Information-theoretic analysis of generalization capability of learning algorithms
This work addresses the fundamental problem of understanding and controlling generalization in machine learning, offering incremental theoretical advancements with practical algorithmic implications.
The authors derived information-theoretic upper bounds on generalization error using mutual information between input and output, providing theoretical guidelines for balancing data fit and generalization, and proposed regularization methods that extend and improve upon prior results by Russo and Zou.
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.