相关论文: Differentially Private Sparse Linear Regression wi…

As one of the most fundamental problems in machine learning, statistics and differential privacy, Differentially Private Stochastic Convex Optimization (DP-SCO) has been extensively studied in recent years. However, most of the previous…

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…

While the traditional goal of statistics is to infer population parameters, modern practice increasingly demands protection of individual privacy. One way to address this need is to adapt classical statistical procedures into…

We study convex optimization problems under differential privacy (DP). With heavy-tailed gradients, existing works achieve suboptimal rates. The main obstacle is that existing gradient estimators have suboptimal tail properties, resulting…

We study the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data. Specifically, we focus on the $\ell_1$-norm linear regression in the $\epsilon$-DP model. While most of the previous work focuses…

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case…

In this paper, we consider the problem of designing Differentially Private (DP) algorithms for Stochastic Convex Optimization (SCO) on heavy-tailed data. The irregularity of such data violates some key assumptions used in almost all…

Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing…

This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which…

In the social sciences, small- to medium-scale datasets are common, and linear regression is canonical. In privacy-aware settings, much work has focused on differentially private (DP) linear regression, but mostly on point estimation with…

In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) $\mathcal{X}$ and for any Lipschitz loss…

The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard $L_0$ constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard…

With the development of big data and machine learning, privacy concerns have become increasingly critical, especially when handling heterogeneous datasets containing sensitive personal information. Differential privacy provides a rigorous…

Recent research shows that modern deep learning models achieve high predictive accuracy partly by memorizing individual training samples. Such memorization raises serious privacy concerns, motivating the widespread adoption of…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

High dimensional sparse linear bandits serve as an efficient model for sequential decision-making problems (e.g. personalized medicine), where high dimensional features (e.g. genomic data) on the users are available, but only a small subset…

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…