Tomer Shoham

Tomer Shoham, Moshe Shenfeld, Noa Velner-Harris et al.

We introduce a simple, general framework that takes any differentially private estimator of any arbitrary quantity as a black box, and from it constructs a differentially private nonparametric confidence interval of that quantity. Our approach repeatedly subsamples the data, applies the private estimator to each subsample, and then post-processes the resulting empirical CDF to a confidence interval. Our analysis uses the randomness from the subsampling to achieve privacy amplification. Under mild assumptions, the empirical CDF we obtain approaches the CDF of the private statistic as the sample size grows. We use this to show that the confidence intervals we estimate are asymptotically valid, tight, and equivalent to their non-private counterparts. We provide empirical evidence that our method performs well compared with the (less-general) state-of-the-art algorithms.

Tomer Shoham, Katrina Ligettt

Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However, despite privacy concerns surrounding many datasets and despite increasing adoption of differential privacy, differentially private ratio statistics have largely been neglected by the literature and have only recently received an initial treatment by Lin et al. [1]. This paper attempts to fill this lacuna, giving results that can guide practice in evaluating ratios when the results must be protected by differential privacy. In particular, we show that even a simple algorithm can provide excellent properties concerning privacy, sample accuracy, and bias, not just asymptotically but also at quite small sample sizes. Additionally, we analyze a differentially private estimator for relative risk, prove its consistency, and develop a method for constructing valid confidence intervals. Our approach bridges a gap in the differential privacy literature and provides a practical solution for ratio estimation in private machine learning pipelines.

Tomer Shoham, Yosef Rinott

We consider a dataset $S$ held by an agency, and a vector query of interest, $f(S) \in \mathbb{R}^k$, to be posed by an analyst, which contains the information required for certain planned statistical inference. The agency releases the requested vector query with noise that guarantees a given level of Differential Privacy -- DP$(\varepsilon,δ)$ -- using the well-known Gaussian mechanism. The analyst can choose to pose the vector query $f(S)$ or to adjust it by a suitable transformation that can make the agency's response more informative. For any given level of privacy DP$(\varepsilon,δ)$ decided by the agency, we study natural situations where the analyst can achieve better statistical inference by adjusting the query with a suitable simple explicit transformation.