  Machine-learning models contain information about the data they were trained
on. This information leaks either through the model itself or through
predictions made by the model. Consequently, when the training data contains
sensitive attributes, assessing the amount of information leakage is paramount.
We propose a method to quantify this leakage using the Fisher information of
the model about the data. Unlike the worst-case a priori guarantees of
differential privacy, Fisher information loss measures leakage with respect to
specific examples, attributes, or sub-populations within the dataset. We
motivate Fisher information loss through the Cram\'{e}r-Rao bound and delineate
the implied threat model. We provide efficient methods to compute Fisher
information loss for output-perturbed generalized linear models. Finally, we
empirically validate Fisher information loss as a useful measure of information
leakage.
