  Interpretable classifiers have recently witnessed an increase in attention
from the data mining community because they are inherently easier to understand
and explain than their more complex counterparts. Examples of interpretable
classification models include decision trees, rule sets, and rule lists.
Learning such models often involves optimizing hyperparameters, which typically
requires substantial amounts of data and may result in relatively large models.
In this paper, we consider the problem of learning compact yet accurate
probabilistic rule lists for multiclass classification. Specifically, we
propose a novel formalization based on probabilistic rule lists and the minimum
description length (MDL) principle. This results in virtually parameter-free
model selection that naturally allows to trade-off model complexity with
goodness of fit, by which overfitting and the need for hyperparameter tuning
are effectively avoided. Finally, we introduce the Classy algorithm, which
greedily finds rule lists according to the proposed criterion. We empirically
demonstrate that Classy selects small probabilistic rule lists that outperform
state-of-the-art classifiers when it comes to the combination of predictive
performance and interpretability. We show that Classy is insensitive to its
only parameter, i.e., the candidate set, and that compression on the training
set correlates with classification performance, validating our MDL-based
selection criterion.
