paradox where two variables present positive dependence in the marginal contingency table but negative in all partial tables defined by different levels of a confounding factor. As far as we know, the problem has not previously been addressed in the context of association rule discovery, but there are approaches (e.g., [@kingfkais; @HuangWebb2005; @causalrules; @webbml]) that prune out certain subtypes of specious rules, together with other search constraints.

We begin from basic definitions, tests and properties of specious rules. We show that specious rules offer a unifying framework that includes many previously proposed forms of redundant or misleading association rules as their special cases. Thus, their removal can drastically reduce the number of discovered associations. On the other hand, efficient detection of specious rules offers a solution to the oft-cited problem of misleading associations in traditional data analysis. We give new theoretical properties that help to identify specious dependencies efficiently, without testing all possible (exponentially many) confounding factors. Based on these, we introduce an efficient algorithm for detection and removal of specious dependencies. We report experiments on mining non-specious, statistical association rules with mutual information, and draw final conclusions.

Definitions and concepts
========================

Unconditional and conditional dependencies
------------------------------------------

According to a 