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Distributionally Robust Logistic Regression

arXiv 1509.09259 ↗First posted 30 Sep 2015math.OC stat.MLcited by 124

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Abstract (arXiv)

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worst-case expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

Key facts. Cited by 124 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Sep 2015.

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Citing papers per year: 2021: 30; 2022: 21; 2023: 28; 2024: 23; 2025: 15; 2026: 7.

124 papers.

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  1. 2021Towards Out-Of-Distribution Generalization: A Surveycited by 431
  2. 2021Towards a Theoretical Framework of Out-of-Distribution Generalizationcited by 94
  3. 2021Distributional Robustness Loss for Long-tail Learningcited by 84
  4. 2024Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimizationcited by 52
  5. 2021Twice regularized MDPs and the equivalence between robustness and regularizationcited by 46
  6. 2021Distributionally Robust Learningcited by 44
  7. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  8. 2023Diagnosing Model Performance Under Distribution Shiftcited by 37
  9. 2022A Unified Wasserstein Distributional Robustness Framework for Adversarial Trainingcited by 36
  10. 2023A Finite Sample Complexity Bound for Distributionally Robust Q-learningcited by 35
  11. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  12. 2024Robust Reinforcement Learning from Corrupted Human Feedbackcited by 25
38 more
  1. 2021Certifying Robustness to Programmable Data Bias in Decision Treescited by 21
  2. 2023Understanding Contrastive Learning via Distributionally Robust Optimizationcited by 21
  3. 2021Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimizationcited by 19
  4. 2021Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimizationcited by 18
  5. 2023The Dataset Multiplicity Problem: How Unreliable Data Impacts Predictionscited by 17
  6. 2022Distributionally Robust Bayesian Optimization with varphi-divergencescited by 16
  7. 2023Outlier-Robust Wasserstein DROcited by 16
  8. 2024Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimizationcited by 15
  9. 2021Distributionally Robust Learning with Stable Adversarial Trainingcited by 14
  10. 2023Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challengescited by 14
  11. 2021Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solutioncited by 13
  12. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 12
  13. 2022Global-Local Regularization Via Distributional Robustnesscited by 11
  14. 2021The s-value: evaluating stability with respect to distributional shiftscited by 10
  15. 2021Coordinate Linear Variance Reduction for Generalized Linear Programmingcited by 10
  16. 2021Quasi-Newton Methods for Saddle Point Problems and Beyondcited by 10
  17. 2024Towards Robust Out-of-Distribution Generalization Bounds via Sharpnesscited by 10
  18. 2021Robust W-GAN-Based Estimation Under Wasserstein Contaminationcited by 9
  19. 2022Minimax risk classifiers with 0-1 losscited by 9
  20. 2022On the Generalization of Wasserstein Robust Federated Learningcited by 9
  21. 2023Bitrate-Constrained DRO: Beyond Worst Case Robustness To Unknown Group Shiftscited by 9
  22. 2023Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Modelscited by 9
  23. 2021Distributed Saddle-Point Problems Under Similaritycited by 8
  24. 2023A first-order augmented Lagrangian method for constrained minimax optimizationcited by 8
  25. 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
  26. 2021Robust Generalization despite Distribution Shift via Minimum Discriminating Informationcited by 6
  27. 2022Metrizing Fairnesscited by 6
  28. 2022Tikhonov Regularization is Optimal Transport Robust under Martingale Constraintscited by 6
  29. 2022Coresets for Wasserstein Distributionally Robust Optimization Problemscited by 6
  30. 2022On Generalization and Regularization via Wasserstein Distributionally Robust Optimizationcited by 6
  31. 2023Uncertainty-Aware Robust Learning on Noisy Graphscited by 6
  32. 2022Learning Distributionally Robust Models at Scale via Composite Optimizationcited by 5
  33. 2023Optimal Transport Model Distributional Robustnesscited by 5
  34. 2024Universal generalization guarantees for Wasserstein distributionally robust modelscited by 5
  35. 2024Evaluating Model Performance Under Worst-case Subpopulationscited by 5
  36. 2024Toward Robust Neural Reconstruction from Sparse Point Setscited by 5
  37. 2025Generalization Bounds and Stopping Rules for Learning with Self-Selected Datacited by 5
  38. 2021Adversarially Robust Kernel Smoothingcited by 4

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