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

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Date(s) - 11 octobre 2013

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Inverse Statistical Learning : From minimax to algorithm\n\nBy Sébastien Loustau, LAREMA, Univ. Angers.\n\nWe 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.\nAfter 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.[