Nonparametric Tree Graphical Models via Kernel Embeddings

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 dene a graphical 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 dened, handling challenging cases such as discrete variables with huge domains, or very complex, non-Gaussian continuous distributions. We also derive kernel belief propagation, a Hilbert-space algorithm for performing inference 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.