Tighter Expected Generalization Error Bounds via Convexity of Information Measures

TL;DR

This paper introduces new expected generalization error bounds using convex information measures, resulting in tighter bounds than previous methods, with applications demonstrated through examples.

Contribution

It develops novel generalization bounds based on convex information measures like Wasserstein and total variation distances, improving tightness over existing bounds.

Findings

Bounds based on Wasserstein and total variation are tighter.

Convexity of information measures enhances bound tightness.

Example demonstrates the bounds' effectiveness.

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.