Related papers: Optimal disclosure risk assessment
We present a simple perturbation mechanism for the release of $d$-dimensional covariance matrices $\Sigma$ under pure differential privacy. For large datasets with at least $n\geq d^2/\varepsilon$ elements, our mechanism recovers the…
We study the performance of a family of randomized parallel coordinate descent methods for minimizing the sum of a nonsmooth and separable convex functions. The problem class includes as a special case L1-regularized L1 regression and the…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
Bessel's correction adjusts the denominator in the sample variance formula from n to n-1 to ensure an unbiased estimator of the population variance. This paper provides rigorous algebraic derivations geometric interpretations and…
A central issue of many statistical learning problems is to select an appropriate model from a set of candidate models. Large models tend to inflate the variance (or overfitting), while small models tend to cause biases (or underfitting)…
We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…
System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…
This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…
We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…
We study a data analyst's problem of acquiring data from self-interested individuals to obtain an accurate estimation of some statistic of a population, subject to an expected budget constraint. Each data holder incurs a cost, which is…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…
In this article, we consider the estimation of unknown parameters of Weibull distribution when the lifetime data are observed in the presence of progressively type-I hybrid censoring scheme. The Newton-Raphson algorithm,…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…