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Title: Dimension-free PAC-Bayesian bounds for vectors and matrices Authors:  Ilaria Giulini - Universite Paris Diderot (France) [presenting]
Abstract: PAC-Bayesian inequalities are used to present new robust estimators for the mean of a random vector and of a random matrix. More precisely, we establish dimension-free bounds and we work under mild polynomial moment assumptions regarding the tail of the sample distribution. Particular attention is devoted to the estimation of the Gram matrix, due to its prominent role in high-dimensional analysis.