## A Bayesian Framework for Learning Rule Sets for Interpretable Classification

Tong Wang, Cynthia Rudin, Finale Doshi-Velez, Yimin Liu, Erica Klampfl, Perry MacNeille; 18(70):1−37, 2017.

### Abstract

We present a machine learning algorithm for building classifiers that are comprised of a small number of short rules. These are restricted disjunctive normal form models. An example of a classifier of this form is as follows: If $X$ satisfies (condition $A$ AND condition $B$) OR (condition $C$) OR $\cdots$, then $Y=1$. Models of this form have the advantage of being interpretable to human experts since they produce a set of rules that concisely describe a specific class. We present two probabilistic models with prior parameters that the user can set to encourage the model to have a desired size and shape, to conform with a domain-specific definition of interpretability. We provide a scalable MAP inference approach and develop theoretical bounds to reduce computation by iteratively pruning the search space. We apply our method (Bayesian Rule Sets -- BRS) to characterize and predict user behavior with respect to in-vehicle context-aware personalized recommender systems. Our method has a major advantage over classical associative classification methods and decision trees in that it does not greedily grow the model.

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