Speaker: Yuting Wei
Abstract: The Lasso estimator is a commonly used estimator for high-dimensional regression models which allows the number of covariates p to be larger than the number of observations n. It is known that in the regime where the ratio n/p is a constant, the Lasso estimator has a non-trivial distribution that involves an extra noise term due to the under-sampling effect. In this talk, I will first discuss the results by Miolane and Montanari'18 which characterizes the exact distribution of the Lasso estimator under standard Gaussian design. Establishing this result uses the Gordon's minimax Theorem developed by Tampoulidis, Oymak, and Hassibiā'16 which finds its root in the Gaussian comparison inequalities. Understanding the distribution of Lasso provides many interesting consequences including but not limited to characterizing the prediction and estimation risk, noise level estimation, model selection etc. If time permits, I will also talk about our recent work generalizing this result to cases beyond the standard Gaussian design and its use in hypothesis testing.