Network Topology Inference from Smooth Signals Under Partial Observability

2024-10-08

arXiv.org

AI Summary

This paper addresses the challenge of inferring network topology from smooth graph signals under partial node observability. Method: We propose the first theoretically grounded first-order algorithmic framework achieving linear convergence. Leveraging the inherent smoothness prior of graph signals, we formulate a nonconvex optimization problem incorporating column-wise sparsity regularization and low-rank constraints, and design two efficient first-order algorithms to solve it. Contribution/Results: We provide rigorous theoretical analysis establishing global convergence with linear convergence rate. Experiments on synthetic and real-world datasets demonstrate that our method significantly outperforms existing approaches in speed, while maintaining scalability to large-scale networks and guaranteed convergence. Our core contribution is the first linearly convergent theoretical framework for topology learning under partial observability, coupled with interpretable structured regularization that jointly enhances both accuracy and computational efficiency.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered hidden nodes and proposed various optimization frameworks, existing methods often lack the practical efficiency needed for large-scale networks or fail to provide theoretical convergence guarantees. In this paper, we address the problem of inferring network topologies from smooth signals with partially observed nodes. We propose a first-order algorithmic framework that includes two variants: one based on column sparsity regularization and the other on a low-rank constraint. We establish theoretical convergence guarantees and demonstrate the linear convergence rate of our algorithms. Extensive experiments on both synthetic and real-world data show that our results align with theoretical predictions, exhibiting not only linear convergence but also superior speed compared to existing methods. To the best of our knowledge, this is the first work to propose a first-order algorithmic framework for inferring network structures from smooth signals under partial observability, offering both guaranteed linear convergence and practical effectiveness for large-scale networks.

Problem

• Infer network topology from partially observed smooth signals
• Develop efficient first-order algorithms for large-scale networks
• Provide theoretical convergence guarantees for topology inference

Innovation

• First-order algorithmic framework for topology inference
• Column sparsity regularization and low-rank constraint variants
• Guaranteed linear convergence for large-scale networks