Related papers: Universal Private Estimators
Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper…
Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP…
Standard techniques for differentially private estimation, such as Laplace or Gaussian noise addition, require guaranteed bounds on the sensitivity of the estimator in question. But such sensitivity bounds are often large or simply unknown.…
This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution…
We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can…
We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which…
This work proposes an algorithmic method to verify differential privacy for estimation mechanisms with performance guarantees. Differential privacy makes it hard to distinguish outputs of a mechanism produced by adjacent inputs. While…
In this paper we study the problem of estimating the unknown mean $\theta$ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime ($\epsilon\le 1$), we identify an optimal privacy…
Differential privacy has become a widely accepted notion of privacy, leading to the introduction and deployment of numerous privatization mechanisms. However, ensuring the privacy guarantee is an error-prone process, both in designing…
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…
Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of…
Objective functions based on Hellinger distance yield robust and efficient estimators of model parameters. Motivated by privacy and regulatory requirements encountered in contemporary applications, we derive in this paper \emph{private…
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 =…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…
This paper extends the idea of a generalized estimator for a scalar parameter (Vos, 2022) to multi-dimensional parameters both with and without nuisance parameters. The title reflects the fact that generalized estimators provide more than…
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is…
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…