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The following problem is considered: given a joint distribution PXY and an event E, bound PXY (E) in terms of PX PY (E) (where PX PY is the product of the marginals of PXY ) and a measure of dependence of X and Y . Such bounds have direct applications in the analysis of the generalization error of learning algorithms, where E represents a large error event and the measure of dependence controls the degree of overfitting. Herein, bounds are demonstrated using several information-theoretic metrics, in particular: mutual information, lautum information, maximal leakage, and J∞. The mutual information bound can outperform comparable bounds in the literature by an arbitrarily large factor.

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