Curved Markov Chain Monte Carlo for Network Learning
This work addresses a bottleneck in network analysis for researchers and practitioners by providing an incremental improvement to MCMC methods through curvature integration.
The authors tackled the problem of slow convergence in Markov chain Monte Carlo (MCMC) sampling for networks by incorporating graph Forman curvature into the sampler, resulting in faster convergence to network statistics as demonstrated on real-world deterministic networks.
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.