– S. Loustaud (LAREMA, Univ. Angers) : Inverse Statistical Learning – From minimax to algorithm Quand 11 octobre 2013 Ajouter au Calendrier Télécharger ICS Calendrier Google iCalendar Office 365 Outlook Live Inverse Statistical Learning : From minimax to algorithm By Sébastien Loustaud, LAREMA, Univ. Angers. We propose to consider the problem of statistical learning when we observe a contaminated sample. More precisely, we state minimax rates of convergence in classification with errors in variables for deconvolution empirical risk minimizers. These fast rates depends on the ill-posedness, the margin and the complexity of the problem. The cornerstone of the proof is a bias variance decomposition of the excess risk. After a theoretical study of the problem, we turn out into more practical considerations by presenting a new algorithm for noisy finite dimensional clustering called noisy K-means. The algorithm is based on a two-step procedure : a deconvolution step to deal with noisy inputs and Newton’s iteration as the popular k-means.