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

TL;DR

This paper introduces methods to improve model generalization under covariate shifts by minimizing Maximum Mean Discrepancy (MMD) between training and test data, addressing distribution and missingness shifts.

Contribution

It proposes three novel techniques—MMD Representation, MMD Mask, and MMD Hybrid—that effectively handle different types of covariate shifts to enhance model robustness.

Findings

Models with MMD loss perform better on shifted test data.

MMD methods improve calibration and extrapolation.

Techniques adapt features to reduce distribution mismatch.

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.