  We show that for a wide class of harmonization/domain-invariance schemes
several undesirable properties are unavoidable. If a predictive machine is made
invariant to a set of domains, the accuracy of the output predictions (as
measured by mutual information) is limited by the domain with the least amount
of information to begin with. If a real label value is highly informative about
the source domain, it cannot be accurately predicted by an invariant predictor.
These results are simple and intuitive, but we believe that it is beneficial to
state them for medical imaging harmonization.
