Valid Bootstraps for Network Embeddings with Applications to Network Visualisation

TL;DR

This paper introduces a new distribution-free bootstrap method for network embeddings that enables uncertainty quantification and validation, improving network visualization and analysis.

Contribution

It proposes a novel, principled bootstrap approach using k-nearest neighbor smoothing that passes an exchangeability test, addressing limitations of existing methods.

Findings

The bootstrap method passes the exchangeable network test in synthetic and real data.

Uncertainty estimates improve the interpretability of network visualizations.

The approach enhances the reliability of network structure inference.

Abstract

Quantifying uncertainty in networks is an important step in modelling relationships and interactions between entities. We consider the challenge of bootstrapping an inhomogeneous random graph when only a single observation of the network is made and the underlying data generating function is unknown. We address this problem by considering embeddings of the observed and bootstrapped network that are statistically indistinguishable. We utilise an exchangeable network test that can empirically validate bootstrap samples generated by any method. Existing methods fail this test, so we propose a principled, distribution-free network bootstrap using k-nearest neighbour smoothing, that can pass this exchangeable network test in many synthetic and real-data scenarios. We demonstrate the utility of this work in combination with the popular data visualisation method t-SNE, where uncertainty estimates from bootstrapping are used to explain whether visible structures represent real statistically sound structures.