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This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…

Methodology · Statistics 2020-09-21 Xi Chen , Weidong Liu , Xiaojun Mao , Zhuoyi Yang

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose $(1+\epsilon)$-th moment is bounded for some $\epsilon\in (0,1]$. Although there exist methods for generalized linear bandits, most of them…

Machine Learning · Computer Science 2023-10-31 Bo Xue , Yimu Wang , Yuanyu Wan , Jinfeng Yi , Lijun Zhang

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…

Machine Learning · Computer Science 2025-10-14 Yunlong Feng , Qiang Wu

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

Statistics Theory · Mathematics 2018-10-11 Qiang Sun , Wenxin Zhou , Jianqing Fan

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

Methodology · Statistics 2022-11-18 Surya T Tokdar , Sheng Jiang , Erika L Cunningham

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…

Statistics Theory · Mathematics 2020-02-19 Zhixian Lei , Kyle Luh , Prayaag Venkat , Fred Zhang

Average calibration of the (variance-based) prediction uncertainties of machine learning regression tasks can be tested in two ways: one is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and…

Machine Learning · Statistics 2024-08-20 Pascal Pernot

We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…

Machine Learning · Computer Science 2023-10-26 Daniel M. Kane , Ilias Diakonikolas , Hanshen Xiao , Sihan Liu

Despite a large amount of effort in dealing with heavy-tailed error in machine learning, little is known when moments of the error can become non-existential: the random noise $\eta$ satisfies Pr$\left[|\eta| > |y|\right] \le…

Machine Learning · Computer Science 2021-10-27 Han Zhong , Jiayi Huang , Lin F. Yang , Liwei Wang

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

Machine Learning · Statistics 2025-02-18 Cullen Anderson , Jeff M. Phillips

This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…

Statistics Theory · Mathematics 2023-07-27 Junren Chen , Michael K. Ng , Di Wang

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…

Machine Learning · Computer Science 2021-06-14 Zifan Liu , Jongho Park , Theodoros Rekatsinas , Christos Tzamos

A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions. In this paper we consider a linear mean regression model…

Statistics Theory · Mathematics 2025-02-06 Philipp Hermann , Hajo Holzmann

We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…

Data Structures and Algorithms · Computer Science 2021-05-04 Lunjia Hu , Omer Reingold

We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+\epsilon)$-th moments for some $\epsilon \in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise…

Machine Learning · Computer Science 2026-03-17 Naoto Tani , Futoshi Futami

We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$…

Data Structures and Algorithms · Computer Science 2019-06-28 Yihe Dong , Samuel B. Hopkins , Jerry Li

In this paper, we study multi-armed bandits (MAB) and stochastic linear bandits (SLB) with heavy-tailed rewards and quantum reward oracle. Unlike the previous work on quantum bandits that assumes bounded/sub-Gaussian distributions for…

Machine Learning · Computer Science 2023-01-25 Yulian Wu , Chaowen Guan , Vaneet Aggarwal , Di Wang

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Machine Learning · Computer Science 2018-03-14 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…

Quantum Physics · Physics 2021-11-16 Yassine Hamoudi

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