On Loopy Belief Propagation – Local Stability Analysis for Non-Vanishing Fields

Christian Knoll, Franz Pernkopf
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:591-600, 2017.

Abstract

In this work we obtain all fixed points of be- lief propagation and perform a local stability analysis. We consider pairwise interactions of binary random variables and investigate the in- fluence of non-vanishing fields and finite-size graphs on the performance of belief propaga- tion; local stability is heavily influenced by these properties. We show why non-vanishing fields help to achieve convergence and increase the accuracy of belief propagation. We fur- ther explain the close connections between the underlying graph structure, the existence of multiple solutions, and the capability of belief propagation (with damping) to converge. Fi- nally we provide insights into why finite-size graphs behave better than infinite-size graphs.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-knoll17a, title = {On Loopy Belief Propagation – Local Stability Analysis for Non-Vanishing Fields}, author = {Knoll, Christian and Pernkopf, Franz}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {591--600}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/knoll17a/knoll17a.pdf}, url = {https://proceedings.mlr.press/r15/knoll17a.html}, abstract = {In this work we obtain all fixed points of be- lief propagation and perform a local stability analysis. We consider pairwise interactions of binary random variables and investigate the in- fluence of non-vanishing fields and finite-size graphs on the performance of belief propaga- tion; local stability is heavily influenced by these properties. We show why non-vanishing fields help to achieve convergence and increase the accuracy of belief propagation. We fur- ther explain the close connections between the underlying graph structure, the existence of multiple solutions, and the capability of belief propagation (with damping) to converge. Fi- nally we provide insights into why finite-size graphs behave better than infinite-size graphs.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On Loopy Belief Propagation – Local Stability Analysis for Non-Vanishing Fields %A Christian Knoll %A Franz Pernkopf %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-knoll17a %I PMLR %P 591--600 %U https://proceedings.mlr.press/r15/knoll17a.html %V R15 %X In this work we obtain all fixed points of be- lief propagation and perform a local stability analysis. We consider pairwise interactions of binary random variables and investigate the in- fluence of non-vanishing fields and finite-size graphs on the performance of belief propaga- tion; local stability is heavily influenced by these properties. We show why non-vanishing fields help to achieve convergence and increase the accuracy of belief propagation. We fur- ther explain the close connections between the underlying graph structure, the existence of multiple solutions, and the capability of belief propagation (with damping) to converge. Fi- nally we provide insights into why finite-size graphs behave better than infinite-size graphs. %Z Reissued by PMLR on 04 October 2026.
APA
Knoll, C. & Pernkopf, F.. (2017). On Loopy Belief Propagation – Local Stability Analysis for Non-Vanishing Fields. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:591-600 Available from https://proceedings.mlr.press/r15/knoll17a.html. Reissued by PMLR on 04 October 2026.

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