@InProceedings{Werner-UAI-2010, IS = { zkontrolovano 31 Jan 2011 }, UPDATE = { 2010-10-19 }, author = {Werner, Tom{\'a}{\v s}}, title = {Primal View on Belief Propagation}, year = {2010}, booktitle = {UAI 2010: Proceedings of the Conference of Uncertainty in Artificial Intelligence}, publisher = {AUAI Press}, address = {Corvallis, Oregon}, isbn = {978-0-9749039-6-5}, book_pages = {753}, pages = {651--657}, month = {July}, day = {8--11}, venue = {Catalina Island, California}, organization = {Association for Uncertainty in Artificial Intelligence}, project = {ICT-215078 DIPLECS only EU, MSM6840770038}, prestige = {important}, psurl = {[[pdf]}, editor = { P. Gr{\" u}nwald and P. Spirtes }, annote = { It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algorithm to solve the Bethe variational problem -- beliefs are infeasible before convergence. Thus, we have no better understanding of BP than as an algorithm to seek for a common zero of a system of non-linear functions, not explicitly related to each other. In this theoretical paper, we show that these functions are in fact explicitly related -- they are the partial derivatives of a single function of reparameterizations. That means, BP seeks for a stationary point of a single function, without any constraints. This function has a very natural form: it is a linear combination of local log-partition functions, exactly as the Bethe entropy is the same linear combination of local entropies. }, keywords = { loopy belief propagation, Bethe free energy }, }