Truncated Simulation and Inference in Edge-Exchangeable Networks

TL;DR

This paper introduces methods for efficient simulation and inference in edge-exchangeable network models using truncation, with theoretical guarantees on approximation accuracy, applicable to a broad class of Bayesian nonparametric models.

Contribution

It develops novel truncation-based algorithms for simulation and inference in edge-exchangeable networks, providing theoretical bounds on their accuracy.

Findings

Methods enable accurate simulation with controlled truncation error

Theoretical guarantees ensure reliability of inference results

Techniques extend to various discrete Bayesian nonparametric models

Abstract

Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the self-product of a realization from a Bayesian nonparametric (BNP) discrete prior; but unlike in standard BNP models, the self-product measure prior is not conjugate the likelihood, hindering the development of exact simulation and inference algorithms. Approximation via finite truncation of the discrete measure is a straightforward alternative, but incurs an unknown approximation error. In this paper, we develop methods for forward simulation and posterior inference in random self-product-measure models based on truncation, and provide theoretical guarantees on the quality of the results as a function of the truncation level. The techniques we present are general and extend to the broader class of discrete Bayesian nonparametric models.