CAREER: Statistical Learning from Data with Graph/Network Structures

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The research aims to develop new statistical methodologies and associated theory that incorporate the network/graph structure in the data. Such data are becoming increasingly common in various fields. Specifically, the investigator studies three different but related problems: a) statistical learning on networks via random walks, which includes semi-supervised classification for two and multiple classes, clustering, and analysis of categorical data; b) learning network structures, which deals with the situation where one is interested in identifying the underlying network structure from the data; c) variable selection with structural constraints, which deals with variable selection when there is inherent structure among the variables or parameters.Recent advances in computing and measurement technologies have led to an explosion in the amount of data that are being collected in all areas of application. Much of these data have complex structure, in the form of text, images, video, audio, streaming data, and so on. This proposal focuses on one important class of problems, viz, data with network or graph structure. Such data are common in diverse engineering and scientific areas, such as biology, computer science, electrical engineering, economics, sociology and so on. While there has been extensive research on networks (primarily outside the field of Statistics), much of it deals with characterizing and modeling network structures. The goal of the current research program is to exploit the network structure as additional information and develop statistical methods that take into account the structure of relationships between the data. The research program will make significant contributions in several areas, including Statistics, Biology, Computer Science, Electrical Engineering, IOE, Physics, Psychology and Sociology. The educational program also includes substantial initiatives that will involve undergraduate and graduate students and expose them to state-of-the-art research in the topics related to the proposal. These include new courses, summer workshops, mentoring, and software development.