ECE Seminar: Structured Estimation in High-Dimensions
Monday, March 4, 2013 - 11:45am to 1:00pm
Sahand Negahban, Ph.D., Postdoctoral Associate, Department of EECS, Massachusetts Institute of Technology
Modern techniques in data accumulation and sensing have led to an explosion in both the volume and variety of data. These advancements have presented us with a tremendous opportunity to perform more sophisticated inference and decision making tasks. Such problems arise in: genomics, rank aggregation, and recommendation systems. Many of the resulting estimation problems are high-dimensional, meaning that the number of parameters to estimate can be far greater than the number of examples. The high-dimensionality and volume of the data leads to substantial challenges, both statistical and computational. A major focus of my work has been developing an understanding of how hidden low-complexity structure in large datasets can be used to develop computationally efficient estimation methods. I will introduce a unified framework for establishing the error behavior of a broad class of estimators under high-dimensional scaling. I will then discuss how to compute these estimates and draw connections between the statistical and computational properties of our methods. Interestingly, the same tools used to establish good high-dimensional estimation performance have a direct impact for optimization: better conditioned statistical problems lead to more efficient computational methods. Sahand Negahban is currently a post-doctoral associate at MIT. He received a Ph.D. in Electrical Engineering and Computer Sciences from UC Berkeley (2012).