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We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in…

Data Structures and Algorithms · Computer Science 2019-05-31 Gautam Kamath , Jerry Li , Vikrant Singhal , Jonathan Ullman

Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…

Probability · Mathematics 2012-06-14 Richard Y. Chen , Alex Gittens , Joel A. Tropp

We revisit the problem of releasing the sample mean of bounded samples in a dataset, privately, under user-level $\varepsilon$-differential privacy (DP). We aim to derive the optimal method of preprocessing data samples, within a canonical…

Information Theory · Computer Science 2026-01-12 V. Arvind Rameshwar , Anshoo Tandon

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…

Machine Learning · Computer Science 2023-10-12 Liyang Zhu , Meng Ding , Vaneet Aggarwal , Jinhui Xu , Di Wang

The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding to queries. However, it can only provide…

Cryptography and Security · Computer Science 2021-10-14 Parastoo Sadeghi , Mehdi Korki

Recent years, local differential privacy (LDP) has been adopted by many web service providers like Google \cite{erlingsson2014rappor}, Apple \cite{apple2017privacy} and Microsoft \cite{bolin2017telemetry} to collect and analyse users' data…

Information Theory · Computer Science 2022-03-15 Zhongzheng Xiong , Jialin Sun , Xiaojun Mao , Jian Wang , Shan Ying , Zengfeng Huang

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

Statistics Theory · Mathematics 2023-01-09 Arun Kumar Kuchibhotla , Abhishek Chakrabortty

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…

Data Structures and Algorithms · Computer Science 2023-11-17 Hongjie Chen , Vincent Cohen-Addad , Tommaso d'Orsi , Alessandro Epasto , Jacob Imola , David Steurer , Stefan Tiegel

We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact…

Information Theory · Computer Science 2026-03-24 Alex Shvets

In recent years, Gaussian noise has become a popular tool in differentially private algorithms, often replacing Laplace noise which dominated the early literature. Gaussian noise is the standard approach to $\textit{approximate}$…

Cryptography and Security · Computer Science 2024-11-19 Joel Daniel Andersson , Rasmus Pagh , Teresa Anna Steiner , Sahel Torkamani

Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood. We analyze DP-SGD in the…

Machine Learning · Computer Science 2026-04-17 Murat Bilgehan Ertan , Marten van Dijk

We characterize the minimum noise amplitude and power for noise-adding mechanisms in $(\epsilon, \delta)$-differential privacy for single real-valued query function. We derive new lower bounds using the duality of linear programming, and…

Cryptography and Security · Computer Science 2019-02-06 Quan Geng , Wei Ding , Ruiqi Guo , Sanjiv Kumar

The Horvitz-Thompson estimate of a total can be seen as as differentially private mechanism applied to this population total. We provide forumlae to compute the $\epsilon$ and $\delta$ parameter for this specific mecanism, coupled or not…

Statistics Theory · Mathematics 2025-06-18 Daniel Bernard Bonnéry , Julien Jamme

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…

Machine Learning · Computer Science 2014-10-21 Raef Bassily , Adam Smith , Abhradeep Thakurta

We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific…

Machine Learning · Computer Science 2025-11-11 Manolis Zampetakis , Felix Zhou

In recent years, differential privacy has been adopted by tech-companies and governmental agencies as the standard for measuring privacy in algorithms. In this article, we study differential privacy in Bayesian posterior sampling settings.…

Statistics Theory · Mathematics 2026-02-13 Shenggang Hu , Louis Aslett , Hongsheng Dai , Murray Pollock , Gareth O. Roberts

Deep heteroscedastic regression models the mean and covariance of the target distribution through neural networks. The challenge arises from heteroscedasticity, which implies that the covariance is sample dependent and is often unknown.…

Machine Learning · Computer Science 2025-02-18 Megh Shukla , Aziz Shameem , Mathieu Salzmann , Alexandre Alahi

The last few years have seen a surge of work on high dimensional statistics under privacy constraints, mostly following two main lines of work: the ``worst case'' line, which does not make any distributional assumptions on the input data;…

Statistics Theory · Mathematics 2022-08-17 Omri Ben-Eliezer , Dan Mikulincer , Ilias Zadik

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

Statistics Theory · Mathematics 2023-01-18 Martin Genzel , Christian Kipp

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

Statistics Theory · Mathematics 2023-03-02 Shuo Tang , Gerald LaMountain , Tales Imbiriba , Pau Closas