Node Copying: A Random Graph Model for Effective Graph Sampling

TL;DR

This paper introduces a simple, scalable node copying model for graph sampling that preserves key structural properties and improves performance in node classification, adversarial robustness, and recommendation systems.

Contribution

The paper presents a novel node copying model for graph sampling that is scalable, preserves structural properties, and enhances various graph-based tasks.

Findings

Higher accuracy in node classification with sparse data.

Improved robustness against adversarial attacks.

Enhanced recall in recommendation systems.

Abstract

There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings, building a generative model conditioned on the observed graph allows to take the graph uncertainty into account. Various existing techniques either rely on restrictive assumptions, fail to preserve topological properties within the samples or are prohibitively expensive for larger graphs. In this work, we introduce the node copying model for constructing a distribution over graphs. Sampling of a random graph is carried out by replacing each node's neighbors by those of a randomly sampled similar node. The sampled graphs preserve key characteristics of the graph structure without explicitly targeting them. Additionally, sampling from this model is extremely simple and scales linearly with the nodes. We show the usefulness of the copying model in three tasks. First, in node classification, a Bayesian formulation based on node copying achieves higher accuracy in sparse data settings. Second, we employ our proposed model to mitigate the effect of adversarial attacks on the graph topology. Last, incorporation of the model in a recommendation system setting improves recall over state-of-the-art methods.