The Feature-First Block Model

TL;DR

This paper introduces the feature-first block model (FFBM), a Bayesian generative framework for analyzing how vertex features influence network structure, enabling automatic feature relevance ranking and efficient inference.

Contribution

The paper presents the FFBM, a novel generative model and Bayesian inference method that automatically utilizes the entire feature space to assess feature impact on network macro-structure.

Findings

Effective inference of feature influence on network structure

Automatic feature relevance ranking

Application to various network datasets

Abstract

Labelled networks are an important class of data, naturally appearing in numerous applications in science and engineering. A typical inference goal is to determine how the vertex labels (or features) affect the network's structure. In this work, we introduce a new generative model, the feature-first block model (FFBM), that facilitates the use of rich queries on labelled networks. We develop a Bayesian framework and devise a two-level Markov chain Monte Carlo approach to efficiently sample from the relevant posterior distribution of the FFBM parameters. This allows us to infer if and how the observed vertex-features affect macro-structure. We apply the proposed methods to a variety of network data to extract the most important features along which the vertices are partitioned. The main advantages of the proposed approach are that the whole feature-space is used automatically and that features can be rank-ordered implicitly according to impact.