# Curved Markov Chain Monte Carlo for Network Learning

arXiv: https://arxiv.org/abs/2110.03413 · HTML: https://mlsanity.com/paper/2110.03413/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 12 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 2 of 2)

- [Forman-Ricci flow for change detection in large dynamic data sets](https://mlsanity.com/paper/1604.06634/) (2016)
- [Geometric Sampling of Networks](https://mlsanity.com/paper/2010.15221/) (2020)

## Built on by (most cited first, 1 of 1)

- [Rewiring Networks for Graph Neural Network Training Using Discrete Geometry](https://mlsanity.com/paper/2207.08026/) (2022)

## Abstract (arXiv)

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.