@TechReport{Werner-TR-2010-05, IS = { zkontrolovano 31 Jan 2011 }, UPDATE = { 2010-10-19 }, author = {Werner, Tom{\'a}{\v s}}, title = {Belief Propagation Fixed Points as Zero Gradients of a Function of Reparameterizations}, institution = {Center for Machine Perception, K13133 FEE Czech Technical University}, address = {Prague, Czech Republic}, year = {2010}, month = {February}, type = {Research Report}, number = {CTU--CMP--2010--05}, issn = {1213-2365}, pages = {15}, figures = {0}, authorship = {100}, psurl = {[Werner-TR-2010-05.pdf]}, project = {ICT-215078 DIPLECS}, annote = {The existing view on loopy belief propagation sees it as an algorithm to find a common zero of a system of non-linear functions, not explicitly related to each other. We show that these functions are in fact related -- they are the partial derivatives of a single function of reparameterizations. Thus, belief propagation searches for a zero gradient of this function. We show that BP fixed points are in one-to-one correspondence to zero gradients of this function and that every zero gradient point of this function is a saddle point. }, keywords = {belief propagation, graphical models, Markov random fields, variational inference}, }