  In this article supervised learning problems are solved using soft rule
ensembles. We first review the importance sampling learning ensembles (ISLE)
approach that is useful for generating hard rules. The soft rules are then
obtained with logistic regression from the corresponding hard rules. In order
to deal with the perfect separation problem related to the logistic regression,
Firth's bias corrected likelihood is used. Various examples and simulation
results show that soft rule ensembles can improve predictive performance over
hard rule ensembles.
