Towards Unification of Statistical Reasoning, OLAP and Association Rule Mining: Semantics and Pragmatics

Over the last decades, various decision support technologies have gained massive ground in practice and theory. Out of these technologies, statistical reasoning was used widely to elucidate insights from data. Later, we have seen the emergence of online analytical processing (OLAP) and association rule mining, which both come with specific rationales and objectives. Unfortunately, both OLAP and association rule mining have been introduced with their own specific formalizations and terminologies. This made and makes it always hard to reuse results from one domain in another. In particular, it is not always easy to see the potential of statistical results in OLAP and association rule mining application scenarios. This paper aims to bridge the artificial gaps between the three decision support techniques, i.e., statistical reasoning, OLAP, and association rule mining and contribute by elaborating the semantic correspondences between their foundations, i.e., probability theory, relational algebra, and the itemset apparatus. Based on the semantic correspondences, we provide that the unification of these techniques can serve as a foundation for designing next-generation multi-paradigm data mining tools.