Related papers: Insufficient Statistics Perturbation: Stable Estim…
In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation…
We initiate a systematic study of algorithms that are both differentially private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private…
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 study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…
This paper establishes the strict optimality in precision for frequency and distribution estimation under local differential privacy (LDP). We prove that a linear estimator with a symmetric and extremal configuration, and a constant support…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
This work studies the distributed empirical risk minimization (ERM) problem under differential privacy (DP) constraint. Standard distributed algorithms achieve DP typically by perturbing all local subgradients with noise, leading to…
We study the problem of differentially private clustering under input-stability assumptions. Despite the ever-growing volume of works on differential privacy in general and differentially private clustering in particular, only three works…
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…
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…
In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to…
Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
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 study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…