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Long-tailed distributions frequently emerge in real-world data, where a large number of minority categories contain a limited number of samples. Such imbalance issue considerably impairs the performance of standard supervised learning…

Machine Learning · Computer Science 2024-03-15 Chaoqun Du , Yulin Wang , Shiji Song , Gao Huang

To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…

Methodology · Statistics 2025-05-27 Promit Chakroborty , Michael D. Shields

Sequential user behavior modeling plays a crucial role in online user-oriented services, such as product purchasing, news feed consumption, and online advertising. The performance of sequential modeling heavily depends on the scale and…

Machine Learning · Computer Science 2020-11-03 Jianwen Yin , Chenghao Liu , Weiqing Wang , Jianling Sun , Steven C. H. Hoi

Deep long-tailed learning, one of the most challenging problems in visual recognition, aims to train well-performing deep models from a large number of images that follow a long-tailed class distribution. In the last decade, deep learning…

Computer Vision and Pattern Recognition · Computer Science 2023-04-18 Yifan Zhang , Bingyi Kang , Bryan Hooi , Shuicheng Yan , Jiashi Feng

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Statistics Theory · Mathematics 2019-10-02 Jun Zhao , Guan'ao Yan , Yi Zhang

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

Methodology · Statistics 2017-11-15 Shrijita Bhattacharya , Michael Kallitsis , Stilian Stoev

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

Probability · Mathematics 2013-10-07 Jaakko Lehtomaa

Long-tailed datasets, where head classes comprise much more training samples than tail classes, cause recognition models to get biased towards the head classes. Weighted loss is one of the most popular ways of mitigating this issue, and a…

Computer Vision and Pattern Recognition · Computer Science 2022-09-08 Saptarshi Sinha , Hiroki Ohashi

Output-length prediction is important for efficient LLM serving, as it directly affects batching, memory reservation, and scheduling. For prompt-only length prediction, most existing methods use a one-shot sampled length as the label,…

Machine Learning · Computer Science 2026-04-10 Jing Wang , Yu-Yang Qian , Ke Xue , Chao Qian , Peng Zhao , Zhi-Hua Zhou

In this paper, we discuss a method to define prior distributions for the threshold of a generalised Pareto distribution, in particular when its applications are directed to heavy-tailed data. We propose to assign prior probabilities to the…

Methodology · Statistics 2016-04-06 Cristiano Villa

We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…

Mathematical Finance · Quantitative Finance 2025-11-21 Akash Deep , Svetlozar T. Rachev , Frank J. Fabozzi

Long-tailed learning has attracted much attention recently, with the goal of improving generalisation for tail classes. Most existing works use supervised learning without considering the prevailing noise in the training dataset. To move…

Machine Learning · Computer Science 2021-08-27 Tong Wei , Jiang-Xin Shi , Wei-Wei Tu , Yu-Feng Li

Long-term forecasting presents unique challenges due to the time and memory complexity of handling long sequences. Existing methods, which rely on sliding windows to process long sequences, struggle to effectively capture long-term…

Machine Learning · Computer Science 2024-03-26 Junwoo Park , Daehoon Gwak , Jaegul Choo , Edward Choi

Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…

Computation · Statistics 2014-08-26 Colin S. Gillespie

The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in…

Methodology · Statistics 2026-02-18 Takuma Yoshida , Koki Momoki , Shuichi Kawano

In the real-world setting, data often follows a long-tailed distribution, where head classes contain significantly more training samples than tail classes. Consequently, models trained on such data tend to be biased toward head classes. The…

Computer Vision and Pattern Recognition · Computer Science 2024-03-15 Fan Zhang , Wei Qin , Weijieying Ren , Lei Wang , Zetong Chen , Richang Hong

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…

Machine Learning · Computer Science 2016-04-19 Daniel Hsu , Sivan Sabato

It is not uncommon that real-world data are distributed with a long tail. For such data, the learning of deep neural networks becomes challenging because it is hard to classify tail classes correctly. In the literature, several existing…

Computer Vision and Pattern Recognition · Computer Science 2024-07-19 Mengke Li , Yiu-ming Cheung , Yang Lu , Zhikai Hu , Weichao Lan , Hui Huang

In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance. This study leverages ideas from…

Methodology · Statistics 2025-11-05 Soham Ghosh , Uttaran Chatterjee , Jyotishka Datta

Long-tail distribution is widely spread in real-world applications. Due to the extremely small ratio of instances, tail categories often show inferior accuracy. In this paper, we find such performance bottleneck is mainly caused by the…

Computer Vision and Pattern Recognition · Computer Science 2022-10-12 Jingru Tan , Bo Li , Xin Lu , Yongqiang Yao , Fengwei Yu , Tong He , Wanli Ouyang
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