# Variational approximations for stochastic dynamics on graphs

## TL;DR

This paper explores mean-field-like variational approximations for stochastic graph dynamics, providing a unified framework that improves accuracy and is validated against Monte Carlo simulations in epidemic models.

## Contribution

It introduces a systematic cluster-variational approach to improve mean-field approximations for stochastic processes on graphs.

## Key findings

- The approach unifies various existing approximation schemes.
- Systematic improvements lead to better accuracy over traditional methods.
- Validated with Monte Carlo simulations on epidemic models.

## Abstract

We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view of various (previously known) approximation schemes, and suggests quite a systematic way to improve the level of accuracy. We compare the different approximations with Monte Carlo simulations on a reversible (susceptible-infected-susceptible) discrete-time epidemic-spreading model on random graphs.