Belief Propagation: Accurate Marginals or Accurate Partition Function – Where is the Difference?

Christian Knoll, Franz Pernkopf
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:627-636, 2020.

Abstract

We analyze belief propagation on patch potential models – these are attractive models with varying local potentials – obtain all of the possibly many fixed points, and gather novel insights into belief propagation’s properties. In particular, we observe and theoretically explain several regions in the parameter space that behave fundamentally different. We specify and elaborate on one specific region that, despite the existence of multiple fixed points, is relatively well behaved and provides insights into the relationship between the accuracy of the marginals and the partition function. We demonstrate the inexistence of a principle relationship between both quantities and provide sufficient conditions for a fixed point to be optimal with respect to approximating both the marginals and the partition function.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-knoll20a, title = {Belief Propagation: Accurate Marginals or Accurate Partition Function – Where is the Difference?}, author = {Knoll, Christian and Pernkopf, Franz}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {627--636}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/knoll20a/knoll20a.pdf}, url = {https://proceedings.mlr.press/v115/knoll20a.html}, abstract = {We analyze belief propagation on patch potential models – these are attractive models with varying local potentials – obtain all of the possibly many fixed points, and gather novel insights into belief propagation’s properties. In particular, we observe and theoretically explain several regions in the parameter space that behave fundamentally different. We specify and elaborate on one specific region that, despite the existence of multiple fixed points, is relatively well behaved and provides insights into the relationship between the accuracy of the marginals and the partition function. We demonstrate the inexistence of a principle relationship between both quantities and provide sufficient conditions for a fixed point to be optimal with respect to approximating both the marginals and the partition function.} }
Endnote
%0 Conference Paper %T Belief Propagation: Accurate Marginals or Accurate Partition Function – Where is the Difference? %A Christian Knoll %A Franz Pernkopf %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-knoll20a %I PMLR %P 627--636 %U https://proceedings.mlr.press/v115/knoll20a.html %V 115 %X We analyze belief propagation on patch potential models – these are attractive models with varying local potentials – obtain all of the possibly many fixed points, and gather novel insights into belief propagation’s properties. In particular, we observe and theoretically explain several regions in the parameter space that behave fundamentally different. We specify and elaborate on one specific region that, despite the existence of multiple fixed points, is relatively well behaved and provides insights into the relationship between the accuracy of the marginals and the partition function. We demonstrate the inexistence of a principle relationship between both quantities and provide sufficient conditions for a fixed point to be optimal with respect to approximating both the marginals and the partition function.
APA
Knoll, C. & Pernkopf, F.. (2020). Belief Propagation: Accurate Marginals or Accurate Partition Function – Where is the Difference?. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:627-636 Available from https://proceedings.mlr.press/v115/knoll20a.html.

Related Material