Abstract:

Differential privacy provides a formal framework for limiting disclosure risk in computations on sensitive data. This dissertation studies differential privacy in structured data-release settings, focusing on two forms of structure: temporal structure in continual release and quantization structure in finite-level release.

First, we propose time-discounted differential privacy (TDDP) for continual release. Standard continual-release privacy definitions do not distinguish events by temporal distance, whereas the time-discounted formulation allows privacy requirements to decay as events become older. We develop mechanisms for this setting and analyze their privacy and utility guarantees.

Second, we analyze the Random Quantization Mechanism (RQM) of Youn et al., a mechanism that provides privacy-preserving randomized quantization through subsampling. The mechanism itself is not a contribution of this thesis; rather, we derive, under specified hyperparameter calibration requirements, a formal privacy characterization of RQM, including Rényi DP guarantees, a max-divergence/pure-DP refinement, and reconstruction-error bounds. These results make precise privacy claims that were not explicitly established in the original presentation of the mechanism. We then study RQM as a randomized quantization procedure, focusing on how preprocessing choices affect its behavior on unbounded and heavy-tailed data.

Finally, we complement the theoretical analysis with an empirical study of RQM in several new settings, beginning with private mean estimation and then considering distributional approximation, clustering, and image obfuscation. The results show that RQM is most natural when quantization is already compatible with the intended data representation, while also highlighting its sensitivity to parameter choices and application context.