Computational Methods for a Class of Network Models

TL;DR

This paper develops and analyzes computational methods, including SMC and PMCMC, for efficient parameter inference in complex network models like the duplication attachment model, where likelihood evaluation is challenging.

Contribution

It introduces SMC and PMCMC algorithms tailored for network models with intractable likelihoods, demonstrating polynomial growth of variance and enabling Bayesian inference.

Findings

SMC methods exhibit polynomial variance growth in network size.

PMCMC algorithms effectively perform Bayesian inference on complex network models.

Numerical illustrations validate the proposed methods.

Abstract

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood function that typically cannot be evaluated in any reasonable computational time. We consider a number of importance sampling (IS) and sequential Monte Carlo (SMC) methods for approximating the likelihood of the network model for a fixed parameter value. It is well-known that for IS, the relative variance of the likelihood estimate typically grows at an exponential rate in the time parameter (here this is associated to the size of the network): we prove that, under assumptions, the SMC method will have relative variance which can grow only polynomially. In order to perform parameter estimation, we develop particle Markov chain Monte Carlo (PMCMC) algorithms to perform Bayesian inference. Such algorithms use the afore-mentioned SMC algorithms within the transition dynamics. The approaches are illustrated numerically.