  In many scientific tasks we are interested in discovering whether there exist
any correlations in our data. This raises many questions, such as how to
reliably and interpretably measure correlation between a multivariate set of
attributes, how to do so without having to make assumptions on distribution of
the data or the type of correlation, and, how to efficiently discover the
top-most reliably correlated attribute sets from data. In this paper we answer
these questions for discovery tasks in categorical data.
  In particular, we propose a corrected-for-chance, consistent, and efficient
estimator for normalized total correlation, by which we obtain a reliable,
naturally interpretable, non-parametric measure for correlation over
multivariate sets. For the discovery of the top-k correlated sets, we derive an
effective algorithmic framework based on a tight bounding function. This
framework offers exact, approximate, and heuristic search. Empirical evaluation
shows that already for small sample sizes the estimator leads to low-regret
optimization outcomes, while the algorithms are shown to be highly effective
for both large and high-dimensional data. Through two case studies we confirm
that our discovery framework identifies interesting and meaningful
correlations.
