MINTY: Rule-based Models that Minimize the Need for Imputing Features with Missing Values

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.

Sharing pattern submodels for prediction with missing values

Missing values are unavoidable in many applications of machine learning and present a challenge both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as a solution. However, independent models do not make efficient use of all available data. Conversely, fitting a shared model to the full data set typically relies on imputation which may be suboptimal when missingness depends on unobserved factors. We propose an alternative approach, called sharing pattern submodels, which make predictions that are a) robust to missing values at test time, b) maintains or improves the predictive power of pattern submodels, and c) has a short description enabling improved interpretability. We identify cases where sharing is provably optimal, even when missingness itself is predictive and when the prediction target depends on unobserved variables. Classification and regression experiments on synthetic data and two healthcare data sets demonstrate that our models achieve a favorable trade-off between pattern specialization and information sharing.