171c3678c36e39fc0074f3e7332a9a66-Supplemental-Conference.pdf

If the label distribution across the clients is skewed and the class conditionals have the same support, then the class probabilities {pi(y |x) |i [m]} are non-identical, i.e., for all i 6= uand i,u [m], there exists x, y such that pi(y | x) 6= pu(y | x). We prove the result by contradiction.