A Return to Biased Nets: New Specifications and Approximate Bayesian Inference

TL;DR

This paper revisits biased net models for network dependence, proposing a consistent Markovian specification with inhibitory bias events and an approximate Bayesian inference method using random forests, demonstrated on friendship networks.

Contribution

It introduces a new consistent Markovian biased net specification with inhibitory bias events and a novel approximate Bayesian inference strategy.

Findings

The Markovian specification avoids previous inconsistencies.

Inhibitory bias events help prevent degeneracies.

The method successfully models friendship ties among college students.

Abstract

The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent ``bias events,'' whose realizations enhance reciprocity, transitivity, or other structural features. Subsequent developments have introduced local specifications of biased nets, which reduce the need for approximations required in early specifications based on tracing processes. Here, we show that while one such specification leads to inconsistencies, a closely related Markovian specification both evades these difficulties and can be extended to incorporate new types of effects. We introduce the notion of inhibitory bias events, with satiation as an example, which are useful for avoiding degeneracies that can arise from closure bias terms. Although our approach does not lead to a computable likelihood, we provide a strategy for approximate Bayesian inference using random forest prevision. We demonstrate our approach on a network of friendship ties among college students, recapitulating a relationship between the sibling bias and tie strength posited in earlier work by Fararo.