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arxiv: 2605.16361 · v1 · pith:NNEMQ4YBnew · submitted 2026-05-09 · 💻 cs.LG · cs.AI· stat.ML

TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification

Xinyu Chen , HanQin Cai , Lijun Ding , Jinhua Zhao This is my paper

Pith reviewed 2026-05-20 22:37 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords heavy-tailed time seriesWikipedia page viewsperiodicity quantificationbenchmark datasettime series forecastingnon-Gaussian lossespower-law distributiontraffic prediction
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The pith

Frequently viewed Wikipedia pages exhibit significantly weaker periodic structure than less-viewed pages.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces TailedTS, a benchmark dataset of roughly 24.69 billion hourly Wikipedia page-view observations from 2024, to evaluate time series models under heavy-tailed and non-Gaussian conditions that are missing from prior benchmarks. Using a sparse autoregression approach, the authors find that the small number of high-traffic pages driving most views display markedly less regular periodic behavior than low-traffic pages. This difference directly affects how forecasting models should be tuned and how servers should be allocated on large platforms. The dataset also supplies standardized tests showing that Gaussian-based predictors lose accuracy on high-volume pages while robust loss functions maintain performance across all scales.

Core claim

The central claim is that frequently-viewed Wikipedia pages exhibit significantly weaker periodic structure than their less-viewed counterparts, quantified through a periodicity framework based on sparse autoregression with sparsity and non-negativity constraints, with direct consequences for server allocation and traffic forecasting on large digital platforms.

What carries the argument

A periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints that measures the strength of periodic patterns across different traffic volumes.

Load-bearing premise

The power-law distribution and periodicity differences observed in 2024 Wikipedia data hold for other heavy-tailed time series outside this platform and time window.

What would settle it

Re-running the sparse autoregression analysis on Wikipedia data from a different year or on hourly traffic from another high-volume platform would show whether the weaker periodicity in popular pages persists.

Figures

Figures reproduced from arXiv: 2605.16361 by HanQin Cai, Jinhua Zhao, Lijun Ding, Xinyu Chen.

Figure 1
Figure 1. Figure 1: Log-log histograms of time series datasets. The plots display the frequency distribution [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Empirical demonstration of the Wikipedia page view time series dataset for January [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Visual comparison of loss functions ρ(εt) highlighting their penalty behaviors. From left to right: the symmetric ℓ2-norm and ℓ1-norm losses; the Huber loss showing the quadratic-to-linear transition at threshold δ; the asymmetric quantile loss for different τ values; and the nonconvex ℓp-norm loss (0 < p < 1) demonstrating redescending-like characteristics for large residuals. 5 Results on Wikipedia Datas… view at source ↗
Figure 4
Figure 4. Figure 4: Seasonality analysis of Wikipedia page view time series with the sparse autoregression [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Prediction results of the ℓp-norm autoregression model on selected Wikipedia pages from the O(104 ) category during the test week. Each panel displays the ground truth hourly page views (cyan) alongside the model’s one-step-ahead predictions (red) over a 168-hour horizon. The nine pages span topics in film, mathematics, technology, science, and general knowledge. 6 Results on Benchmark Datasets To verify t… view at source ↗
Figure 6
Figure 6. Figure 6: Empirical distributions of benchmark time series datasets. The histograms illustrate [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sample of the Wikipedia page view time series dataset (January 2024). The dataset consists [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sample of the Wikipedia page view time series dataset (May 2024). The dataset consists of [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
read the original abstract

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces TailedTS, a large-scale benchmark dataset from Wikipedia hourly page views in 2024 comprising ~24.69 billion data points across ~3 million unique pages per month in Parquet format. It emphasizes the power-law distribution of traffic (5% of pages account for >70% of views) as a testbed for heavy-tailed, zero-inflated, non-Gaussian time series. The authors propose a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, reporting that frequently-viewed pages exhibit significantly weaker periodic structure than less-viewed counterparts. They also supply standardized forecasting benchmarks under non-Gaussian losses (ℓ1, Huber, quantile, ℓp) showing that robust estimators outperform Gaussian-based ones on high-volume categories.

