Semi-supervised Learning based on Distributionally Robust Optimization

Abstract

We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to restrict the support of the worst case distribution in our DRO formulation. We enable the implementation of our DRO formulation by proposing a stochastic gradient descent algorithm which allows to easily implement the training procedure. We demonstrate that our Semi-supervised DRO method is able to improve the generalization error over natural supervised procedures and state-of-the-art SSL estimators. Finally, we include a discussion on the large sample behavior of the optimal uncertainty region in the DRO formulation. Our discussion exposes important aspects such as the role of dimension reduction in SSL.

References in corpus (5)

• Generalizing to Unseen Domains via Adversarial Data Augmentation
• Certifying Some Distributional Robustness with Principled Adversarial Training
• Robust Wasserstein Profile Inference and Applications to Machine Learning
• Sample Out-Of-Sample Inference Based on Wasserstein Distance
• A Distributionally Robust Boosting Algorithm

Cited by in corpus (2)

• Robust Wasserstein Profile Inference and Applications to Machine Learning
• Sample Out-Of-Sample Inference Based on Wasserstein Distance