Computationally-efficient Graph Modeling with Refined Graph Random Features

2025-10-08

AI Summary

Existing graph random features (GRFs) suffer from three key limitations in approximating node kernels: (i) inability to capture long-range dependencies, (ii) reliance on inefficient long random walks, and (iii) rigid, fixed-length termination mechanisms. To address these, we propose GRFs++, an efficient and high-accuracy graph kernel approximation method. Its core contributions are: (1) a random walk concatenation technique that replaces single long walks with multiple unbiased short walks—preserving theoretical unbiasedness while drastically reducing sampling overhead; and (2) a probabilistic walk-length distribution model that relaxes fixed-step constraints, thereby enhancing kernel expressivity. Computationally, GRFs++ leverages matrix–matrix multiplication for scalable implementation, maintaining linear time complexity while significantly improving kernel approximation accuracy. Extensive experiments demonstrate that GRFs++ consistently outperforms state-of-the-art GRFs variants on node classification and graph classification benchmarks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel walk-stitching technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential, inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves the approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase all our claims and complement our results with theoretical analysis.

Problem

• Improve computational efficiency of graph kernel approximations
• Enhance modeling of distant node relationships in graphs
• Extend graph random walk strategies for better accuracy

Innovation

• Refined GRFs use walk-stitching for unbiased node relationships
• GRFs++ replace long sequential walks with parallel short walks
• Extended walk termination strategies improve kernel accuracy efficiently