Heavy-Tailed Distributions

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Overview

Heavy-tailed distributions produce extreme observations more often than Gaussian models predict, affecting risk estimates, learning, and optimization. Researchers describe their tails with tools such as regular variation and extreme-value theory, or use Student-t, Cauchy, stable, and Phase-Type models; robust estimators often rely on clipping, truncation, or median-of-means methods. Applications include financial risk and extreme-event forecasting, heavy-tailed bandits, stochastic optimization, and generative models evaluated on tail probabilities and extreme quantiles. A central tension is that matching or preserving heavy tails can improve extreme-value predictions, while scarce tail data make estimation unstable and can slow learning or optimization.

Latest papers

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56 papers8 papers in the last four weeks, up 60% on the four weeks before. 0.0% of all new papers.

  1. Privately Clipping Heavy-Tailed Data

    Oct 26, 2026Matthew Joseph, Alex KuleszaDifferential PrivacyHeavy-Tailed Distributions

    Google Research

  2. Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process

    Oct 15, 2026Siddhesh KulkarniBayesian InferenceHeavy-Tailed Distributions

    a Bristol Myers Squibb, 5 Giralda Farms, Madison, NJ 07940, USA

  3. From Global to Tail Convergence: Dynamics of αα-Stable Score-Based Generative Models

    Oct 14, 2026Ianis Hammani, Claire BoyerScore-Based Generative ModelingDiffusion Models

    ENS Paris Saclay, LMO · LMO, IUF

  4. Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models

    Oct 12, 2026Hamza Cherkaoui, Hélène Halconruy, Antonio OcelloDiffusion ModelsPost-Hoc Calibration

    SAMOVAR, Télécom SudParis Institut Polytechnique de Paris Palaiseau, France · SAMOVAR, Télécom SudParis Institut Polytechnique de Paris Modal’X, Université Paris Nanterre Nanterre, France · CREST, ENSAE Paris Institut Polytechnique de Paris Palaiseau, France

  5. Prediction with Expert Advice under Heavy-Tailed Losses

    Oct 10, 2026Yuki Shibukawa, Shinji ItoMinimax RegretHeavy-Tailed Distributions

    The University of Tokyo and RIKEN

  6. Why Heavy-Tailed Weight Spectra Predict Model Quality

    Oct 9, 2026Joseph Wilson, Chris van der Heide, Liam Hodgkinson +3Neural Network GeneralizationHeavy-Tailed Distributions

    School of Mathematics and Physics University of Queensland · Dept. of Electrical and Electronic Engineering University of Melbourne · School of Mathematics and Statistics University of Melbourne +3

  7. Residual Modeling Closes the Regression and Generative Policy Gap in Robot Learning

    Oct 8, 2026Yuchen Zhou, Jiacheng You, Weikang Wan +3Robot Policy LearningRobot Imitation Learning

    University of Pennsylvania · Tsinghua University · UC San Diego

  8. Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data

    Oct 6, 2026Kaito Takanami, Takashi Takahashi, Yoshiyuki KabashimaStatistical Physics of LearningHigh-Dimensional Asymptotics

    Graduate School of Science, The University of Tokyo · Institute for Physics of Intelligence, The University of Tokyo · Trans-Scale Quantum Science Institute, The University of Tokyo

  9. Attention Kernels for Learning Maps Between Heavy-Tailed Measures

    Sep 30, 2026Kailen Hargenrader, Edoardo Calvello, Bohan ChenSoftmax AttentionAttention Mechanisms

    Computing and Mathematical Sciences California Institute of Technology · Lawrence Berkeley National Laboratory University of California, Berkeley ICSI

  10. Robust Bayesian Optimization with Q-Exponential Surrogates

    Sep 26, 2026Richard Cornelius Suwandi, Zhidi Lin, Feng Yin +1Bayesian OptimizationUCB Algorithms

    School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, China · School of Computing and Data Science, The University of Hong Kong, Hong Kong SAR, China · Signal Processing Group, Technische Universität Darmstadt, Germany

  11. Distributed Stochastic Approximation Algorithms and Heavy-Tailed Age of Information

    Sep 23, 2026Adrian Redder, Arunselvan Ramaswamy, Holger KarlStochastic ApproximationAge of Information

    Dept. of Electrical Engineering and Information Technology, Paderborn University, Germany · Dept. of Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, India · Hasso-Plattner Institute (HPI), Digital Engineering Faculty, University of Potsdam, Germany

  12. Dimension-Corrected Hitting Times for Heavy-Tailed Spectral Emergence in Neural Optimizer Dynamics

    Sep 14, 2026Zongmin LiuHeavy-Tailed DistributionsNeural Network Training Dynamics

