There is increasing interest in broad application areas in defining flexible
joint models for data having a variety of measurement scales, while also
allowing data of complex types, such as functions, images and documents. We
consider a general framework for nonparametric Bayes joint modeling through
mixture models that incorporate dependence across data types through a joint
mixing measure. The mixing measure is assigned a novel infinite tensor
factorization (ITF) prior that allows flexible dependence in cluster allocation
across data types. The ITF prior is formulated as a tensor product of
stick-breaking processes. Focusing on a convenient special case corresponding
to a Parafac factorization, we provide basic theory justifying the flexibility
of the proposed prior and resulting asymptotic properties. Focusing on ITF
mixtures of product kernels, we develop a new Gibbs sampling algorithm for
routine implementation relying on slice sampling. The methods are compared with
alternative joint mixture models based on Dirichlet processes and related
approaches through simulations and real data applications.Comment: Appearing in Proceedings of the 16th International Conference on
Artificial Intelligence and Statistics (AISTATS) 2013, Scottsdale, AZ, US