Heterogeneous message passing for heterogeneous networks

TL;DR

This paper introduces a heterogeneous message passing approach that assigns different approximation levels to nodes in networks, improving accuracy and speed over traditional methods, especially in complex real-world networks.

Contribution

The paper proposes a node-based heterogeneous message passing method that enhances accuracy and efficiency in network analysis by tailoring approximations to individual nodes.

Findings

Increased accuracy in 81% of networks tested.

Faster computation in 64% of cases.

Both improved accuracy and speed in 49% of networks.

Abstract

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain their accuracy level in networks rich with short cycles. However, MP may already be computationally challenging on very large networks and additional costs incurred by correcting for cycles could be prohibitive. We show how the issue can be addressed. By allowing each node in the network to have its own level of approximation, one can focus on improving the accuracy of MP approaches in a targeted manner. We perform a systematic analysis of 109 real-world networks and show that our node-based MP approximation is able to increase both the accuracy and speed of traditional MP approaches. We find that, compared to conventional MP, a heterogeneous approach based on a simple heuristic is more accurate in 81% of tested networks, faster in 64% of cases, and both more accurate and faster in 49% of cases.