Inference of Common Multidimensional Equally-Distributed Attributes

Given two relations containing multiple measurements - possibly with uncertainties - our objective is to find which sets of attributes from the first have a corresponding set on the second, using exclusively a sample of the data. This approach could be used even when the associated metadata is damaged, missing or incomplete, or when the volume is too big for exact methods. This problem is similar to the search of Inclusion Dependencies (IND), a type of rule over two relations asserting that for a set of attributes X from the first, every combination of values appears on a set Y from the second. Existing IND can be found exploiting the existence of a partial order relation called specialization. However, this relation is based on set theory, requiring the values to be directly comparable. Statistical tests are an intuitive possible replacement, but it has not been studied how would they affect the underlying assumptions. In this paper we formally review the effect that a statistical approach has over the inference rules applied to IND discovery. Our results confirm the intuitive thought that statistical tests can be used, but not in a directly equivalent manner. We provide a workable alternative based on a "hierarchy of null hypotheses", allowing for the automatic discovery of multi-dimensional equally distributed sets of attributes.