On the Importance of Sampling in Training GCNs: Tighter Analysis and Variance Reduction

TL;DR

This paper introduces a variance reduction schema for sampling-based training of GCNs, providing theoretical convergence guarantees and demonstrating improved efficiency on large graphs.

Contribution

It proposes a general doubly variance reduction schema that accelerates sampling methods for GCN training with proven convergence guarantees.

Findings

The schema achieves an $ ext{O}(1/T)$ convergence rate.

It effectively reduces variance in both forward and backward passes.

Experimental results show improved training efficiency on large real-world graphs.

Abstract

Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of semi-supervised node classification tasks. Despite their great success, training GCNs on large graphs suffers from computational and memory issues. A potential path to circumvent these obstacles is sampling-based methods, where at each layer a subset of nodes is sampled. Although recent studies have empirically demonstrated the effectiveness of sampling-based methods, these works lack theoretical convergence guarantees under realistic settings and cannot fully leverage the information of evolving parameters during optimization. In this paper, we describe and analyze a general doubly variance reduction schema that can accelerate any sampling method under the memory budget. The motivating impetus for the proposed schema is a careful analysis of the variance of sampling methods where it is shown that the induced variance can be decomposed into node embedding approximation variance (zeroth-order variance) during forward propagation and layerwise-gradient variance (first-order variance) during backward propagation. We theoretically analyze the convergence of the proposed schema and show that it enjoys an $\mathcal{O}(1/T)$ convergence rate. We complement our theoretical results by integrating the proposed schema in different sampling methods and applying them to different large real-world graphs.