Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics of a theoretical model are not fully understood. Using adversarial networks, we include a priori known sources of systematic and theoretical uncertainties during the training. This paves the way to a more reliable event classification on an event-by-event basis, as well as novel approaches to perform parameter fits of particle physics data. We demonstrate the benefits of the method explicitly in an example considering effective field theory extensions of Higgs boson production in association with jets.