Private Statistical Estimation via Truncation

TL;DR

This paper presents a new framework for differentially private statistical estimation using data truncation, enabling efficient and near-optimal privacy-preserving estimation for exponential family distributions with unbounded support.

Contribution

It introduces a general approach leveraging truncated statistics for DP estimation, extending applicability to unbounded exponential families and providing improved convergence guarantees.

Findings

Developed computationally efficient DP estimators for Gaussian parameters.

Achieved near-optimal sample complexity in DP estimation.

Provided improved uniform convergence bounds for exponential family log-likelihoods.

Abstract

We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific sensitivity analysis, limiting their applicability. By leveraging techniques from truncated statistics, we develop computationally efficient DP estimators for exponential family distributions, including Gaussian mean and covariance estimation, achieving near-optimal sample complexity. Previous works on exponential families only consider bounded or one-dimensional families. Our approach mitigates sensitivity through truncation while carefully correcting for the introduced bias using maximum likelihood estimation and DP stochastic gradient descent. Along the way, we establish improved uniform convergence guarantees for the log-likelihood function of exponential families, which may be of independent interest. Our results provide a general blueprint for DP algorithm design via truncated statistics.