Report
Private Query Release via the Johnson-Lindenstrauss Transform
| العنوان: | Private Query Release via the Johnson-Lindenstrauss Transform |
|---|---|
| المؤلفون: | Nikolov, Aleksandar |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Computer Science - Data Structures and Algorithms, Computer Science - Cryptography and Security, Computer Science - Machine Learning, Statistics - Machine Learning |
| الوصف: | We introduce a new method for releasing answers to statistical queries with differential privacy, based on the Johnson-Lindenstrauss lemma. The key idea is to randomly project the query answers to a lower dimensional space so that the distance between any two vectors of feasible query answers is preserved up to an additive error. Then we answer the projected queries using a simple noise-adding mechanism, and lift the answers up to the original dimension. Using this method, we give, for the first time, purely differentially private mechanisms with optimal worst case sample complexity under average error for answering a workload of $k$ queries over a universe of size $N$. As other applications, we give the first purely private efficient mechanisms with optimal sample complexity for computing the covariance of a bounded high-dimensional distribution, and for answering 2-way marginal queries. We also show that, up to the dependence on the error, a variant of our mechanism is nearly optimal for every given query workload. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.07410 |
| رقم الانضمام: | edsarx.2208.07410 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |