  Deploying machine learning models in production may allow adversaries to
infer sensitive information about training data. There is a vast literature
analyzing different types of inference risks, ranging from membership inference
to reconstruction attacks. Inspired by the success of games (i.e.,
probabilistic experiments) to study security properties in cryptography, some
authors describe privacy inference risks in machine learning using a similar
game-based style. However, adversary capabilities and goals are often stated in
subtly different ways from one presentation to the other, which makes it hard
to relate and compose results. In this paper, we present a game-based framework
to systematize the body of knowledge on privacy inference risks in machine
learning. We use this framework to (1) provide a unifying structure for
definitions of inference risks, (2) formally establish known relations among
definitions, and (3) to uncover hitherto unknown relations that would have been
difficult to spot otherwise.
