Year: 2024
Type: preprint
Abstract: Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly for all the classes. In practice, however, there are significant variations in generalization performance among different classes, which cannot be captured by the existing generalization bounds. In this work, we tackle this problem by theoretically studying the class-generalization error, which quantifies the generalization performance of each individual class. We derive a novel information-theoretic bound for class-generalization error using the KL divergence, and we further obtain several tighter bounds using the conditional mutual information (CMI), which are significantly easier to estimate in practice. We empirically validate our proposed bounds in different neural networks and show that they accurately capture the complex class-generalization error behavior. Moreover, we show that the theoretical tools developed in this paper can be applied in several applications beyond this context.
Source: arXiv (Cornell University)
Authors: Laakom, Firas, Bu, Yuheng, Gabbouj, Moncef
Institutions: Tampere University, University of Tampere, University of Florida
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390690259