  Statistically significant patterns mining (SSPM) is an essential and
challenging data mining task in the field of knowledge discovery in databases
(KDD), in which each pattern is evaluated via a hypothesis test. Our study aims
to introduce a preference relation into patterns and to discover the most
preferred patterns under the constraint of statistical significance, which has
never been considered in existing SSPM problems. We propose an iterative
multiple testing procedure that can alternately reject a hypothesis and safely
ignore the hypotheses that are less useful than the rejected hypothesis. One
advantage of filtering out patterns with low utility is that it avoids
consumption of the significance budget by rejection of useless (that is,
uninteresting) patterns. This allows the significance budget to be focused on
useful patterns, leading to more useful discoveries.
  We show that the proposed method can control the familywise error rate (FWER)
under certain assumptions, that can be satisfied by a realistic problem class
in SSPM.\@We also show that the proposed method always discovers a set of
patterns that is at least equally or more useful than those discovered using
the standard Tarone-Bonferroni method SSPM.\@Finally, we conducted several
experiments with both synthetic and real-world data to evaluate the performance
of our method. As a result, in the experiments with real-world datasets, the
proposed method discovered a larger number of more useful patterns than the
existing method for all five conducted tasks.
