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We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$…

Machine Learning · Computer Science 2025-11-26 Gavin Brown , Samuel B. Hopkins , Adam Smith

We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/\alpha^2$ samples from such a distribution with mean $\mu$ and…

Machine Learning · Computer Science 2024-03-27 Gavin Brown , Marco Gaboardi , Adam Smith , Jonathan Ullman , Lydia Zakynthinou

We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss.…

Machine Learning · Computer Science 2020-07-23 Aditya Dhar , Jason Huang

We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…

Data Structures and Algorithms · Computer Science 2022-07-26 Shyam Narayanan

We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator…

Machine Learning · Statistics 2023-01-18 John Duchi , Saminul Haque , Rohith Kuditipudi

We study person-level differentially private (DP) mean estimation in the case where each person holds multiple samples. DP here requires the usual notion of distributional stability when $\textit{all}$ of a person's datapoints can be…

Data Structures and Algorithms · Computer Science 2024-07-22 Sushant Agarwal , Gautam Kamath , Mahbod Majid , Argyris Mouzakis , Rose Silver , Jonathan Ullman

In this work, we study high-dimensional mean estimation under user-level differential privacy, and design an $(\varepsilon,\delta)$-differentially private mechanism using as few users as possible. In particular, we provide a nearly optimal…

Data Structures and Algorithms · Computer Science 2022-06-14 Hossein Esfandiari , Vahab Mirrokni , Shyam Narayanan

In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…

Data Structures and Algorithms · Computer Science 2023-06-02 Daniel Alabi , Pravesh K. Kothari , Pranay Tankala , Prayaag Venkat , Fred Zhang

We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…

Statistics Theory · Mathematics 2024-01-05 Shyam Narayanan

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^d$. All previous estimators are either…

Machine Learning · Statistics 2022-02-15 Gautam Kamath , Argyris Mouzakis , Vikrant Singhal , Thomas Steinke , Jonathan Ullman

We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically…

Machine Learning · Statistics 2026-02-10 Sourav Biswas , Yihe Dong , Gautam Kamath , Jonathan Ullman

We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…

Machine Learning · Statistics 2021-12-08 Pravesh K. Kothari , Pasin Manurangsi , Ameya Velingker

We initiate the study of differentially private (DP) estimation with access to a small amount of public data. For private estimation of d-dimensional Gaussians, we assume that the public data comes from a Gaussian that may have vanishing…

Machine Learning · Computer Science 2023-04-07 Alex Bie , Gautam Kamath , Vikrant Singhal

We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising…

Data Structures and Algorithms · Computer Science 2023-05-24 Maryam Aliakbarpour , Rose Silver , Thomas Steinke , Jonathan Ullman

We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…

Cryptography and Security · Computer Science 2023-04-04 Wei Dong , Ke Yi

This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance…

Data Structures and Algorithms · Computer Science 2019-04-12 Marco Gaboardi , Ryan Rogers , Or Sheffet

We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…

Data Structures and Algorithms · Computer Science 2025-01-10 Ilias Diakonikolas , Daniel M. Kane , Sihan Liu , Thanasis Pittas

We develop differentially private hypothesis testing methods for the small sample regime. Given a sample $\cal D$ from a categorical distribution $p$ over some domain $\Sigma$, an explicitly described distribution $q$ over $\Sigma$, some…

Data Structures and Algorithms · Computer Science 2017-06-08 Bryan Cai , Constantinos Daskalakis , Gautam Kamath

Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly…

Cryptography and Security · Computer Science 2021-07-06 Joerg Drechsler , Ira Globus-Harris , Audra McMillan , Jayshree Sarathy , Adam Smith

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

Statistics Theory · Mathematics 2022-10-13 Yihan Zhang , Nir Weinberger
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