CAREER: Quantifying diffusion and dynamics on healthcare, innovation and communication networks

为了对医疗和技术创新等涉及国家利益的事项提供见解而收集的许多现代数据收集，除了传统的单位一级衡量外，通常还在网络范围内衡量迅速演变的相互作用。这个项目开发了一个综合的研究和教育计划，以便能够对相互作用和其他组合测量进行科学和定量的分析，因为它们随着时间的推移而变化。正在解决的技术问题包括但不限于：便于对大规模网络进行定量分析的有效表示；信息和行为如何作为其所在的网络环境的结果随时间演变的模型；以及执行这些模型中的关键参数估计的快速算法。这些方法将在探索的案例研究中得到演示：医疗创新在医生中的传播及其对健康的影响；美国的技术创新动态和竞业禁止协议的作用；从被动监控的总流量估计网络上的点对点通信。作为观察到的数据差异的来源，交互作用和其他组合测量的存在带来了新的统计和推理挑战。例如，广义线性模型理论需要扩展到网络上的响应。对网络上的过程进行分析时，由于涉及大量的未知量来描述较少的观测数据，因此常常会引出使推理问题不适定的约束。估计可能需要从极端受限的参数空间采样并在其上进行积分。重要的是，相互作用不一定编码统计相关性。从这个意义上说，处理观察到的相互作用需要原创思维；它们所涉及的数据设置不适合用经典方法进行分析，在经典方法中，相互作用被推断为编码单位水平观察之间的相关性的一种手段。这个项目用统计和机器学习的方法解决技术挑战。预期的技术成果包括但不限于：(1)多变量和动态网络的一种新的小波分解；(2)给定网络上信息扩散的统计模型，以及连续时间的非均匀网络动态模型；(3)这些模型的可伸缩估计算法；(4)大数据推理的理论基础。这项研究将在哈佛大学和工业伙伴的合作下进行定性和定量的评估。建议的研究与跨学科教育计划相结合，该计划将吸引本科生在国家重要问题的背景下进行统计学和计算机科学的交叉研究。它将提供机会，积极鼓励来自代表性不足群体的学生从事统计和计算机科学方面的职业。该教育方案的主要内容包括开发统计机器学习课程；在YouTube上向所有人提供讲座；在国家和国际会议和讲习班上提供教程；以及一本专著。外联活动包括面向广大社区的开放源码软件和网络工具，以及与工业伙伴的合作努力，以利用新的计算工具和算法，使其在世界各地的用户群受益。有关该项目的更多详细信息，请访问：http://www.fas.harvard.edu/~airoldi/career.html.

Many modern data collections, gathered for the purpose of providing insights into matters of national interest such as medical and technological innovation, typically measure quickly evolving interactions, in addition to traditional unit-level measurements, in the context of a network. This project develops an integrated research and educational program to enable scientific and quantitative analyses of interactions and other combinatorial measurements as they change over time. Technical problems being addressed include, but are not limited to: an efficient representation that facilitates quantitative analyses of large-scale networks; models of how information and behavior evolve over time as a consequence of the network context they are embedded in; and fast algorithms to perform estimation of critical parameters in these models. These methods will be demonstrated on case studies exploring: the diffusion of medical innovations among physicians and its impact on health; technological innovation dynamics in the United States and the role of non-compete agreements; the estimation of point-to-point communications on a network, from aggregate traffic that is passively monitored.The presence of interactions and other combinatorial measurements as a source of observed variation in the data creates new statistical and inferential challenges. For instance, generalized linear model theory needs to be extended to responses on a network. The analysis of processes on a network often induces constraints that make the inferential problems ill posed, since they involve a large number of unknown quantities to describe few observations. Estimation may require sampling from, and integrating over, extremely constrained parameter spaces. Importantly, interactions do not necessarily encode statistical dependence. In this sense, dealing with observed interactions requires original thinking; the data settings they entail are not amenable to analysis with classical methods, in which interactions are inferred as a means to encode dependence among unit-level observations. This project tackles technical challenges with a statistical and machine learning approach. Anticipated technical results include, but are not limited to: (1) a new wavelet decomposition of multivariate and dynamic networks; (2) statistical models of diffusion of information on a given network, and models of inhomogeneous network dynamics in continuous time; (3) scalable estimation algorithms for these models; and (4) theoretical foundations of inference with big data. This research will be evaluated qualitatively and quantitatively, at Harvard and in collaboration with industrial partners.The proposed research is integrated with an interdisciplinary educational program, which will attract undergraduates to research at the intersection of statistics and computer science, in the context of problems of national importance. It will provide opportunities to actively encourage students from underrepresented groups to pursue careers in statistics and computer science. Key elements of the educational program include the development of a statistical machine learning curriculum; lectures on YouTube available to everyone; tutorials at national and international conferences and workshops; and a monograph. Outreach activities include open-source software and webtools for the community at-large, and a collaborative effort with industrial partners to leverage the new computational tools and algorithms for benefiting their pools of users worldwide. Additional details regarding the project can be found at: http://www.fas.harvard.edu/~airoldi/career.html.