1,598 research outputs found
Differential Privacy in Metric Spaces: Numerical, Categorical and Functional Data Under the One Roof
We study Differential Privacy in the abstract setting of Probability on
metric spaces. Numerical, categorical and functional data can be handled in a
uniform manner in this setting. We demonstrate how mechanisms based on data
sanitisation and those that rely on adding noise to query responses fit within
this framework. We prove that once the sanitisation is differentially private,
then so is the query response for any query. We show how to construct
sanitisations for high-dimensional databases using simple 1-dimensional
mechanisms. We also provide lower bounds on the expected error for
differentially private sanitisations in the general metric space setting.
Finally, we consider the question of sufficient sets for differential privacy
and show that for relaxed differential privacy, any algebra generating the
Borel -algebra is a sufficient set for relaxed differential privacy.Comment: 18 Page
Differentially Private Functional Summaries via the Independent Component Laplace Process
In this work, we propose a new mechanism for releasing differentially private
functional summaries called the Independent Component Laplace Process, or ICLP,
mechanism. By treating the functional summaries of interest as truly
infinite-dimensional objects and perturbing them with the ICLP noise, this new
mechanism relaxes assumptions on data trajectories and preserves higher utility
compared to classical finite-dimensional subspace embedding approaches in the
literature. We establish the feasibility of the proposed mechanism in multiple
function spaces. Several statistical estimation problems are considered, and we
demonstrate by slightly over-smoothing the summary, the privacy cost will not
dominate the statistical error and is asymptotically negligible. Numerical
experiments on synthetic and real datasets demonstrate the efficacy of the
proposed mechanism
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