– S. Loustaud (LAREMA, Univ. Angers) : Inverse Statistical Learning – From minimax to algorithm

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Date(s) - 11/10/2013
14 h 00 min - 15 h 00 min

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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.