Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are obtained in this context by Monte Carlo events, which do furnish an accurate but abstract and implicit representation of the likelihood. Strategies based on statistical learning are currently being developed to infer the likelihood function explicitly by training a continuous-output classifier on Monte Carlo events. In this paper, we investigate the usage of Monte Carlo events that incorporate the dependence on the parameters of interest by reweighting. This enables more accurate likelihood learning with less training data and a more robust learning scheme that is more suited for automation and extensive deployment. We illustrate these advantages in the context of LHC precision probes of new Effective Field Theory interactions.