Non-Parametric Methods for Analysis of Time-Varying Network Data

随机网络广泛存在于生物学、社会学、遗传学、生态学、信息技术、国家安全等诸多领域。虽然许多应用涉及时态网络数据，但与动态网络相关的研究在范围上相对有限。该项目的目标是通过开发统计上可靠的和计算上可行的方法来研究依赖时间的网络来填补这一空白。尽管这项研究在很大程度上是方法论的，但由此产生的技术可以用于各种领域，包括医学、分子生物学、统计遗传学、国家安全和社会科学。特别是，拟议的理论和算法将与佛罗里达儿童医院的功能脑图谱和脑计算机接口实验室合作，应用于与癫痫疾病相关的大脑网络的分析。由于该项目提出了一种融合应用和理论的综合方法，其结果将对依赖于动态随机网络数据分析的各种领域大有裨益。应用包括：(A)了解与言语有关的大脑区域之间的联系的方法，从而形成更安全和更有效的癫痫治疗选择；(B)分析与特定疾病有关的大脑区域之间依赖时间的联系的工具；(C)分析蛋白质和临时基因网络之间的酶影响的技术；以及(D)根据动态的社交媒体数据检测恐怖分子或黑客团体。教育和培训活动包括开发专题研究生课程、培训研究生和组织跨学科研讨会。国际和平协会计划通过参与妇女参与科学和工程(WISE)计划来促进多样性。该项目的目标是开发用于分析时态网络的非参数技术，该技术需要对网络进行一些简单的假设，并保持网络结构在时间上的连续性。虽然为时间无关网络开发的方法可以逐帧应用于时间网络，但它们完全忽略了网络结构和参数在时间上的连续性。此外，大多数研究时态网络模型的研究假设了改变节点成员资格的特定机制以及连接概率的参数形式。将使用现代代数技术来简化模型，并通过预言不等式和极小极大研究来保证精度。这项研究将极大地推动非参数统计领域的发展，特别是新兴的网络数据分析领域。该项目将通过开发非参数估计和聚类技术，大大拓宽适用于时变网络数据分析的方法范围，这些技术需要很少的简单非参数假设，在计算上是可行的，并具有高精度保证。

Stochastic networks are observed in many domains including biology, sociology, genetics, ecology, information technology, and national security. While many applications involve temporal network data, the research related to dynamic networks has been relatively limited in scope. The goal of the project is to fill this gap through the development of statistically sound and computationally viable approaches for studying time-dependent networks. Although the research is largely methodological, the resulting techniques can be used in a variety of fields including medicine, molecular biology, statistical genetics, national security, and the social sciences. In particular, the proposed theories and algorithms will be applied to the analysis of brain networks associated with epilepsy disease, in collaboration with the Functional Brain Mapping and Brain Computer Interface Lab at the Florida Hospital for Children. Since the project presents an integrated approach merging applications and theory, the results will be greatly beneficial for a variety of fields that rely on analysis of dynamic stochastic network data. Applications include (a) methods for understanding connections between brain regions associated with speech, resulting in safer and more efficient epileptic treatment options; (b) tools for analysis of time-dependent connections between brain regions associated with particular diseases; (c) techniques for analysis of the enzymatic influences between proteins and temporal gene networks; and (d) detection of terrorist or hacker groups on the basis of dynamic social media data. Educational and training activities include development of Special Topics graduate courses, training of graduate students, and organization of interdisciplinary seminars. The PI plans to promote diversity through participation in the Women in Science and Engineering (WISE) program. The objective of the project is the development of nonparametric techniques for the analysis of temporal networks that require a few simple assumptions on the network, and preserve continuity of the network's structure in time. Although approaches developed for a time independent network can be applied to a temporal network frame-by-frame, they totally ignore continuity of the network structure and parameters in time. In addition, the majority of research investigating temporal network models assumes specific mechanisms for changing nodes' memberships as well as parametric forms for the connection probabilities. Modern algebraic techniques will be used to simplify the model, and precision guarantees via oracle inequalities and minimax studies obtained. The research will substantially advance the fields of non-parametric statistics in general, and the emerging field of network data analysis in particular. The project will significantly broaden the range of methods applicable to the analysis of time-varying network data by developing techniques for non-parametric estimation and clustering that require few simple nonparametric assumptions, are computationally viable, and have guarantees of high precision.