In this article supervised learning problems are solved using soft rule ensembles. First, we review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. Soft rules are obtained with logistic regression using the corresponding hard rules and training data. Soft rule ensembles work well when both the response and the input variables are continuous because soft rules provide smooth transitions around the boundaries of hard rules. Finally, various examples and simulation results are provided to illustrate and evaluate the performance of soft rule ensembles.

In this article supervised learning problems are solved using soft rule ensembles. First, we review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. Soft rules are obtained with logistic regression using the corresponding hard rules and training data. Soft rule ensembles work well when both the response and the input variables are continuous because soft rules provide smooth transitions around the boundaries of hard rules. Finally, various examples and simulation results are provided to illustrate and evaluate the performance of soft rule ensembles.

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.