English
Related papers

Related papers: Sample-Optimal Private Regression in Polynomial Ti…

200 papers

We study the problem of privately estimating the parameters of $d$-dimensional Gaussian Mixture Models (GMMs) with $k$ components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to…

Machine Learning · Statistics 2023-06-09 Jamil Arbas , Hassan Ashtiani , Christopher Liaw

In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual…

Machine Learning · Computer Science 2021-11-25 Xiyang Liu , Weihao Kong , Sham Kakade , Sewoong Oh

Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical…

Machine Learning · Statistics 2025-04-08 Xintao Xia , Linjun Zhang , Zhanrui Cai

The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important…

Machine Learning · Computer Science 2018-06-08 Borja Balle , Yu-Xiang Wang

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

Machine Learning · Computer Science 2018-06-04 Ilias Diakonikolas , Weihao Kong , Alistair Stewart

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

Data Structures and Algorithms · Computer Science 2023-12-05 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy…

Machine Learning · Computer Science 2019-08-29 Ilya Mironov , Kunal Talwar , Li Zhang

Differentially private distributed stochastic optimization has become a hot topic due to the urgent need of privacy protection in distributed stochastic optimization. In this paper, two-time scale stochastic approximation-type algorithms…

Systems and Control · Electrical Eng. & Systems 2024-03-19 Jimin Wang , Ji-Feng Zhang

We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erd\H{o}s-R\'enyi random graphs and their generalization, inhomogeneous random graphs. We further prove…

Data Structures and Algorithms · Computer Science 2024-06-05 Hongjie Chen , Jingqiu Ding , Yiding Hua , David Steurer

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

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

Machine Learning · Computer Science 2017-05-18 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…

Machine Learning · Statistics 2020-07-14 Jules Depersin

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 provide the first $\widetilde{\mathcal{O}}\left(d\right)$-sample algorithm for sampling from unbounded Gaussian distributions under the constraint of $\left(\varepsilon, \delta\right)$-differential privacy. This is a quadratic…

Data Structures and Algorithms · Computer Science 2025-03-04 Valentio Iverson , Gautam Kamath , Argyris Mouzakis

We study the optimal sample complexity of a given workload of linear queries under the constraints of differential privacy. The sample complexity of a query answering mechanism under error parameter $\alpha$ is the smallest $n$ such that…

Data Structures and Algorithms · Computer Science 2016-12-12 Assimakis Kattis , Aleksandar Nikolov

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Data Structures and Algorithms · Computer Science 2017-11-07 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

Machine Learning · Computer Science 2024-11-01 Chih-Hung Liu , Gleb Novikov

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 investigate unbiased high-dimensional mean estimators in differential privacy. We consider differentially private mechanisms whose expected output equals the mean of the input dataset, for every dataset drawn from a fixed bounded…

Statistics Theory · Mathematics 2023-12-22 Aleksandar Nikolov , Haohua Tang

We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our…

Data Structures and Algorithms · Computer Science 2020-06-15 Arun Jambulapati , Jerry Li , Kevin Tian