  Given two distinct datasets, an important question is if they have arisen
from the the same data generating function or alternatively how their data
generating functions diverge from one another. In this paper, we introduce an
approach for measuring the distance between two datasets with high
dimensionality using variational autoencoders. This approach is augmented by a
permutation hypothesis test in order to check the hypothesis that the data
generating distributions are the same within a significance level. We evaluate
both the distance measurement and hypothesis testing approaches on generated
and on public datasets. According to the results the proposed approach can be
used for data exploration (e.g. by quantifying the discrepancy/separability
between categories of images), which can be particularly useful in the early
phases of the pipeline of most machine learning projects.
