Computing and Mathematical Sciences Colloquium

Monday February 2, 2015 4:00 PM

Post-Selection Inference for Forward Stepwise and Least Angle Regression

Speaker: Professor Robert Tibshirani, Depts. of Health Research and Policy, and Statistics, Stanford University
Location: Annenberg 105
In this talk I propose new inference tools for least angle and forward stepwise regression. I first present a general scheme for valid inference after any selection event that can be described as the observation vector y falling into a polyhedron. Following this, I derive a new procedure called the "spacing test" which provides exact conditional tests at any step of the least angle regression (LAR) algorithm, as well as "selection intervals" for the appropriate underlying regression parameters. Remarkably, these tests and intervals account correctly for the adaptive selection performed by LAR. I will apply the same framework to yield selection-adjusted tests and intervals for forward stepwise regression in linear models, generalized linear models and other settings such as the Cox model. Finally I will briefly discuss current work extending these ideas to the PCA setting. Joint work with Jonathan Taylor, Richard Lockhart and Ryan J. Tibshirani.
Series Computing and Mathematical Sciences Colloquium Series

Contact: Carmen Nemer-Sirois at (626) 395-4561 carmens@caltech.edu