Related papers: Locally Differentially Private Minimum Finding
We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…
Training differentially private machine learning models requires constraining an individual's contribution to the optimization process. This is achieved by clipping the $2$-norm of their gradient at a predetermined threshold prior to…
We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local…
Although robust learning and local differential privacy are both widely studied fields of research, combining the two settings is just starting to be explored. We consider the problem of estimating a discrete distribution in total variation…
We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal $\tilde{O}(\sqrt{T})$ regret bounds. In the full-information setting, our results demonstrate…
We develop lower bounds for estimation under local privacy constraints---including differential privacy and its relaxations to approximate or R\'{e}nyi differential privacy---by showing an equivalence between private estimation and…
We revisit the problem of finding a minimum enclosing ball with differential privacy: Given a set of $n$ points in the Euclidean space $\mathbb{R}^d$ and an integer $t\leq n$, the goal is to find a ball of the smallest radius $r_{opt}$…
We develop differentially private hypothesis testing methods for the small sample regime. Given a sample $\cal D$ from a categorical distribution $p$ over some domain $\Sigma$, an explicitly described distribution $q$ over $\Sigma$, some…
Our research delves into the balance between maintaining privacy and preserving statistical accuracy when dealing with multivariate data that is subject to \textit{componentwise local differential privacy} (CLDP). With CLDP, each component…
In the approximate quantiles problem, the goal is to output $m$ quantile estimates, the ranks of which are as close as possible to $m$ given quantiles $0 \leq q_1 \leq\dots \leq q_m \leq 1$. We present a mechanism for approximate quantiles…
We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…
In recent years, Local Differential Privacy (LDP), a robust privacy-preserving methodology, has gained widespread adoption in real-world applications. With LDP, users can perturb their data on their devices before sending it out for…
We consider the problem of mean estimation under user-level local differential privacy, where $n$ users are contributing through their local pool of data samples. Previous work assume that the number of data samples is the same across…
In this paper, we investigate the problem of differentially private distributed optimization. Recognizing that lower sensitivity leads to higher accuracy, we analyze the key factors influencing the sensitivity of differentially private…
We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the…
We study the problem of sampling from a distribution under local differential privacy (LDP). Given a private distribution $P \in \mathcal{P}$, the goal is to generate a single sample from a distribution that remains close to $P$ in…
In this paper, we investigate the differentially private estimation of data depth functions and their associated medians. We introduce several methods for privatizing depth values at a fixed point, and show that for some depth functions,…
In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case…
Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between…
Designing privacy-preserving machine learning algorithms has received great attention in recent years, especially in the setting when the data contains sensitive information. Differential privacy (DP) is a widely used mechanism for data…