Optimal Prediction in the Linearly Transformed Spiked Model

Friday, December 8, 2017 - 11:15am - 12:15pm
Lind 305
William Leeb (Princeton University)
The linearly transformed spiked model generalizes the well-known spiked covariance model of Johnstone, but incorporates the action of a linear filter or projection on the signal component. As such, it is a more realistic model for many applications, including missing data problems and image deconvolution. I will describe new results in random matrix theory that are used to derive optimal predictors for this model in high dimensions. I will also explain surprising results contrasting in-sample and out-of-sample prediction, which are new even for the standard spiked model. I will also briefly explain recent work on the related problem of multireference alignment.

William Leeb is a postdoctoral research associate in the Program in Applied and Computational Mathematics at Princeton University, where he is supported by a fellowship from the Simons Collaboration on Algorithms and Geometry. Prior to this, he earned his Ph.D in Mathematics from Yale University in 2015 under the supervision of Ronald Coifman. His research centers on low-rank signal recovery, high-dimensional statistics, and metric approximation.