Significance. The public release of this billion-scale, heavy-tailed dataset is a clear strength and fills a gap relative to M4/M5/UCI benchmarks. If the periodicity and forecasting results hold after robustness checks, they carry direct implications for traffic prediction and resource allocation on platforms with power-law usage patterns. The work applies existing sparse autoregression rather than deriving new theory, so its primary value lies in the empirical benchmark and the scale of the released data.

major comments (1)
  1. [Periodicity quantification framework] The periodicity claim (abstract and the section introducing the sparse autoregression framework) rests on outputs from the constrained model without reported normalization for the orders-of-magnitude variance differences between high- and low-traffic series. High-traffic pages obey the reported power-law and therefore exhibit substantially higher variance and different zero-inflation; the measured difference in periodic strength could arise from interaction between the sparsity/non-negativity constraints and signal amplitude rather than genuine structural disparity. Explicit checks against scale-invariant alternatives (e.g., per-series z-scoring, log-transform, or direct comparison of autocorrelation peaks/Fourier power ratios) are needed to substantiate the claim.
minor comments (2)
  1. [Abstract] The abstract states that the dataset enables 'standardized prediction benchmarks' but does not list the precise train/validation/test splits, forecast horizons, or cross-validation scheme used for the reported loss comparisons.
  2. [Dataset construction] Provide the exact data filtering rules, handling of missing hours, and implementation details of the sparsity constraint (e.g., regularization parameter selection) so that the benchmark can be reproduced and extended.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript introducing TailedTS. We address the single major comment point by point below and will revise the manuscript to incorporate additional robustness checks as suggested.

read point-by-point responses

  1. Referee: The periodicity claim (abstract and the section introducing the sparse autoregression framework) rests on outputs from the constrained model without reported normalization for the orders-of-magnitude variance differences between high- and low-traffic series. High-traffic pages obey the reported power-law and therefore exhibit substantially higher variance and different zero-inflation; the measured difference in periodic strength could arise from interaction between the sparsity/non-negativity constraints and signal amplitude rather than genuine structural disparity. Explicit checks against scale-invariant alternatives (e.g., per-series z-scoring, log-transform, or direct comparison of autocorrelation peaks/Fourier power ratios) are needed to substantiate the claim.

    Authors: We appreciate the referee's identification of this potential scale-related confound. The sparse autoregression model with sparsity and non-negativity constraints was applied independently to each series to quantify periodic components in a manner suited to the zero-inflated count data. Nevertheless, we agree that the lack of explicit normalization leaves open the possibility that variance differences driven by the power-law distribution could influence the measured periodic strength. In the revised manuscript we will add the suggested scale-invariant checks: (i) per-series z-scoring prior to model fitting, (ii) log-transform variants where feasible, and (iii) direct comparisons of autocorrelation peaks and Fourier power ratios across traffic-volume strata. These results will be presented alongside the original constrained-model outputs to confirm that the weaker periodic structure in high-traffic pages is not an artifact of amplitude differences. revision: yes

Circularity Check

0 steps flagged

No circularity: external dataset and applied framework yield independent empirical finding

full rationale

The paper releases an external Wikipedia 2024 traffic dataset and applies a periodicity quantification framework (sparse autoregression with sparsity/non-negativity constraints) to it. The central claim—that high-traffic pages show weaker periodicity—is an output of that application on the new data, not a quantity defined by or fitted to the same model. No equations reduce a prediction to its own inputs by construction, no self-citation chain bears the load of the result, and the dataset itself is independent of the analysis. This is a standard data-release plus empirical application pattern with no detectable circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the representativeness of Wikipedia traffic as a heavy-tailed exemplar and on the validity of the sparse autoregression formulation for quantifying periodicity; no free parameters are explicitly fitted in the abstract description, and no new entities are postulated.

axioms (2)
  • domain assumption Wikipedia hourly page views constitute a representative heavy-tailed, zero-inflated time series domain absent from prior benchmarks.
    Invoked in the motivation and dataset construction paragraphs to justify the benchmark's value.
  • domain assumption Sparse autoregression with sparsity and non-negativity constraints provides a valid measure of periodic structure.
    Stated as the basis for the periodicity quantification framework.

