Grafting for combinatorial binary model using frequent itemset mining

We consider the class of linear predictors over all logical conjunctions of binary attributes, which we refer to as the class of combinatorial binary models (CBMs) in this paper. CBMs are of high knowledge interpretability but naïve learning of them from labeled data requires exponentially high computational cost with respect to the length of the conjunctions. On the other hand, in the case of large-scale datasets, long conjunctions are effective for learning predictors. To overcome this computational difficulty, we propose an algorithm, GRAfting for Binary datasets (GRAB) , which efficiently learns CBMs within the L_1 -regularized loss minimization framework. The key idea of GRAB is to adopt weighted frequent itemset mining for the most time-consuming step in the grafting algorithm, which is designed to solve large-scale L_1 -RERM problems by an iterative approach. Furthermore, we experimentally showed that linear predictors of CBMs are effective in terms of prediction accuracy and knowledge discovery.