A Simple Algorithm for Scalable Monte Carlo Inference

TL;DR

This paper introduces a simple, scalable Monte Carlo inference algorithm for exponential family models, significantly expanding the size of networks and datasets that can be analyzed efficiently across various scientific fields.

Contribution

The paper presents a novel, efficient algorithm for maximum likelihood estimation in exponential family models, building on the Equilibrium Expectation approach, enabling analysis of larger complex networks.

Findings

Algorithm increases the size of network data manageable by Monte Carlo inference

Demonstrates effectiveness on empirical data from various scientific fields

Potential to extend to large samples of dependent observations

Abstract

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of parameters of exponential family distributions - a family of statistical models, that includes Ising model, Markov Random Field and Exponential Random Graph models. Computational experiments and analysis of empirical data demonstrate that the algorithm increases by orders of magnitude the size of network data amenable to Monte Carlo based inference. We report results suggesting that the applicability of the algorithm may readily be extended to the analysis of large samples of dependent observations commonly found in biology, sociology, astrophysics, and ecology.