Statistics Colloquium: STA 290Thursday, January 9th, 2014 at 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Po-Ling Loh , University of California, Berkeley
Title: "Nonconvex methods for high-dimensional regression with noisy and missing data"
Abstract: Noisy and missing data are prevalent in many real-world statistical estimation problems. Popular techniques for handling nonidealities in data, such as imputation and expectation-maximization, are often difficult to analyze theoretically and/or terminate in local optima of nonconvex functions -- these problems are only exacerbated in high-dimensional settings. We present new methods for obtaining high-dimensional regression estimators in the presence of corrupted data, and provide theoretical guarantees for the statistical consistency of our methods. Although our estimators also arise as minima of nonconvex functions, we show the rather surprising result that all stationary points are clustered around a global minimum. Motivated by a fundamental connection between linear regression and inverse covariance matrices, we demonstrate an important application of our method for graphical model estimation with noisy and missing data.