Information-theoretic analysis of generalization capability of learning algorithms

TL;DR

This paper develops information-theoretic bounds on the generalization error of learning algorithms using mutual information, offering insights and methods to improve generalization by controlling this information measure.

Contribution

It introduces new upper bounds on generalization error based on mutual information and proposes regularization methods to optimize this balance.

Findings

Derived mutual information-based generalization bounds

Proposed regularization techniques for better generalization

Improved upon recent theoretical results by Russo and Zou

Abstract

We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems, and give theoretical guidelines for striking the right balance between data fit and generalization by controlling the input-output mutual information. We propose a number of methods for this purpose, among which are algorithms that regularize the ERM algorithm with relative entropy or with random noise. Our work extends and leads to nontrivial improvements on the recent results of Russo and Zou.