Modern techniques in data accumulation and sensing have led to an explosion in both the volume and variety of data. Many modern datasets are high-dimensional, meaning that the number of parameters to estimate can be far greater than the number of examples. This feature leads to various 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 and statistically efficient methods. In this talk, I first discuss a unified framework for establishing consistency and convergence rates for a broad class of M-estimators under high-dimensional scaling. Interestingly, the same tools used to establish good statistical properties have a direct impact for optimization: better conditioned statistical problems lead to more efficient computational methods. Finally, I will discuss some newer research on rank aggregation methods.