  In this paper we present a fully Bayesian latent variable model which
exploits conditional nonlinear(in)-dependence structures to learn an efficient
latent representation. The latent space is factorized to represent shared and
private information from multiple views of the data. In contrast to previous
approaches, we introduce a relaxation to the discrete segmentation and allow
for a "softly" shared latent space. Further, Bayesian techniques allow us to
automatically estimate the dimensionality of the latent spaces. The model is
capable of capturing structure underlying extremely high dimensional spaces.
This is illustrated by modelling unprocessed images with tenths of thousands of
pixels. This also allows us to directly generate novel images from the trained
model by sampling from the discovered latent spaces. We also demonstrate the
model by prediction of human pose in an ambiguous setting. Our Bayesian
framework allows us to perform disambiguation in a principled manner by
including latent space priors which incorporate the dynamic nature of the data.
