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Related papers: Private High-Dimensional Hypothesis Testing

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We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

Machine Learning · Statistics 2020-10-21 Ishaq Aden-Ali , Hassan Ashtiani , Gautam Kamath

We study distributed goodness-of-fit testing for discrete distribution under bandwidth and differential privacy constraints. Information constraint distributed goodness-of-fit testing is a problem that has received considerable attention…

Statistics Theory · Mathematics 2024-11-05 Lasse Vuursteen

We study the problem of testing the covariance matrix of a high-dimensional Gaussian in a robust setting, where the input distribution has been corrupted in Huber's contamination model. Specifically, we are given i.i.d. samples from a…

Machine Learning · Computer Science 2021-01-01 Ilias Diakonikolas , Daniel M. Kane

We consider the problem of learning mixtures of Gaussians under the constraint of approximate differential privacy. We prove that $\widetilde{O}(k^2 d \log^{3/2}(1/\delta) / \alpha^2 \varepsilon)$ samples are sufficient to learn a mixture…

Machine Learning · Computer Science 2021-06-07 Ishaq Aden-Ali , Hassan Ashtiani , Christopher Liaw

We give the first polynomial-time algorithm to estimate the mean of a $d$-variate probability distribution with bounded covariance from $\tilde{O}(d)$ independent samples subject to pure differential privacy. Prior algorithms for this…

Data Structures and Algorithms · Computer Science 2022-06-06 Samuel B. Hopkins , Gautam Kamath , Mahbod Majid

In this work, we present a connection between Lipschitz property testing and a relaxed notion of differential privacy, where we assume that the datasets are being sampled from a domain according to some distribution defined on it.…

Cryptography and Security · Computer Science 2012-09-19 Kashyap Dixit , Madhav Jha , Abhradeep Thakurta

Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…

Machine Learning · Computer Science 2021-10-11 Gilles Blanchard , Jean-Baptiste Fermanian

In this work, we study trade-offs between accuracy and privacy in the context of linear queries over histograms. This is a rich class of queries that includes contingency tables and range queries, and has been a focus of a long line of…

Data Structures and Algorithms · Computer Science 2013-08-05 Aleksandar Nikolov , Kunal Talwar , Li Zhang

We initiate the study of differentially private learning in the proportional dimensionality regime, in which the number of data samples $n$ and problem dimension $d$ approach infinity at rates proportional to one another, meaning that…

Machine Learning · Computer Science 2025-02-20 Cynthia Dwork , Pranay Tankala , Linjun Zhang

What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…

Data Structures and Algorithms · Computer Science 2022-05-13 Omar Fawzi , Nicolas Flammarion , Aurélien Garivier , Aadil Oufkir

We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform…

Data Structures and Algorithms · Computer Science 2021-01-21 Jayadev Acharya , Clément L. Canonne , Cody Freitag , Ziteng Sun , Himanshu Tyagi

We initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close…

Machine Learning · Computer Science 2022-11-16 Sofya Raskhodnikova , Satchit Sivakumar , Adam Smith , Marika Swanberg

We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…

Data Structures and Algorithms · Computer Science 2019-01-17 Ilias Diakonikolas , Themis Gouleakis , John Peebles , Eric Price

Given $n$ i.i.d. random matrices $A_i \in \mathbb{R}^{d \times d}$ that share a common expectation $\Sigma$, the objective of Differentially Private Stochastic PCA is to identify a subspace of dimension $k$ that captures the largest…

Machine Learning · Statistics 2025-08-15 Johanna Düngler , Amartya Sanyal

We introduce $\pi$-test, a privacy-preserving algorithm for testing statistical independence between data distributed across multiple parties. Our algorithm relies on privately estimating the distance correlation between datasets, a…

Statistics Theory · Mathematics 2023-09-28 Praneeth Vepakomma , Mohammad Mohammadi Amiri , Clément L. Canonne , Ramesh Raskar , Alex Pentland

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…

Data Structures and Algorithms · Computer Science 2016-01-22 Clément L. Canonne , Ilias Diakonikolas , Themis Gouleakis , Ronitt Rubinfeld

Much of the literature on differential privacy focuses on item-level privacy, where loosely speaking, the goal is to provide privacy per item or training example. However, recently many practical applications such as federated learning…

Machine Learning · Computer Science 2021-01-13 Yuhan Liu , Ananda Theertha Suresh , Felix Yu , Sanjiv Kumar , Michael Riley

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…

Data Structures and Algorithms · Computer Science 2020-06-25 Jerry Li , Guanghao Ye

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…

Machine Learning · Computer Science 2020-02-18 Ilmun Kim , Aaditya Ramdas , Aarti Singh , Larry Wasserman

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…

Machine Learning · Statistics 2025-08-08 Ziliang Shen , Caixing Wang , Shaoli Wang , Yibo Yan