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# Nonparametric Tree Graphical Models

*Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics*, PMLR 9:765-772, 2010.

#### Abstract

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 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 defined, handling challenging cases such as discrete variables whose domains are huge, or very complex, non-Gaussian continuous distributions. We also derive \emphkernel 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.