It’s all in the mix: Wasserstein classification and regression with mixed features
File(s)
Accepted version
Author(s)
Belbasi, Reza
Selvi, Aras
Wiesemann, Wolfram
Type
Journal Article
Abstract
Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by distributionally robust problem formulations that consider all data-generating distributions close to the empirical distribution derived from historical samples, where “closeness” is determined by the Wasserstein distance. Although such formulations show significant promise in prediction tasks where all input features are continuous, they scale exponentially when discrete features are present. Methodology/results: We demonstrate that distributionally robust mixed-feature classification and regression problems can indeed be solved in polynomial time. Our proof relies on classical ellipsoid method-based solution schemes that do not scale well in practice. To overcome this limitation, we develop a practically efficient (yet, in the worst case, exponential-time) cutting-plane-based algorithm that admits a polynomial-time separation oracle, despite the presence of exponentially many constraints. We compare our method against alternative techniques both theoretically and empirically on standard benchmark instances. Managerial implications: Data-driven operations management problems often involve prediction models with discrete features. We develop and analyze distributionally robust prediction models that faithfully account for the presence of discrete features, and we demonstrate that our models can significantly outperform existing methods that are agnostic to the presence of discrete features both theoretically and on standard benchmark instances.
Date Issued
2026-03-09
Date Acceptance
2026-01-24
Citation
Manufacturing & Service Operations Management, 2026
ISSN
1523-4614
Publisher
Institute for Operations Research and Management Sciences
Journal / Book Title
Manufacturing & Service Operations Management
Copyright Statement
Copyright © 2026, INFORMS. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published online
Date Publish Online
2026-03-09