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.

翻译：学习复杂网络的图拓扑结构面临数据有限和模型不精确的挑战。现有研究中的常见解决方法是引入强调图拓扑结构特性的先验，例如稀疏性或模块性。我们另辟蹊径，开发直接受复杂网络动力学启发的先验。聚焦于以线性二次博弈均衡为行动模型的社会网络，我们假设社会网络拓扑是针对社会福利函数进行优化的。利用这一先验知识，我们提出一种网络博弈诱导的正则化器以辅助图学习。随后，我们将图拓扑学习问题表述为一个双层规划。我们开发了一种双时间尺度梯度算法来解决后者。我们对双层规划的最优图结构进行了理论分析，并证明其与多个人工网络的拓扑结构相符。实证结果表明，所提出的方法能够产生可靠的图拓扑估计。