  Density modeling is notoriously difficult for high dimensional data. One
approach to the problem is to search for a lower dimensional manifold which
captures the main characteristics of the data. Recently, the Gaussian Process
Latent Variable Model (GPLVM) has successfully been used to find low
dimensional manifolds in a variety of complex data. The GPLVM consists of a set
of points in a low dimensional latent space, and a stochastic map to the
observed space. We show how it can be interpreted as a density model in the
observed space. However, the GPLVM is not trained as a density model and
therefore yields bad density estimates. We propose a new training strategy and
obtain improved generalisation performance and better density estimates in
comparative evaluations on several benchmark data sets.
