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In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…

Statistics Theory · Mathematics 2012-11-02 Joan del castillo , Jalila Daoudi , Isabel Serra

Long-tailed problems in healthcare emerge from data imbalance due to variability in the prevalence and representation of different medical conditions, warranting the requirement of precise and dependable classification methods. Traditional…

Computer Vision and Pattern Recognition · Computer Science 2024-10-08 Pankhi Kashyap , Pavni Tandon , Sunny Gupta , Abhishek Tiwari , Ritwik Kulkarni , Kshitij Sharad Jadhav

The real-world data distribution is essentially long-tailed, which poses great challenge to the deep model. In this work, we propose a new method, Gradual Balanced Loss and Adaptive Feature Generator (GLAG) to alleviate imbalance. GLAG…

Computer Vision and Pattern Recognition · Computer Science 2022-03-02 Zihan Zhang , Xiang Xiang

For regularized estimation, the upper tail behavior of the random Lipschitz coefficient associated with empirical loss functions is known to play an important role in the error bound of Lasso for high dimensional generalized linear models.…

Statistics Theory · Mathematics 2010-09-07 Zhiyi Chi

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…

Methodology · Statistics 2024-11-26 Shamriddha De , Joyee Ghosh

We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…

Systems and Control · Electrical Eng. & Systems 2025-05-29 Vinay Kanakeri , Aritra Mitra

Long-tailed class distributions are prevalent among the practical applications of object detection and instance segmentation. Prior work in long-tail instance segmentation addresses the imbalance of losses between rare and frequent…

Computer Vision and Pattern Recognition · Computer Science 2021-04-20 Ting-I Hsieh , Esther Robb , Hwann-Tzong Chen , Jia-Bin Huang

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Optimization and Control · Mathematics 2025-05-12 Chao Sun , Huiming Zhang , Bo Chen , Li Yu

Real-world data is laden with outlying values. The challenge for machine learning is that the learner typically has no prior knowledge of whether the feedback it receives (losses, gradients, etc.) will be heavy-tailed or not. In this work,…

Machine Learning · Statistics 2020-12-16 Matthew J. Holland

As a safety critical task, autonomous driving requires accurate predictions of road users' future trajectories for safe motion planning, particularly under challenging conditions. Yet, many recent deep learning methods suffer from a…

Computer Vision and Pattern Recognition · Computer Science 2024-05-01 Junrui Zhang , Mozhgan Pourkeshavarz , Amir Rasouli

The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…

Methodology · Statistics 2019-05-09 Abhik Ghosh

Stochastic local search (SLS) is a successful paradigm for solving the satisfiability problem of propositional logic. A recent development in this area involves solving not the original instance, but a modified, yet logically equivalent…

Data Structures and Algorithms · Computer Science 2021-07-02 Florian Wörz , Jan-Hendrik Lorenz

Long-tail motion forecasting is a core challenge for autonomous driving, where rare yet safety-critical events-such as abrupt maneuvers and dense multi-agent interactions-dominate real-world risk. Existing approaches struggle in these…

Computational Engineering, Finance, and Science · Computer Science 2025-11-11 Bin Rao , Chengyue Wang , Haicheng Liao , Qianfang Wang , Yanchen Guan , Jiaxun Zhang , Xingcheng Liu , Meixin Zhu , Kanye Ye Wang , Zhenning Li

Recently, long-tailed image classification harvests lots of research attention, since the data distribution is long-tailed in many real-world situations. Piles of algorithms are devised to address the data imbalance problem by biasing the…

Computer Vision and Pattern Recognition · Computer Science 2023-02-06 Chaowei Fang , Dingwen Zhang , Wen Zheng , Xue Li , Le Yang , Lechao Cheng , Junwei Han

Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are…

Machine Learning · Computer Science 2025-06-02 Christopher Subich , Syed Zahid Husain , Leo Separovic , Jing Yang

Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. This paper proposes a semi-parametric approach to estimate the probability that a…

Methodology · Statistics 2024-12-31 Anna Kiriliouk , Chen Zhou

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…

Methodology · Statistics 2024-05-01 Arnab Hazra , Raphaël Huser , David Bolin

In this paper, we propose the Generalized Parametric Contrastive Learning (GPaCo/PaCo) which works well on both imbalanced and balanced data. Based on theoretical analysis, we observe that supervised contrastive loss tends to bias…

Computer Vision and Pattern Recognition · Computer Science 2023-05-30 Jiequan Cui , Zhisheng Zhong , Zhuotao Tian , Shu Liu , Bei Yu , Jiaya Jia

Differentially Private Stochastic Gradient Descent (DPSGD) is widely utilized to preserve training data privacy in deep learning, which first clips the gradients to a predefined norm and then injects calibrated noise into the training…

Machine Learning · Computer Science 2024-05-29 Haichao Sha , Yang Cao , Yong Liu , Yuncheng Wu , Ruixuan Liu , Hong Chen

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…

Machine Learning · Computer Science 2026-05-14 Hamza Cherkaoui , Hélène Halconruy , Antonio Ocello