RRL: A Scalable Classifier for Interpretable Rule-Based Representation Learning

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to tackle these issues, but they sacrifice the model interpretability. In this paper, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent. An improved design of logical activation functions is also devised to increase the scalability of RRL and enable it to discretize the continuous features end-to-end. Exhaustive experiments on 9 small and 4 large data sets show that RRL outperforms the competitive approaches, has low complexity close to the simple decision trees, and is rational for its main technical contributions.