CIF: Small: Collaborative Research: Inference by Social Sampling

从科学和工程的角度来看，分布式环境中的学习和推理都很重要。这个问题的一个典型例子是一个由单个传感器或代理组成的网络，它们试图推断出控制其局部观测的全局分布。通过传递消息，代理可以单独对全局现象做出推断。本研究探讨了通信和网络范例，这些范例可以使单个代理网络协作估计高维空间上的分布，即使单个观察在准确性、空间或时间上受到严重限制。研究人员特别研究了个体决策者如何整合两种信息：本地观察和来自网络中邻居的信息。观察和信息传递都可以看作是抽样：个体对自己的环境进行抽样，对邻居的意见进行抽样。该方法的核心是代理根据对全局兴趣分布的内部估计随机生成简单的消息。该项目的第一个主要目标是开发一个数学框架和分析技术，以了解这种有限的学习和交流形式是否以及何时足以让个人估计和学习控制所有节点观测的分布和/或全局参数。该技术方法是随机逼近、随机算法和统计物理等分析技术的混合。这项工作的应用范围包括社交网络中信息和意见形成的数学建模，分布式优化的通信协议以及数据网络中参数的估计。这项工作将涵盖几个相关的问题：估计网络中保存的高维数据直方图，使用贝叶斯和非贝叶斯技术混合的参数估计，以及估计更复杂的生成模型。工作的最后一部分是将这些方法应用于对等网络和社会网络建模。这项工作的更广泛的影响是进一步发展网络科学的跨学科领域，它影响了定量社会科学和工程。pi将开发教育材料并组织研究活动，以帮助将对网络和社会学习感兴趣的不同研究团体聚集在一起。

Learning and inference in distributed settings is an important from both a scientific and engineering perspective. A typical instance of the problem is a network of individual sensors or agents attempting to infer a global distribution that governs their local observations. By passing messages the agents can individually make inference about a global phenomenon. This research investigates communication and networking paradigms that can enable a network of individual agents to collaboratively estimate distributions over high dimensional spaces, even when individual observations are severely limited in accuracy, space, or time. In particular, the investigators study how individual decision makers can integrate two kinds of information: local observations and messages from their neighbors in the network. Both observation and messaging can be thought of as sampling : individuals sample their own environment and sample the opinions of their neighbors. Central to the approach is that the agents generate simple messages at random from an internal estimate of the global distribution of interest. The first major goal of this project is to develop a mathematical framework and analysis techniques to understand if and when this limited form of learning and communication is sufficient for an individual to estimate and learn distributions and/or global parameters governing the observations of all nodes. The technical approach is a blend of analysis techniques ranging from stochastic approximation, randomized algorithms, and statistical physics. Applications for this work range from mathematical modeling of messages and opinion formation in social networks, communication protocols for distributed optimization, and estimation of parameters in data networks. The work will cover several related problems : estimating high-dimensional histograms of data held in the network, parametric estimation using a mix of Bayesian and non-Bayesian techniques, and estimation of more complex generative models. The final part of the work is to apply these methods to peer-peer networks and social network modeling. The broader impact of this work is to further develop the interdisciplinary field of network science, which impacts both quantitative social sciences and engineering. The PIs will develop educational materials and organize research activities to help bring together different research communities interested in networks and social learning.