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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

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

Machine Learning · Statistics 2022-10-11 Takeyuki Sasai

We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…

Statistics Theory · Mathematics 2021-05-13 Martin Bladt , Hansjoerg Albrecher , Jan Beirlant

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

Machine Learning · Computer Science 2022-02-28 Che-Ping Tsai , Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

Machine Learning · Computer Science 2018-10-26 Lijun Zhang , Zhi-Hua Zhou

Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…

Computer Vision and Pattern Recognition · Computer Science 2022-02-14 Xiaohua Chen , Yucan Zhou , Dayan Wu , Wanqian Zhang , Yu Zhou , Bo Li , Weiping Wang

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

Methodology · Statistics 2025-09-16 Xiaoyu Zhang , Di Wang , Guodong Li , Defeng Sun

In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…

Signal Processing · Electrical Eng. & Systems 2024-11-19 Yifan Yu , Shengjie Xiu , Daniel P. Palomar

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Statistics Theory · Mathematics 2024-04-03 Jinyuan Chang , Qiao Hu , Cheng Liu , Cheng Yong Tang

We tackle the problem of producing compact models, maximizing their accuracy for a given model size. A standard solution is to train networks with Quantization Aware Training, where the weights are quantized during training and the…

Machine Learning · Computer Science 2021-03-02 Angela Fan , Pierre Stock , Benjamin Graham , Edouard Grave , Remi Gribonval , Herve Jegou , Armand Joulin

The composite quantile regression (CQR) was introduced by Zou and Yuan [Ann. Statist. 36 (2008) 1108--1126] as a robust regression method for linear models with heavy-tailed errors while achieving high efficiency. Its penalized counterpart…

Methodology · Statistics 2023-10-16 Haeseong Moon , Wen-Xin Zhou

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Statistics Theory · Mathematics 2023-05-11 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…

Statistics Theory · Mathematics 2017-05-08 Jianqing Fan , Weichen Wang , Ziwei Zhu

Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…

Statistics Theory · Mathematics 2019-08-20 Jun Zhao , Guan'ao Yan , Yi Zhang

We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…

Information Theory · Computer Science 2017-02-16 Joe-Mei Feng , Felix Krahmer , Rayan Saab

Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…

Machine Learning · Computer Science 2021-05-25 John Y. Shin

Quantization is one of the core components in lossy image compression. For neural image compression, end-to-end optimization requires differentiable approximations of quantization, which can generally be grouped into three categories:…

Image and Video Processing · Electrical Eng. & Systems 2024-03-26 Zongyu Guo , Zhizheng Zhang , Runsen Feng , Zhibo Chen

We revisit the classic regret-minimization problem in the stochastic multi-armed bandit setting when the arm-distributions are allowed to be heavy-tailed. Regret minimization has been well studied in simpler settings of either bounded…

Machine Learning · Computer Science 2021-02-09 Shubhada Agrawal , Sandeep Juneja , Wouter M. Koolen

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

Machine Learning · Statistics 2019-01-16 Martin Azizyan , Akshay Krishnamurthy , Aarti Singh