  The data association problem is concerned with separating data coming from
different generating processes, for example when data come from different data
sources, contain significant noise, or exhibit multimodality. We present a
fully Bayesian approach to this problem. Our model is capable of simultaneously
solving the data association problem and the induced supervised learning
problems. Underpinning our approach is the use of Gaussian process priors to
encode the structure of both the data and the data associations. We present an
efficient learning scheme based on doubly stochastic variational inference and
discuss how it can be applied to deep Gaussian process priors.
