DeepAI AI Chat
Log In Sign Up

Subset-Based Instance Optimality in Private Estimation

by   Travis Dick, et al.

We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset D, with the best private benchmark algorithm that (a) knows D in advance and (b) is evaluated by its worst-case performance on large subsets of D. That is, the benchmark algorithm need not perform well when potentially extreme points are added to D; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and ℓ_p-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.


page 1

page 2

page 3

page 4


A Nearly Instance-optimal Differentially Private Mechanism for Conjunctive Queries

Releasing the result size of conjunctive queries and graph pattern queri...

Differentially Private Quantiles

Quantiles are often used for summarizing and understanding data. If that...

Differentially Private Stochastic Linear Bandits: (Almost) for Free

In this paper, we propose differentially private algorithms for the prob...

Instance-Optimality in Interactive Decision Making: Toward a Non-Asymptotic Theory

We consider the development of adaptive, instance-dependent algorithms f...

Differentially Private Covariance Revisited

In this paper, we present three new error bounds, in terms of the Froben...

Preprocessing Imprecise Points for the Pareto Front

In the preprocessing model for uncertain data we are given a set of regi...

FriendlyCore: Practical Differentially Private Aggregation

Differentially private algorithms for common metric aggregation tasks, s...