We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The upper bounds provide theoretical guidelines for striking the right balance between data fit and generalization by controlling the input-output mutual information of a learning algorithm. The results can also be used to analyze the generalization capability of learning algorithms under adaptive composition, and the bias-accuracy tradeoffs in adaptive data analytics. Our work extends and leads to nontrivial improvements on the recent results of Russo and Zou.
The following lemma from REF provides an upper bound on the generalization error using the mutual information I(S; W ) between the training data set S and the output hypothesis W .
Information-theoretic analysis of generalization capability of learning algorithms
ArXiv
ArXiv
Computer Science Mathematics