  Conditional density estimation (density regression) estimates the
distribution of a response variable y conditional on covariates x. Utilizing a
partition model framework, a conditional density estimation method is proposed
using logistic Gaussian processes. The partition is created using a Voronoi
tessellation and is learned from the data using a reversible jump Markov chain
Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible
through a Laplace approximation on the latent variables of the logistic
Gaussian process model. This approximation marginalizes the parameters in each
partition element, allowing an efficient search of the posterior distribution
of the tessellation. The method has desirable consistency properties. In
simulation and applications, the model successfully estimates the partition
structure and conditional distribution of y.
