Title: Lasso principal support vector machines for sufficient dimension reduction
Authors: Andreas Artemiou - Cardiff University (United Kingdom) [presenting]
Eugen Pircalabelu - Université catholique de Louvain (Belgium)
Abstract: A new method is developed for performing dimension reduction for high-dimensional settings. The proposed procedure is based on a principal support vector machine framework where principal projections are used to overcome the non-invertibility of the covariance matrix. Using a series of equivalences, we show that one can accurately recover the central subspace using a projection on a lower-dimensional subspace and then apply an l1 penalization strategy to obtain sparse estimators of the sufficient directions. Based next on a desparsified estimator, we provide an inferential procedure for high-dimensional models that allows testing for the importance of variables in determining the sufficient direction. Theoretical properties of the methodology are illustrated, and simulated and real data experiments demonstrate computational advantages.