  Given well-shuffled data, can we determine whether the data items are
statistically (in)dependent? Formally, we consider the problem of testing
whether a set of exchangeable random variables are independent. We will show
that this is possible and develop tests that can confidently reject the null
hypothesis that data is independent and identically distributed and have high
power for (some) exchangeable distributions. We will make no structural
assumptions on the underlying sample space. One potential application is in
Deep Learning, where data is often scraped from the whole internet, with
duplications abound, which can render data non-iid and test-set evaluation
prone to give wrong answers.
