  We provide a distribution-free test that can be used to determine whether any
two joint distributions $p$ and $q$ are statistically different by inspection
of a large enough set of samples. Following recent efforts from Long et al.
[1], we rely on joint kernel distribution embedding to extend the kernel
two-sample test of Gretton et al. [2] to the case of joint probability
distributions. Our main result can be directly applied to verify if a
dataset-shift has occurred between training and test distributions in a
learning framework, without further assuming the shift has occurred only in the
input, in the target or in the conditional distribution.
