Tighter Expected Generalization Error Bounds via Convexity of Information Measures

Abstract

Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each input training sample. Multiple generalization error upper bounds based on different information measures are provided, including Wasserstein distance, total variation distance, KL divergence, and Jensen-Shannon divergence. Due to the convexity of the information measures, the proposed bounds in terms of Wasserstein distance and total variation distance are shown to be tighter than their counterparts based on individual samples in the literature. An example is provided to demonstrate the tightness of the proposed generalization error bounds.

Integral Probability Metrics PAC-Bayes Bounds

“…7, Cor. 8 multiplies the dominant term of the bound by a nonuniform (data and algorithm-dependent) factor of D TV (Q, P ), which is guaranteed to tighten the bound.Note that the total-variation based bound ofAminian et al (2022) andRodríguez Gálvez et al (2021) assume Lipschitz loss function, while our TV bound allows non continuous loss functions such as the zero-one loss. The TV based bound ofWang et al (2019) (Thm.…”