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Title: Polynomial-time estimation of the mean Authors:  Olivier Collier - Université Paris-Nanterre (France) [presenting]
Abstract: Independent Gaussian observations in high dimension are considered which share the same mean for the most part, while the other means can be arbitrarily large. We study the problem of robustly estimating the common mean in the minimax sense. But more precisely, we aim at finding feasible procedures, i.e. computable in polynomial time. First, we show the relation between robustly estimating the mean and estimating some linear functionals of the outliers. Then, we define a group-LASSO-like procedure for estimating the mean, which has better performance as previously existing methods. However, computational tractability comes with a loss of minimax-rate-optimality in some regimes.