Distributionally Robust Feature Selection

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is costly, e.g. requiring adding survey questions or physical sensors, and we must be able to use the selected features to create high-quality downstream models for different populations. Our method frames the problem as a continuous relaxation of traditional variable selection using a noising mechanism, without requiring backpropagation through model training processes. By optimizing over the variance of a Bayes-optimal predictor, we develop a model-agnostic framework that balances overall performance of downstream prediction across populations. We validate our approach through experiments on both synthetic datasets and real-world data.