Message Passing for Collective Graphical Models

Tao Sun, Dan Sheldon, Akshat Kumar
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:853-861, 2015.

Abstract

Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-sunc15, title = {Message Passing for Collective Graphical Models}, author = {Sun, Tao and Sheldon, Dan and Kumar, Akshat}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {853--861}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/sunc15.pdf}, url = {https://proceedings.mlr.press/v37/sunc15.html}, abstract = {Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility.} }
Endnote
%0 Conference Paper %T Message Passing for Collective Graphical Models %A Tao Sun %A Dan Sheldon %A Akshat Kumar %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-sunc15 %I PMLR %P 853--861 %U https://proceedings.mlr.press/v37/sunc15.html %V 37 %X Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility.
RIS
TY - CPAPER TI - Message Passing for Collective Graphical Models AU - Tao Sun AU - Dan Sheldon AU - Akshat Kumar BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-sunc15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 853 EP - 861 L1 - http://proceedings.mlr.press/v37/sunc15.pdf UR - https://proceedings.mlr.press/v37/sunc15.html AB - Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility. ER -
APA
Sun, T., Sheldon, D. & Kumar, A.. (2015). Message Passing for Collective Graphical Models. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:853-861 Available from https://proceedings.mlr.press/v37/sunc15.html.

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