An Expectation Maximization Framework for Yule-Simon Preferential Attachment Models

TL;DR

This paper introduces an EM algorithm for estimating the Yule-Simon distribution parameter, enabling both frequentist and Bayesian inference, with proven convergence and applications in network degree distribution analysis.

Contribution

The paper develops a novel EM framework for Yule-Simon parameter estimation, providing convergence proofs, standard errors, and applicability to real-world network data.

Findings

The EM algorithm converges reliably for Yule-Simon models.

Standard errors for parameter estimates are derived within the EM framework.

Application to graph degree distributions demonstrates practical utility.

Abstract

In this paper we develop an Expectation Maximization(EM) algorithm to estimate the parameter of a Yule-Simon distribution. The Yule-Simon distribution exhibits the "rich get richer" effect whereby an 80-20 type of rule tends to dominate. These distributions are ubiquitous in industrial settings. The EM algorithm presented provides both frequentist and Bayesian estimates of the $\lambda$ parameter. By placing the estimation method within the EM framework we are able to derive Standard errors of the resulting estimate. Additionally, we prove convergence of the Yule-Simon EM algorithm and study the rate of convergence. An explicit, closed form solution for the rate of convergence of the algorithm is given. Applications including graph node degree distribution estimation are listed.