    Stanford University

  13. A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

    Sep 3, 2026Xin Yu, Shuwei Huang, Jicheng Liu +4Causal Effect EstimationHeavy-Tailed Distributions

    Huazhong University of Science and Technology · Tencent

  14. Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails

    Sep 3, 2026Shi Fu, Huibo Xu, Qixin Zhang +1Sparse RecoveryHeavy-Tailed Noise

    Generative AI Lab, College of Computing and Data Science, Nanyang Technological University, Singapore

  15. Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

    Aug 12, 2026Thejani Gamage, Hyemin Gu, Zhizhen Zhang +3Wasserstein Gradient FlowsGenerative Modeling

    Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA · School of Data and Information Sciences (SDIS) and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC

  16. Parameter-Free Heavy-Tailed Bandits

    Jul 31, 2026Gianmarco Genalti, Alberto Maria MetelliMulti-Armed BanditsHeavy-Tailed Noise

    Politecnico di Milano

  17. HOMER: Huber-of-Means for Efficient and Robust Estimation in Hilbert Spaces

    Jul 29, 2026Kisung You, Boram ChoRobust Mean EstimationHeavy-Tailed Distributions

    Baruch College · Yale University

  18. Heavy-Tailed Flow Matching via Random Clocks

    Jul 15, 2026Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi +2Flow MatchingHeavy-Tailed Noise

    Department of Applied Mathematics and Statistics, Johns Hopkins University. · School of Computing, National University of Singapore. · Department of Computer Science, Johns Hopkins University.

  19. Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization

    Jul 9, 2026Ryusei Yamada, Naoki Sato, Hideaki IidukaHeavy-Tailed NoiseStochastic Optimization Convergence

    Meiji University, Japan

  20. Model Merging as Probabilistic Inference in Fine-Tuning Parameter Space

    Jul 2, 2026Long Minh Bui, Tuan Anh Le Van, Tung Phi Duc +3Product of ExpertsEnergy-Based Models

    Washington State University · Hanoi University of Science and Technology

  21. Heads, Not Backbones: Output Heads Dominate Architectures on Fat-Tailed Returns

    Jun 29, 2026Sichao He, Yansong ZhangMixture Density NetworksQuantitative Finance

    Peking University · Academy for Advanced Interdisciplinary Studies · Beijing, China +2

  22. Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS

    Jun 29, 2026Flor Martinez-Sermeno, Arturo Jaramillo, Johan Van HorebeekMultidimensional ScalingDimensionality Reduction

  23. The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails

    Jun 25, 2026Xavier FonsecaRegret MinimizationPortfolio Optimization

    Academy for AI, Games and Media, Breda University of Applied Sciences, Breda, The Netherlands.

  24. High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence

    Jun 24, 2026Dhruv Sarkar, Aprameyo Chakrabartty, Vaneet AggarwalStochastic OptimizationOptimization Convergence Analysis

    Indian Institute of Technology Kharagpur · Mohamed bin Zayed University of Artificial Intelligence · Purdue University

  25. Open Problem: Is AdamW Effective Under Heavy-Tailed Noise?

    Jun 22, 2026Dingzhi Yu, Hongyi Tao, Yuanyu Wan +2Stochastic OptimizationHeavy-Tailed Noise

    1Nanjing University · 2Zhejiang University · 3Fudan University

  26. Tail-Shape Estimation in LLM Evaluation Is Fragile: A Protocol for Diagnosing False Positives

    Jun 15, 2026Luca ZhouLLM EvaluationLanguage Model Safety Evaluation

    Sapienza University of Rome

  27. Gradient boosting for extremes: sampling theory and application to insurance

    Jun 12, 2026Stéphane Lhaut, Olivier LopezGradient-Boosted Decision TreesHeavy-Tailed Distributions

    1CREST, CNRS, Ecole polytechnique, Groupe ENSAE-ENSAI, ENSAE Paris, Institut Polytechnique de Paris, Palaiseau, France

  28. Quantum enhanced rare event discovery and sampling

    Jun 4, 2026Naixu Guo, Po-Wei Huang, Qisheng Wang +4Heavy-Tailed DistributionsRare-Event Estimation

    Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore · Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom · School of Computer Science, Shanghai Jiao Tong University, Shanghai 200240, China +4

  29. Variance Reduction for Heavy-Tailed Monetization Metrics in Ranking Experiments via Post-Stratification

    Jun 2, 2026Neeti Pokharna, Olivier Jeunen, Yatharth Saraf +1Causal Effect EstimationA/b Testing

    ShareChat · Bengaluru, Karnataka, India · Aampe +3

  30. Bregman meets Lévy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time

    Jun 2, 2026Pierre-Louis Cauvin, Panayotis MertikopoulosStochastic OptimizationStochastic Differential Equations

    Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, 38000 Grenoble, France.