相关论文: Better Locally Private Sparse Estimation Given Mul…

Previous work on user-level differential privacy (DP) [Ghazi et al. NeurIPS 2021, Bun et al. STOC 2023] obtained generic algorithms that work for various learning tasks. However, their focus was on the example-rich regime, where the users…

This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…

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…

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…

In this work, we study local minimax convergence estimation rates subject to $\epsilon$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of…

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…

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization…

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…

The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…

Differentially private federated learning is crucial for maintaining privacy in distributed environments. This paper investigates the challenges of high-dimensional estimation and inference under the constraints of differential privacy.…

We study privacy-preserving sparse linear regression in the high-dimensional regime, focusing on the LASSO estimator. We analyze two widely used mechanisms for differential privacy: output perturbation, which injects noise into the…

We consider the estimation of a density at a fixed point under a local differential privacy constraint, where the observations are anonymised before being available for statistical inference. We propose both a privatised version of a…

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…

In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to…

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…

To the best of our knowledge, there are no methods today for training differentially private regression models on sparse input data. To remedy this, we adapt the Frank-Wolfe algorithm for $L_1$ penalized linear regression to be aware of…

Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have…