Private Statistical Estimation via Truncation
This provides a general blueprint for differentially private algorithm design, addressing a key limitation in privacy-preserving statistics for applications with unbounded data.
The paper tackles the challenge of differentially private statistical estimation with unbounded data support by introducing a truncation framework, achieving near-optimal sample complexity for exponential family distributions like Gaussian mean and covariance estimation.
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.