Differentially private black-box evaluation extended to high dimensions
Original title: Private Evaluation of High-Dimensional Functions
The method reduces evaluation to private quasi-concave optimization and replaces multiplicative sample overhead with additive overhead.
Researchers propose generic black-box evaluators that privately approximate an arbitrary high-dimensional function when sensitivity may be unknown. The evaluator may query the function only on subsets formed by removing a bounded number of records. Outputs fall in the convex hull of those values with high probability, generalizing prior real-valued results and recovering private center-point guarantees. The same reduction improves user-level quasi-concave and convex optimization versus sample-and-aggregate.
- Evaluators cover both pure and approximate differential privacy.
- Utility is geometric: the output lies in a convex hull of neighborhood values.
- The work recovers Beimel et al. center-point guarantees with additive Tukey-depth approximation.
- High-dimensional private evaluation and private QCO are equivalent up to a dimension factor.
From the original article
1 min read at arxiv.orgWe study differentially private black-box evaluation of arbitrary high-dimensional functions. Given a dataset $S$ and query access to a function $f$---whose sensitivity may be unknown or unbounded---the goal is to privately output an approximation to $f(S)$. The black-box evaluator can only query the value of $f$ over a down neighborhood of $S$ (i.
By Mohammad Afzali · arxiv.org
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