  We present an algorithm for building probabilistic rule lists that is two
orders of magnitude faster than previous work. Rule list algorithms are
competitors for decision tree algorithms. They are associative classifiers, in
that they are built from pre-mined association rules. They have a logical
structure that is a sequence of IF-THEN rules, identical to a decision list or
one-sided decision tree. Instead of using greedy splitting and pruning like
decision tree algorithms, we fully optimize over rule lists, striking a
practical balance between accuracy, interpretability, and computational speed.
The algorithm presented here uses a mixture of theoretical bounds (tight enough
to have practical implications as a screening or bounding procedure),
computational reuse, and highly tuned language libraries to achieve
computational efficiency. Currently, for many practical problems, this method
achieves better accuracy and sparsity than decision trees; further, in many
cases, the computational time is practical and often less than that of decision
trees. The result is a probabilistic classifier (which estimates P(y = 1|x) for
each x) that optimizes the posterior of a Bayesian hierarchical model over rule
lists.
