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Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

Machine Learning · Statistics 2017-02-27 Simon S. Du , Sivaraman Balakrishnan , Aarti Singh

We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally…

Cryptography and Security · Computer Science 2022-09-21 Tong Yao , Shreyas Sundaram

We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting,…

Machine Learning · Statistics 2026-01-13 Pedro Abdalla , Junren Chen

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

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…

Statistical Finance · Quantitative Finance 2024-05-29 Arnab Chakrabarti , Rituparna Sen

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Statistics Theory · Mathematics 2025-05-07 Alejandro Cholaquidis , Ricardo Fraiman , Leonardo Moreno , Gonzalo Perera

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient…

Data Structures and Algorithms · Computer Science 2021-01-20 Samuel B. Hopkins , Jerry Li , Fred Zhang

We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…

Data Structures and Algorithms · Computer Science 2023-05-04 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…

Statistics Theory · Mathematics 2023-05-05 Pierre Alquier , Mathieu Gerber

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

Machine Learning · Statistics 2020-02-10 Muhammad Osama , Dave Zachariah , Peter Stoica

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

Machine Learning · Computer Science 2019-06-12 Yu Cheng , Ilias Diakonikolas , Rong Ge , David Woodruff

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Machine Learning · Computer Science 2025-03-13 Kadir Özçoban , Murat Manguoğlu , Emrullah Fatih Yetkin

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Data Structures and Algorithms · Computer Science 2019-03-18 Ilias Diakonikolas , Gautam Kamath , Daniel Kane , Jerry Li , Ankur Moitra , Alistair Stewart

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

Methodology · Statistics 2026-02-11 Liujun Chen , Chen Zhou

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

Machine Learning · Computer Science 2020-05-05 Yu Cheng , Ilias Diakonikolas , Rong Ge , Mahdi Soltanolkotabi

Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…

Computation · Statistics 2019-08-16 Mark Huber

In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…

Machine Learning · Statistics 2020-10-20 Di Wang , Xiangyu Guo , Shi Li , Jinhui Xu

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…

Data Analysis, Statistics and Probability · Physics 2025-10-02 Eslam Abdelaleem , K. Michael Martini , Ilya Nemenman

We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…

Statistics Theory · Mathematics 2021-03-17 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia