Improved subsample-and-aggregate via the private modified winsorized mean

TL;DR

This paper introduces a new differentially private mean estimator called the private modified winsorized mean, which improves aggregation in subsample-and-aggregate frameworks, demonstrating optimality and robustness through theoretical analysis and empirical results.

Contribution

The paper proposes the private modified winsorized mean as a novel, minimax optimal aggregator for differential privacy, with proven robustness and empirical performance advantages.

Findings

The private modified winsorized mean is minimax optimal for various distributions.

It performs well empirically compared to other private mean estimators.

Finite sample bounds reveal the importance of estimator bias and robustness in subsample aggregation.

Abstract

We develop a univariate, differentially private mean estimator, called the private modified winsorized mean, designed to be used as the aggregator in subsample-and-aggregate. We demonstrate, via real data analysis, that common differentially private multivariate mean estimators may not perform well as the aggregator, even in large datasets, motivating our developments.We show that the modified winsorized mean is minimax optimal for several, large classes of distributions, even under adversarial contamination. We also demonstrate that, empirically, the private modified winsorized mean performs well compared to other private mean estimates. We consider the modified winsorized mean as the aggregator in subsample-and-aggregate, deriving a finite sample deviations bound for a subsample-and-aggregate estimate generated with the new aggregator. This result yields two important insights: (i) the optimal choice of subsamples depends on the bias of the estimator computed on the subsamples, and (ii) the rate of convergence of the subsample-and-aggregate estimator depends on the robustness of the estimator computed on the subsamples.