Nonparametric Tree Graphical Models

Le Song, Arthur Gretton, Carlos Guestrin
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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-song10a, title = {Nonparametric Tree Graphical Models}, author = {Song, Le and Gretton, Arthur and Guestrin, Carlos}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {765--772}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/song10a/song10a.pdf}, url = {https://proceedings.mlr.press/v9/song10a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Nonparametric Tree Graphical Models %A Le Song %A Arthur Gretton %A Carlos Guestrin %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-song10a %I PMLR %P 765--772 %U https://proceedings.mlr.press/v9/song10a.html %V 9 %X 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 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.
RIS
TY - CPAPER TI - Nonparametric Tree Graphical Models AU - Le Song AU - Arthur Gretton AU - Carlos Guestrin BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-song10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 765 EP - 772 L1 - http://proceedings.mlr.press/v9/song10a/song10a.pdf UR - https://proceedings.mlr.press/v9/song10a.html AB - 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 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. ER -
APA
Song, L., Gretton, A. & Guestrin, C.. (2010). Nonparametric Tree Graphical Models. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:765-772 Available from https://proceedings.mlr.press/v9/song10a.html.

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