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Problem definition: A key challenge in supervised learning is data scarcity,which can cause prediction models to overfit to the training data and performpoorly out of sample. A contemporary approach to combat overfitting is offeredby distributionally robust problem formulations that consider alldata-generating distributions close to the empirical distribution derived fromhistorical samples, where 'closeness' is determined by the Wassersteindistance. While such formulations show significant promise in prediction taskswhere all input features are continuous, they scale exponentially when discretefeatures are present. Methodology/results: We demonstrate that distributionallyrobust mixed-feature classification and regression problems can indeed besolved in polynomial time. Our proof relies on classical ellipsoid method-basedsolution schemes that do not scale well in practice. To overcome thislimitation, we develop a practically efficient (yet, in the worst case,exponential time) cutting plane-based algorithm that admits a polynomial timeseparation oracle, despite the presence of exponentially many constraints. Wecompare our method against alternative techniques both theoretically andempirically on standard benchmark instances. Managerial implications:Data-driven operations management problems often involve prediction models withdiscrete features. We develop and analyze distributionally robust predictionmodels that faithfully account for the presence of discrete features, and wedemonstrate that our models can significantly outperform existing methods thatare agnostic to the presence of discrete features, both theoretically and onstandard benchmark instances.

It's All in the Mix: Wasserstein Classification and Regression with Mixed Features