Reasoning About Uncertainty in High-Dimensional Regression

• Activity Number: 465
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Adel Javanmard*
• Companies: University of Southern California
• Keywords: Hypothesis testing ; Lasso ; High-dimensional models ; Confidence intervals

Abstract

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an $\ell_1$-penalized least squares estimator, known as Lasso. Unfortunately, unlike for linear estimators (e.g., ordinary least squares), no well-established method exists to compute confidence intervals or p-values on the basis of the Lasso estimator. Recently, a line of work has addressed this problem by constructing a "de-biased" version of the Lasso estimator. In this talk, I will review this approach and show that the resulting confidence intervals have nearly optimal size. Further, when testing for the null hypothesis that a certain parameter is vanishing, this method has nearly optimal power. I will also discuss the performance of this method under optimal order of sample size. Time permitting, I will review applications to healthcare analytics and decision making, and discuss future perspectives for this research area.