Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming

TL;DR

This paper introduces improved linear programming methods for likelihood inference in exponential-family random graph models, enhancing the convex hull testing process crucial for network data analysis.

Contribution

It presents novel linear programming techniques for convex hull testing, specifically tailored for exponential-family network models, with improvements over existing algorithms.

Findings

Enhanced convex hull testing algorithm implemented in 'ergm' package.

More efficient likelihood-based inference for network models.

Practical improvements facilitate better statistical analysis of network data.

Abstract

This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a particular approximation to the loglikelihood function for an exponential family model; in particular, we discuss the application to network models here. While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. Furthermore, this article details several substantial improvements to the convex hull-testing algorithm currently implemented in the widely used 'ergm' package for network modeling.