Related papers: CoinPress: Practical Private Mean and Covariance E…
Statistical tools which satisfy rigorous privacy guarantees are necessary for modern data analysis. It is well-known that robustness against contamination is linked to differential privacy. Despite this fact, using multivariate medians for…
We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is…
Kaplan-Meier estimators are essential tools in survival analysis, capturing the survival behavior of a cohort. Their accuracy improves with large, diverse datasets, encouraging data holders to collaborate for more precise estimations.…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…
We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…
Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…
We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a…
We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss.…
A key tool for building differentially private systems is adding Gaussian noise to the output of a function evaluated on a sensitive dataset. Unfortunately, using a continuous distribution presents several practical challenges. First and…
We study mean estimation for Gaussian distributions under \textit{personalized differential privacy} (PDP), where each record has its own privacy budget. PDP is commonly considered in two variants: \textit{bounded} and \textit{unbounded}…
Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…