  Rule models are often preferred in prediction tasks with tabular inputs as
they can be easily interpreted using natural language and provide predictive
performance on par with more complex models. However, most rule models'
predictions are undefined or ambiguous when some inputs are missing, forcing
users to rely on statistical imputation models or heuristics like zero
imputation, undermining the interpretability of the models. In this work, we
propose fitting concise yet precise rule models that learn to avoid relying on
features with missing values and, therefore, limit their reliance on imputation
at test time. We develop MINTY, a method that learns rules in the form of
disjunctions between variables that act as replacements for each other when one
or more is missing. This results in a sparse linear rule model, regularized to
have small dependence on features with missing values, that allows a trade-off
between goodness of fit, interpretability, and robustness to missing values at
test time. We demonstrate the value of MINTY in experiments using synthetic and
real-world data sets and find its predictive performance comparable or
favorable to baselines, with smaller reliance on features with missing values.
