other algorithmic stability measures, such as differential privacy [@Dwork-14] and (approximate) max-information [@dwork15-06a]. These bounds are of the high-probability variety, but are typically weaker than the aforementioned maximal leakage bound [@esposito19-12a Sec. V]. All of the single-draw bounds mentioned here are data-independent.

#### Contributions {#contributions .unnumbered}

In this paper, we derive bounds of all three flavors—average, PAC-Bayesian, and single-draw—for both the standard setting and the random-subset setting. In the standard setting, we use the subgaussianity of the loss function, together with a change of measure argument, to obtain an exponential inequality in terms of the *information density* between the hypothesis $W$ and the training data ${\boldsymbol{Z}}$. This exponential inequality provides a framework that can be used to recover several known results, which were originally derived using a host of different tools. In this sense, it provides a unifying approach for deriving information-theoretic generalization bounds. Through simple manipulations of the exponential inequality, we recover the average generalization bound in [@xu17-05a Thm. 1] and the data-dependent PAC-Bayesian bound in [@guedj19-10a Prop. 3]. We also derive a novel data-dependent single-draw bound. Moreover, by further relaxing the PAC-Bayesian bound and the single-draw bound, we obtain two novel data-independent bounds that are explicit in the 