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We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we propose an improvement of the previous approach we proposed in , which relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter domain adaptation bound for the target risk. While this bound stands indoi:10.1016/j.neucom.2019.10.105 fatcat:kxc2yfvawvhnnnef5bdwxxlif4