Related papers: New Lower Bounds for Private Estimation and a Gene…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
We consider the problem of approximating a $d \times d$ covariance matrix $M$ with a rank-$k$ matrix under $(\varepsilon,\delta)$-differential privacy. We present and analyze a complex variant of the Gaussian mechanism and obtain upper…
The standard closed form lower bound on $\sigma$ for providing $(\epsilon, \delta)$-differential privacy by adding zero mean Gaussian noise with variance $\sigma^2$ is $\sigma > \Delta\sqrt {2}(\epsilon^{-1}) \sqrt {\log \left(…
We study person-level differentially private (DP) mean estimation in the case where each person holds multiple samples. DP here requires the usual notion of distributional stability when $\textit{all}$ of a person's datapoints can be…
In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…
The Gaussian mechanism is one differential privacy mechanism commonly used to protect numerical data. However, it may be ill-suited to some applications because it has unbounded support and thus can produce invalid numerical answers to…
In this paper, we present two new algorithms for covariance estimation under concentrated differential privacy (zCDP). The first algorithm achieves a Frobenius error of $\tilde{O}(d^{1/4}\sqrt{\mathrm{tr}}/\sqrt{n} + \sqrt{d}/n)$, where…
We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…
We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded $k$-th moments. Roughly speaking, in the univariate case, we show that $n =…
Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over…
Bootstrap is a common tool for quantifying uncertainty in data analysis. However, besides additional computational costs in the application of the bootstrap on massive data, a challenging problem in bootstrap based inference under…
We propose a numerical accountant for evaluating the tight $(\varepsilon,\delta)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently…
A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank…
We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for…
This paper aims to construct a valid and efficient confidence interval for the extrema of parameters under privacy protection. The usual statistical inference on the extrema of parameters often suffers from the selection bias issue, and the…
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important…
Given a matrix $A \in \mathbb{R}^{m\times d}$ with singular values $\sigma_1\geq \cdots \geq \sigma_d$, and a random matrix $G \in \mathbb{R}^{m\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive new bounds on the Frobenius…
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…