Statistical Modeling for Complex Networks

最近的技术进步导致在许多应用领域收集的数据呈爆炸式增长。这些数据中的许多具有复杂的结构，例如以文本、图像、视频、音频、流数据等的形式。本项目关注的是一种重要的复杂数据结构，即网络或图形。这样的数据在不同的工程和科学领域很常见，包括生物学、医学、社会学、计算机科学、电气工程、经济学等。虽然已经有了关于网络的广泛研究，但大部分都只涉及两人关系的存在或不存在。然而，现实世界中的关系往往更为复杂。目前的研究计划旨在超越成对的存在/不存在关系，并开发统计方法来表征更复杂的网络结构并对其建模。该研究计划将在多个领域做出重大贡献，包括统计学、生物学、计算机科学、医疗保健、电气工程、医学、物理学、心理学和社会学。研究人员计划通过指导本科生和研究生，开发一门新课程，并组织跨学科研讨会来培训STEM工作人员。该教育计划还包括在维持一个由相当大比例的女性组成的研究小组方面的重大举措，以及继续积极招募和支持不同的学生群体。该研究旨在开发新的统计方法和相关理论，将更高级别的结构纳入网络建模。这种数据结构在各个领域中正变得越来越常见。具体地说，研究人员的目标是研究三个不同但相关的问题：a)利用网络中的子图或高阶结构，并为具有依赖边的网络开发新的社区检测方法；b)开发新的潜在空间模型和理论，以适应著名的平衡理论，即，对于已签署的网络，“我朋友的朋友就是我的朋友”和“我的敌人的敌人就是我的朋友”；C)开发新的潜在空间模型和理论，用于较少研究但经常遇到的多元关系，即同时涉及两个以上节点的超图，使用行列式点法。该奖项反映了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。

Recent advances in technology have led to an explosion of data being collected in many areas of application. Many of these data have complex structures, in the form of text, images, video, audio, streaming data, etc, for example. This project focuses on one important type of complex data structure, networks, or graphs. Such data are common in diverse engineering and scientific areas, including biology, medicine, sociology, computer science, electrical engineering, economics, and so on. While there has been extensive research on networks, much of it only deals with the presence/absence of pairwise relationships. However, real-world relationships are often more complicated. The current research program aims to go beyond the pairwise presence/absence relationship and develop statistical methods to characterize and model more complex network structures. The research program will make significant contributions in several areas, including Statistics, Biology, Computer Science, Healthcare, Electrical Engineering, Medicine, Physics, Psychology, and Sociology. The investigators plan to train STEM workforce members by mentoring undergraduate and graduate students, developing a new course, and organizing interdisciplinary workshops. The educational program also includes substantial initiatives in maintaining a research group with a significant portion of women and continuing to actively recruit and support a diverse group of students.The research aims to develop new statistical methodologies and associated theory that incorporate higher-order structures into network modeling. Such data structures are becoming increasingly common in various fields. Specifically, the investigators aim to study three different but related problems: a) leveraging subgraphs or higher-order structures in a network and developing new community detection methods for networks with dependent edges; b) developing novel latent space models and theory that accommodate the well-known balance theory, i.e., "the friend of my friend is my friend" and "the enemy of my enemy is my friend," for signed networks; c) developing new latent space models and theory for the less studied, though commonly encountered, polyadic relations that involve more than two nodes simultaneously, i.e., hypergraphs, using determinantal point processes.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.