Network Games Induced Prior for Graph Topology Learning

TL;DR

This paper introduces a novel prior for graph topology learning based on social network dynamics modeled by linear quadratic games, improving the estimation of complex network structures.

Contribution

It develops a network games induced regularizer and a bilevel optimization framework for more accurate graph topology inference from limited data.

Findings

Theoretical insights align with real-world network topologies.

The proposed method reliably estimates graph structures.

Empirical results outperform existing priors in topology learning.

Abstract

Learning the graph topology of a complex network is challenging due to limited data availability and imprecise data models. A common remedy in existing works is to incorporate priors such as sparsity or modularity which highlight on the structural property of graph topology. We depart from these approaches to develop priors that are directly inspired by complex network dynamics. Focusing on social networks with actions modeled by equilibriums of linear quadratic games, we postulate that the social network topologies are optimized with respect to a social welfare function. Utilizing this prior knowledge, we propose a network games induced regularizer to assist graph learning. We then formulate the graph topology learning problem as a bilevel program. We develop a two-timescale gradient algorithm to tackle the latter. We draw theoretical insights on the optimal graph structure of the bilevel program and show that they agree with the topology in several man-made networks. Empirically, we demonstrate the proposed formulation gives rise to reliable estimate of graph topology.