A distribution shift between the training and test data can severely harm performance of machine learning models. Importance weighting addresses this issue by assigning different weights to data points during training. We argue that existing heuristics for determining the weights are suboptimal, as they neglect the increase of the variance of the estimated model due to the finite sample size of the training data. We interpret the optimal weights in terms of a bias-variance trade-off, and propose a bi-level optimization procedure in which the weights and model parameters are optimized simultaneously. We apply this optimization to existing importance weighting techniques for last-layer retraining of deep neural networks in the presence of sub-population shifts and show empirically that optimizing weights significantly improves generalization performance.

The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability evaluation criterion is defined as the minimal perturbation required on our observed dataset to induce a prescribed deterioration in risk evaluation. In this paper, we utilize the optimal transport (OT) discrepancy with moment constraints on the \textit{(sample, density)} space to quantify this perturbation. Therefore, our stability evaluation criterion can address both \emph{data corruptions} and \emph{sub-population shifts} -- the two most common types of distribution shifts in real-world scenarios. To further realize practical benefits, we present a series of tractable convex formulations and computational methods tailored to different classes of loss functions. The key technical tool to achieve this is the strong duality theorem provided in this paper. Empirically, we validate the practical utility of our stability evaluation criterion across a host of real-world applications. These empirical studies showcase the criterion's ability not only to compare the stability of different learning models and features but also to provide valuable guidelines and strategies to further improve models.

Sub-population shift is a specific type of domain shift that highlights changes in data distribution within specific sub-groups or populations between training and testing. Sub-population shift accounts for a significant source of algorithmic bias and calls for distributional robustness. Recent studies found inherent distributional robustness in multi-modality foundation models, such as the vision-language model CLIP, yet this robustness is vulnerable through parameter fine-tuning. In this paper, we propose leveraging the connection of robustness among different modalities and reshaping the distributional robustness of one modality with another. Specifically, in the context of the distributional robustness of CLIP, we propose to leverage natural language inputs to debias the image feature representations, to improve worst-case performance on sub-populations. Our extensive empirical studies show that image representations debiased by natural language can achieve significant performance improvement and reduction of performance instability under sub-population shifts.