Graphical Approaches to Modeling High-Dimensional Data

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This research involves theoretical and applied research on learning and representation of high-dimensional data. The term high dimensionality refers to the property that the number of variablesor ?unknowns? is typically much larger than the number of observations available at hand. A keychallenge is being able to represent and learn such phenomena with sample and computationalrequirements scaling favorably in the number of dimensions. This project addresses these challengesthrough a graphical approach by exploiting the inherent graphical structure present in many largedata-sets.This research considers modeling high-dimensional data through probabilistic graphical models,also known as Markov random fields. An important research thrust of this proposal is to developnovel algorithms for learning and inference under the framework of graphical models. Anotherimportant thrust of this proposal is to develop efficient scalable models for representing high-dimensional data beyond the traditional framework of graphical models. This research establishesstrong theoretical guarantees for the developed methods, as well as applies them to real data invarious domains, including genetic and financial data, and data from large online social networkssuch as Facebook and Twitter.