ZooBP: Belief Propagation for Heterogeneous Networks

Given a heterogeneous network, with nodes of di↵erent types – e.g., products, users and sellers from an online recommendation site like Amazon – and labels for a few nodes (‘honest’, ‘suspicious’, etc), can we find a closed formula for Belief Propagation (BP), exact or approximate? Can we say whether it will converge? BP, traditionally an inference algorithm for graphical models, exploits so-called “network e↵ects” to perform graph classification tasks when labels for a subset of nodes are provided; and it has been successful in numerous settings like fraudulent entity detection in online retailers and classification in social networks. However, it does not have a closed-form nor does it provide convergence guarantees in general. We propose ZooBP, a method to perform fast BP on undirected heterogeneous graphs with provable convergence guarantees. ZooBP has the following advantages: (1) Generality: It works on heterogeneous graphs with multiple types of nodes and edges; (2) Closed-form solution: ZooBP gives a closed-form solution as well as convergence guarantees; (3) Scalability: ZooBP is linear on the graph size and is up to 600⇥ faster than BP, running on graphs with 3.3 million edges in a few seconds. (4) E↵ectiveness: Applied on real data (a Flipkart e-commerce network with users, products and sellers), ZooBP identifies fraudulent users with a near-perfect precision of 92.3 % over the top 300 results.