ECE Seminar: Structured Estimation in High-Dimensions
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).