Mathieu Sauvenier

will give a presentation on

Direction Identification and Minimax Estimation by Generalized Eigenvalue Problem in High Dimensional Sparse Regression

Abstract:

“In high dimensional sparse linear regression, a selection and an estimation of the parameters are studied based on an $l_0-$constraint on the direction of the vector of parameters. We first establish a general result for the direction of the vector of parameters, that is identified through the leading generalized eigenspace of measurable matrices. Based on this result we suggest addressing the Best Subset Selection problem in a new perspective by solving an empirical generalized eigenvalue problem to estimate the direction of the high-dimensional parameter. We then study a new estimator founded on the RIFLE algorithm and show a non-asymptotic bound of the $L^2$ risk, the minimax convergence of the estimator and a Central Limit Theorem. Simulations show the superiority of the proposed inference over some known $l_0$ constrained estimators.”