相关论文: Geometrizing rates of convergence under local diff…

We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning…

We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…

We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the…

We revisit the classical problem of nonparametric density estimation but impose local differential privacy constraints. Under such constraints, the original multivariate data $X_1,\ldots,X_n \in \mathbb{R}^d$ cannot be directly observed,…

We consider a setup in which confidential i.i.d. samples $X_1,\dotsc,X_n$ from an unknown finite-support distribution $\boldsymbol{p}$ are passed through $n$ copies of a discrete privatization channel (a.k.a. mechanism) producing outputs…

We consider the estimation of the cumulative hazard function, and equivalently the distribution function, with censored data under a setup that preserves the privacy of the survival database. This is done through a $\alpha$-locally…

We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in…

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 =…

We systematically investigate the preservation of differential privacy in functional data analysis, beginning with functional mean estimation and extending to varying coefficient model estimation. Our work introduces a distributed learning…

Convex programming with linear constraints plays an important role in the operation of a number of everyday systems. However, absent any additional protections, revealing or acting on the solutions to such problems may reveal information…

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 study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential…

We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for…

We study the problem of online conditional distribution estimation with \emph{unbounded} label sets under local differential privacy. Let $\mathcal{F}$ be a distribution-valued function class with unbounded label set. We aim at estimating…

We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…

We investigate the problem of estimating a random variable $Y\in \mathcal{Y}$ under a privacy constraint dictated by another random variable $X\in \mathcal{X}$, where estimation efficiency and privacy are assessed in terms of two different…

The challenge of producing accurate statistics while respecting the privacy of the individuals in a sample is an important area of research. We study minimax lower bounds for classes of differentially private estimators. In particular, we…

We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp minimax rates of convergence for…

We consider the problem of privately estimating a parameter $\mathbb{E}[h(X_1,\dots,X_k)]$, where $X_1$, $X_2$, $\dots$, $X_k$ are i.i.d. data from some distribution and $h$ is a permutation-invariant function. Without privacy constraints,…

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…