DeepAI AI Chat
Log In Sign Up

Private Query Release Assisted by Public Data

04/23/2020
by   Raef Bassily, et al.
0

We study the problem of differentially private query release assisted by access to public data. In this problem, the goal is to answer a large class H of statistical queries with error no more than α using a combination of public and private samples. The algorithm is required to satisfy differential privacy only with respect to the private samples. We study the limits of this task in terms of the private and public sample complexities. First, we show that we can solve the problem for any query class H of finite VC-dimension using only d/α public samples and √(p)d^3/2/α^2 private samples, where d and p are the VC-dimension and dual VC-dimension of H, respectively. In comparison, with only private samples, this problem cannot be solved even for simple query classes with VC-dimension one, and without any private samples, a larger public sample of size d/α^2 is needed. Next, we give sample complexity lower bounds that exhibit tight dependence on p and α. For the class of decision stumps, we give a lower bound of √(p)/α on the private sample complexity whenever the public sample size is less than 1/α^2. Given our upper bounds, this shows that the dependence on √(p) is necessary in the private sample complexity. We also give a lower bound of 1/α on the public sample complexity for a broad family of query classes, which by our upper bound, is tight in α.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/31/2019

Privately Answering Classification Queries in the Agnostic PAC Model

We revisit the problem of differentially private release of classificati...
10/25/2019

Limits of Private Learning with Access to Public Data

We consider learning problems where the training set consists of two typ...
11/11/2022

Õptimal Differentially Private Learning of Thresholds and Quasi-Concave Optimization

The problem of learning threshold functions is a fundamental one in mach...
03/10/2020

Closure Properties for Private Classification and Online Prediction

Let H be a class of boolean functions and consider acomposed class H' th...
11/24/2020

InstaHide's Sample Complexity When Mixing Two Private Images

Inspired by InstaHide challenge [Huang, Song, Li and Arora'20], [Chen, S...
01/31/2023

Tight Data Access Bounds for Private Top-k Selection

We study the top-k selection problem under the differential privacy mode...
01/12/2022

On the Statistical Complexity of Sample Amplification

Given n i.i.d. samples drawn from an unknown distribution P, when is it ...