values of the unnormalized density, using the
recentlydeveloped technique of exchange sampling . Third, we extend this MCMC algorithm
to draw samples from the predictive distribution on data space that arises when the posterior on
density functions is integrated out. This is our primary result. Finally, we demonstrate a sampling