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。 该问题的一个典型实例是单个传感器或代理的网络试图推断管理其本地观测的全局分布。 通过传递消息，代理可以单独对全球现象进行推断。 本研究调查的通信和网络的范例，可以使网络的个人代理，以协同估计分布在高维空间，即使个人的意见是严重限制的准确性，空间或时间。特别是，研究人员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被认为是采样：个体对自己的环境进行采样，并对邻居的意见进行采样。 该方法的核心是，代理随机生成简单的消息，从内部估计的全球分布的兴趣。 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支配所有节点观测的分布和/或全局参数。 技术方法是一个混合的分析技术，从随机近似，随机算法和统计物理。 这项工作的应用范围从社交网络中的消息和意见形成的数学建模，分布式优化的通信协议，以及数据网络中的参数估计。 这项工作将涵盖几个相关的问题：估计网络中保存的数据的高维直方图，使用贝叶斯和非贝叶斯技术的混合进行参数估计，以及估计更复杂的生成模型。 最后将这些方法应用到对等网络和社会网络建模中。 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，这影响了定量社会科学和工程学。 PI将开发教育材料并组织研究活动，以帮助汇集对网络和社会学习感兴趣的不同研究社区。

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.