Linearized and Turbo Belief Propagation.
Wolfgang Gatterbauer, Stephan Günnemann, Danai Koutra, Christos Faloutsos · arXiv (Cornell University) · 2014
How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label the class of a node in a network based on its neighbors and appropriate assumptions of ho-mophily (“birds of a feather flock together”) or heterophily (“opposites attract”). One of the most widely used methods for this kind of reasoning is Belief Propagation (BP) which iteratively propagates the information from a few nodes with explicit beliefs throughout the network until it converges. However, one main problem with BP is that there are no guarantees of convergence in general graphs with loops. This paper introduces Linearized Belief Propagation (LPB), a linearization of BP that allows a closed-form solu-tion via intuitive matrix calculations and, thus, comes with convergence guarantees. It handles homophily, heterophily, and more general cases that arise in multi-class settings. The paper also introduces Turbo Belief Propagation (TBP), a “localized ” version of LBP for which the final class assign-ments depend only on the nearest labeled neighbors. TBP (in contrast to standard BP and LBP) allows fast incremen-tal updates in case of new explicit labels or new edges in the graph. We show an intuitive connection between LBP and TBP by proving that the labeling assignments for both are identical in the limit of decreasing coupling strengths between nodes in the graph. Importantly, the linearized matrix equations of both new methods allow compact imple-mentations in SQL. Finally, our runtime experiments show that both new methods are orders of magnitude faster than standard BP while leading to almost identical node labels. 1.