  We present theoretical analysis and a suite of tests and procedures for
addressing a broad class of redundant and misleading association rules we call
\emph{specious rules}. Specious dependencies, also known as \emph{spurious},
\emph{apparent}, or \emph{illusory associations}, refer to a well-known
phenomenon where marginal dependencies are merely products of interactions with
other variables and disappear when conditioned on those variables.
  The most extreme example is Yule-Simpson's 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. It is
accepted wisdom that in data of any nontrivial dimensionality it is infeasible
to control for all of the exponentially many possible confounds of this nature.
In this paper, we consider the problem of specious dependencies in the context
of statistical association rule mining. We define specious rules and show they
offer a unifying framework which covers many types of previously proposed
redundant or misleading association rules. After theoretical analysis, we
introduce practical algorithms for detecting and pruning out specious
association rules efficiently under many key goodness measures, including
mutual information and exact hypergeometric probabilities. We demonstrate that
the procedure greatly reduces the number of associations discovered, providing
an elegant and effective solution to the problem of association mining
discovering large numbers of misleading and redundant rules.
