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Summary: NONPARAMETRIC BAYESIAN DENSITY MODELING
WITH GAUSSIAN PROCESSES
By Ryan P. Adams, Iain Murray and David J.C. MacKay
University of Toronto and University of Cambridge
We present the Gaussian process density sampler (GPDS), an
exchangeable generative model for use in nonparametric Bayesian
density estimation. Samples drawn from the GPDS are consistent
with exact, independent samples from a distribution defined by a
density that is a transformation of a function drawn from a Gaussian
process prior. Our formulation allows us to infer an unknown density
from data using Markov chain Monte Carlo, which gives samples
from the posterior distribution over density functions and from the
predictive distribution on data space. We describe two such MCMC
methods. Both methods also allow inference of the hyperparameters
of the Gaussian process.
1. Introduction. We propose a method for incorporating a Gaussian
process into a prior on probability density functions. While such construc-
tions have been proposed before [Leonard, 1978, Thorburn, 1986, Lenk, 1988,
1991, Csat´o, 2002, Tokdar and Ghosh, 2007, Tokdar, 2007], ours is the first
that allows a procedure for drawing exact and exchangeable data samples
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