First, I will review the lasso method and show an example of its utility in cancer diagnosis via mass spectometry. Then I will consider the testing the significance of the terms in a fitted regression, fit via the lasso or forward stepwise regression. I will present a novel statistical framework for this problem, one that provides p-values and confidence intervals that properly account for the inherent selection in the fitting procedure. I will give other examples of this procedure, including graphical models and PCA, and describe an R language package for its computation.
This work is joint with Richard Lockhart (Simon Fraser University), Jonathan Taylor (Stanford Univ) and Ryan Tibshirani (Carnegie Mellon University) and involves many other students at Stanford.