We present a non-parametric Bayesian latent variable model capable of
learning dependency structures across dimensions in a multivariate setting. Our
approach is based on flexible Gaussian process priors for the generative
mappings and interchangeable Dirichlet process priors to learn the structure.
The introduction of the Dirichlet process as a specific structural prior allows
our model to circumvent issues associated with previous Gaussian process latent
variable models. Inference is performed by deriving an efficient variational
bound on the marginal log-likelihood on the model.