Estimating parameters of a directed weighted graph model with beta-distributed edge-weights

TL;DR

This paper introduces a directed weighted graph model with beta-distributed edge-weights, providing methods for parameter estimation, proving the existence and uniqueness of maximum likelihood estimates, and demonstrating applications through simulations.

Contribution

It presents a novel directed weighted graph model with beta-distributed edges and develops a consistent, convergent algorithm for parameter estimation based on exponential family theory.

Findings

ML estimates exist and are unique

Algorithm converges using digamma function properties

Simulation results validate the model and estimation method

Abstract

We introduce a directed, weighted random graph model, where the edge-weights are independent and beta-distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix are sufficient statistics for the parameters, and use the theory of exponential families to prove that the ML estimate of the parameters exists and is unique. Then an algorithm to find this estimate is introduced together with convergence proof that uses properties of the digamma function. Simulation results and applications are also presented.