Lower Bounds for Locally Private Estimation via Communication Complexity

by   John Duchi, et al.

We develop lower bounds for estimation under local privacy constraints---including differential privacy and its relaxations to approximate or Rényi differential privacy of all orders---by showing an equivalence between private estimation and communication-restricted estimation problems. Our results are strong enough to apply to arbitrarily interactive privacy mechanisms, and they also give sharp lower bounds for all levels of differential privacy protections, that is, privacy mechanisms with privacy levels ε∈ [0, ∞). As a particular consequence of our results, we show that the minimax mean-squared error for estimating the mean of a bounded or Gaussian random vector in d dimensions scales as d/n·d/{ε, ε ^2}.


page 1

page 2

page 3

page 4


Fisher information under local differential privacy

We develop data processing inequalities that describe how Fisher informa...

Property Testing for Differential Privacy

We consider the problem of property testing for differential privacy: wi...

Four accuracy bounds and one estimator for frequency estimation under local differential privacy

We present four lower bounds on the mean squared error of both frequency...

Private Heavy Hitters and Range Queries in the Shuffled Model

An exciting new development in differential privacy is the shuffled mode...

Minimax rate for multivariate data under componentwise local differential privacy constraints

Our research delves into the balance between maintaining privacy and pre...

The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information

We identify fundamental tradeoffs between statistical utility and privac...

Locally Differentially Private Sparse Vector Aggregation

Vector mean estimation is a central primitive in federated analytics. In...

Please sign up or login with your details

Forgot password? Click here to reset