PAC-Bayesian inequalities have already proved to be a great tool to obtain dimension free generalization bounds, such as margin bounds for Support Vector Machines. In this talk, we will play with PAC-Bayesian inequalities and influence functions to present new robust estimators for the mean of random vectors and random matrices, as well as for linear least squares regression. A common theme of the presentation will be to establish dimension free bounds and to work under mild polynomial moment assumptions regarding the tail of the sample distribution.

Joint work with Ilaria Giulini.