Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given dataset. Privacy restrictions may require the curator of the data or the respondents themselves to share data with the test only after applying a randomizing privacy mechanism. This work considers mutual information (MI) as the privacy metric for measuring leakage. In addition, motivated by the Chernoff-Stein lemma, the relative entropy between pairs of distributions of the output (generated by the privacy mechanism) is chosen as the utility metric. For these metrics, the goal is to find the optimal privacy-utility trade-off (PUT) and the corresponding optimal privacy mechanism for both binary and m-ary hypothesis testing. Focusing on the high privacy regime, Euclidean information-theoretic approximations of the binary and m-ary PUT problems are developed. The solutions for the approximation problems clarify that an MI-based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihoods.
@cite_24: Our previous work [1] defined the notion of perfect location privacy for location-based services (LBS) and demon­strated how it can be achieved under basic user models. In this paper, we extend our work by studying perfect location privacy within a more complex scenario in which a user's movements are dependent upon the time domain. We model a mobile user's path using Markov chains and show that perfect location privacy is achievable for the user if her pseudonym is changed before o(n 2 |E|-r) observations by the adversary, where |E| is the number of edges in the Markov model and r is the number of all possible locations. We support our results with simulations.
@cite_15: 
@cite_16: In this paper, we study the problem of privacy information leakage in a smart grid. The privacy risk is assumed to be caused by an unauthorized binary hypothesis testing of the consumer's behaviour based on the smart meter readings of energy supplies from the energy provider. Another energy supplies are produced by an alternative energy source. A controller equipped with an energy storage device manages the energy inflows to satisfy the energy demand of the consumer. We study the optimal energy control strategy which minimizes the asymptotic exponential decay rate of the minimum Type II error probability in the unauthorized hypothesis testing to suppress the privacy risk. Our study shows that the cardinality of the energy supplies from the energy provider for the optimal control strategy is no more than two. This result implies a simple objective of the optimal energy control strategy. When additional side information is available for the adversary, the optimal control strategy and privacy risk are compared with the case of leaking smart meter readings to the adversary only.
The theoretical analysis done by Montazeri et al @cite_15 @cite_24 and Li and Oechtering @cite_16 are related to the one presented here in that they also make use of large deviation (information-theoretic) results in hypothesis testing. However, we apply these powerful theoretical tools to a different setting, in which data is purposefully randomized before disclosure in order to provide privacy, while guaranteeing utility in terms of a successful hypothesis test. Whereas they consider a hypothesis testing adversary, here we consider a precise hypothesis test as part of the utility metric.