Maximum Mean Discrepancy for Generalization in the Presence of Distribution and Missingness Shift

Liwen Ouyang, Aaron Key

Keywords: maximum mean discrepancy, data shift, covariate shift, representation learning, missing data

Abstract: Covariate shifts are a common problem in predictive modeling on real-world problems. This paper proposes addressing the covariate shift problem by minimizing Maximum Mean Discrepancy (MMD) statistics between the training and test sets in either feature input space, feature representation space, or both. We designed three techniques that we call MMD Representation, MMD Mask, and MMD Hybrid to deal with the scenarios where only a distribution shift exists, only a missingness shift exists, or both types of shift exist, respectively. We find that integrating an MMD loss component helps models use the best features for generalization and avoid dangerous extrapolation as much as possible for each test sample. Models treated with this MMD approach show better performance, calibration, and extrapolation on the test set.

One-sentence Summary: This paper develops a novel approach to train a more robust machine learning model when distribution shift and/or missingness shift exist between train and test data.