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 variables or ?unknowns? is typically much larger than the number of observations available at hand. A key challenge is being able to represent and learn such phenomena with sample and computational requirements scaling favorably in the number of dimensions. This project addresses these challenges through a graphical approach by exploiting the inherent graphical structure present in many large data-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 develop novel algorithms for learning and inference under the framework of graphical models. Another important thrust of this proposal is to develop efficient scalable models for representing high- dimensional data beyond the traditional framework of graphical models. This research establishes strong theoretical guarantees for the developed methods, as well as applies them to real data in various domains, including genetic and financial data, and data from large online social networks such as Facebook and Twitter.