  This paper introduces the combinatorial Boolean model (CBM), which is defined
as the class of linear combinations of conjunctions of Boolean attributes. This
paper addresses the issue of learning CBM from labeled data. CBM is of high
knowledge interpretability but na\"{i}ve learning of it requires exponentially
large computation time with respect to data dimension and sample size. To
overcome this computational difficulty, we propose an algorithm GRAB (GRAfting
for Boolean datasets), which efficiently learns CBM within the
$L_1$-regularized loss minimization framework. The key idea of GRAB is to
reduce the loss minimization problem to the weighted frequent itemset mining,
in which frequent patterns are efficiently computable. We employ benchmark
datasets to empirically demonstrate that GRAB is effective in terms of
computational efficiency, prediction accuracy and knowledge discovery.
