Nonparametric tree graphical models
We introduce a nonparametric representation for graphical model on trees which expresses marginals as Hilbert space embeddings and conditionals as embedding operators. This formulation allows us to define a graphi- cal model solely on the basis of the feature space representation of its variables. Thus, this nonparametric model can be applied to general domains where kernels are defined, handling challenging cases such as discrete variables with huge domains, or very com- plex, non-Gaussian continuous distributions. We also derive kernel belief propagation, a Hilbert-space algorithm for performing infer- ence in our model. We show that our method outperforms state-of-the-art techniques in a cross-lingual document retrieval task and a camera rotation estimation problem.