2021/01/22 by Borja Rodríguez-Gálvez, Rodríguez-Gálvez, Borja, Germán Bassi +5 · 3 citations
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2101.09315
openalex publication_date 2021/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample setting from Steinke and Zakynthinou [1]. Moreover, when the loss function is bounded and the geometry of the space is ignored by the choice of the metric in the Wasserstein distance, these bounds recover from below (and thus, are tighter than) current bounds based on the relative entropy. In particular, they generate new, non-vacuous bounds based on the relative entropy. Therefore, these results can be seen as a bridge between works that account for the geometry of the hypothesis space and those based on the relative entropy, which is agnostic to such geometry. Furthermore, it is shown how to produce various new bounds based on different information measures (e.g., the lautum information or several f-divergences) based on these bounds and how to derive similar bounds with respect to the backward channel using the presented proof techniques.