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.
