Curved Markov Chain Monte Carlo for Network Learning

TL;DR

This paper introduces a novel Markov chain Monte Carlo method that incorporates graph curvature to improve network learning efficiency, demonstrating faster convergence on real-world network data.

Contribution

It develops a curved MCMC approach using Forman curvature, enhancing sampling efficiency in network analysis.

Findings

Faster convergence to network statistics

Effective on real-world deterministic networks

Integrates curvature into transition probabilities

Abstract

We present a geometrically enhanced Markov chain Monte Carlo sampler for networks based on a discrete curvature measure defined on graphs. Specifically, we incorporate the concept of graph Forman curvature into sampling procedures on both the nodes and edges of a network explicitly, via the transition probability of the Markov chain, as well as implicitly, via the target stationary distribution, which gives a novel, curved Markov chain Monte Carlo approach to learning networks. We show that integrating curvature into the sampler results in faster convergence to a wide range of network statistics demonstrated on deterministic networks drawn from real-world data.