Statistics/Probability Seminar
Speaker: Mayukh Choudhury, IIT Bombay
Host: Debraj Das
Title: Asymptotic Theory of $K$-fold Cross-validation in Lasso and the Validity of Bootstrap
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, October 16
Venue: Ramanujan Hall (meet.google.com/bgr-tffn-cem)
Abstract: Lasso is one of the widely used regularization methods in regression. Statisticians usually implement Lasso in practice by choosing the penalty parameter in a data-dependent way, the most popular being the $K-$fold cross-validation (or $K-$fold CV). However, inferential properties, such as the variable selection consistency and $n^{1/2}-$consistency, of the $K-$fold CV based Lasso estimator and validity of the Bootstrap approximation are still unknown. In this talk, we will discuss about $n^{1/2}-$consistency of the $K$-fold CV based penalty and utilizing that we explore the aforementioned inferential properties of the underlying Lasso estimator. Additionally, we establish the validity of Bootstrap in approximating the distribution of the $K-$fold CV based Lasso estimator. We validate our Bootstrap method in finite samples based on simulations.