Variational Inference for Complex Networks

大规模复杂网络在包括社会科学、生物科学和物理科学在内的各种科学学科中变得越来越常见。这样的复杂网络挑战了经典方法的计算极限，使得在合理的时间内进行统计网络推理是不可行的。该项目将开发高效的算法，这些算法在计算上对大规模复杂网络是可行的，并在性能上有可证明的统计保证。建议的方法将应用于社会和生物网络数据，包括大脑网络，并将用于研究与听力损失相关的疾病，如耳鸣。拟议的研究是高度跨学科的，为具有广泛背景和兴趣的研究生和本科生提供了参与的机会。建议的方法将纳入相关课程。研究成果将向科学界传播，所有研究开发的软件将以开源的形式免费向公众分发。该项目将开发复杂网络的变分方法，包括动态、多层和异质网络，并研究这些网络的变分方法的理论性质，为性能提供可证明的统计保证。PI研究的网络模型包括动态网络和动态多层网络的潜在空间模型，多层网络的随机分块模型，异质网络的各种模型，以及其他复杂网络的模型。所提出的变分推理过程使处理大规模复杂网络数据成为可能。PI将研究的理论性质包括参数估计的一致性和变分方法的社区检测。建议的方法将应用于来自社会科学和自然科学的真实网络数据。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Large-scale complex networks are becoming increasingly common in a variety of scientific disciplines, including social sciences, biological sciences, and physical sciences. Such complex networks challenge the computational limit of classical methods, making it infeasible to carry out statistical network inference within a reasonable amount of time. This project will develop efficient algorithms that are computationally feasible for large-scale complex networks and have provable statistical guarantees on performance. The proposed methods will be applied to social and biological network data, including brain networks, and will be used for the study of disorders associated with hearing loss, such as tinnitus. The proposed research is highly interdisciplinary and provides an opportunity for involvement of graduate and undergraduate students with a broad range of backgrounds and interests. The proposed methods will be incorporated into relevant courses. Research results will be disseminated to the scientific communities and all software developed in this research will be freely distributed as open-source to the public.The project will develop variational methods for complex networks, including dynamic, multi-layer, and heterogeneous networks, and investigate theoretical properties of the variational methods on these networks to provide provable statistical guarantees on performance. The network models the PI studies include latent space models for dynamic networks and dynamic multi-layer networks, stochastic block models for multi-layer networks, various models for heterogeneous networks, and other models for complex networks. The proposed variational inference procedure makes it possible to handle large scale complex network data. The theoretical properties the PI will investigate include consistency of parameter estimation and community detection for variational methods. The proposed methods will be applied to real network data from social and natural sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.