Joint Network Topology Inference via Structured Fusion Regularization

TL;DR

This paper introduces a novel structured fusion regularization method for jointly inferring multiple complex network topologies, capturing sparse, homogeneous, and heterogeneous patterns with theoretical guarantees and scalable algorithms.

Contribution

It proposes a flexible graph estimator using a Gram matrix-based regularization to model complex topological patterns among multiple networks, with efficient ADMM algorithms and theoretical error bounds.

Findings

Outperforms existing methods in simulated data

Effectively models complex topological patterns

Provides theoretical guarantees on estimation error

Abstract

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component shared among multiple networks. However, in practice, a more intricate topological pattern, comprising simultaneously of sparse, homogeneity and heterogeneity components, would exhibit in multiple networks. In this paper, we propose a general graph estimator based on a novel structured fusion regularization that enables us to jointly learn multiple graph Laplacian matrices with such complex topological patterns, and enjoys both high computational efficiency and rigorous theoretical guarantee. Moreover, in the proposed regularization term, the topological pattern among networks is characterized by a Gram matrix, endowing our graph estimator with the ability of flexible modelling different types of topological patterns by different choices of the Gram matrix. Computationally, the regularization term, coupling the parameters together, makes the formulated optimization problem intractable and thus, we develop a computationally-scalable algorithm based on the alternating direction method of multipliers (ADMM) to solve it efficiently. Theoretically, we provide a theoretical analysis of the proposed graph estimator, which establishes a non-asymptotic bound of the estimation error under the high-dimensional setting and reflects the effect of several key factors on the convergence rate of our algorithm. Finally, the superior performance of the proposed method is illustrated through simulated and real data examples.