Distance Assessment and Hypothesis Testing of High-Dimensional Samples using Variational Autoencoders

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.