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Works this paper leans on

50 extracted references · 50 canonical work pages · 4 internal anchors

  1. [1]

    Cambridge University Press, 2022

    Jayakrishnan Nair, Adam Wierman, and Bert Zwart.The fundamentals of heavy tails: Properties, emergence, and estimation, volume 53. Cambridge University Press, 2022

    work page 2022

  2. [2]

    Weak Signals and Heavy Tails: Learning Theory meets Extreme Value Analysis

    Stephan Clémençon and Anne Sabourin. Weak signals and heavy tails: Machine-learning meets extreme value theory.arXiv preprint arXiv:2504.06984, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  3. [3]

    The heavy-tail phenomenon in sgd

    Mert Gurbuzbalaban, Umut Simsekli, and Lingjiong Zhu. The heavy-tail phenomenon in sgd. InInternational Conference on Machine Learning, pages 3964–3975. PMLR, 2021

    work page 2021

  4. [4]

    On empirical risk minimization with dependent and heavy-tailed data.Advances in Neural Information Processing Systems, 34:8913–8926, 2021

    Abhishek Roy, Krishnakumar Balasubramanian, and Murat A Erdogdu. On empirical risk minimization with dependent and heavy-tailed data.Advances in Neural Information Processing Systems, 34:8913–8926, 2021

    work page 2021

  5. [5]

    The m4 competition: 100,000 time series and 61 forecasting methods.International Journal of Forecasting, 36(1):54– 74, 2020

    Spyros Makridakis, Evangelos Spiliotis, and Vassilios Assimakopoulos. The m4 competition: 100,000 time series and 61 forecasting methods.International Journal of Forecasting, 36(1):54– 74, 2020

    work page 2020

  6. [6]

    The m5 competi- tion: Background, organization, and implementation.International Journal of Forecasting, 38(4):1325–1336, 2022

    Spyros Makridakis, Evangelos Spiliotis, and Vassilios Assimakopoulos. The m5 competi- tion: Background, organization, and implementation.International Journal of Forecasting, 38(4):1325–1336, 2022

    work page 2022

  7. [7]

    ElectricityLoadDiagrams20112014

    Artur Trindade. ElectricityLoadDiagrams20112014. UCI Machine Learning Repository, 2015. DOI: https://doi.org/10.24432/C58C86

    work page doi:10.24432/c58c86 2015

  8. [8]

    Modeling long-and short-term temporal patterns with deep neural networks

    Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. InThe 41st international ACM SIGIR conference on research & development in information retrieval, pages 95–104, 2018

    work page 2018

  9. [9]

    Kdd cup dataset (without missing values), June 2020

    Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero- Manso. Kdd cup dataset (without missing values), June 2020

    work page 2020

  10. [10]

    Weather dataset, August 2020

    Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Pablo Montero-Manso, and Rob Hyndman. Weather dataset, August 2020

    work page 2020

  11. [11]

    Individual household electric power consumption data set

    Georges Hebrail and Alice Berard. Individual household electric power consumption data set. UCI Machine Learning Repository, 2012

    work page 2012

  12. [12]

    Springer science & business media, 2009

    Peter J Brockwell and Richard A Davis.Time series: theory and methods. Springer science & business media, 2009

    work page 2009

  13. [13]

    John Wiley & Sons, 2015

    George EP Box, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung.Time series analysis: forecasting and control. John Wiley & Sons, 2015

    work page 2015

  14. [14]

    Long short-term memory.Neural computation, 9(8):1735–1780, 1997

    Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory.Neural computation, 9(8):1735–1780, 1997

    work page 1997

  15. [15]

    Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

    Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks on sequence modeling.arXiv preprint arXiv:1412.3555, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  16. [16]

    Learning phrase representations using rnn encoder– decoder for statistical machine translation

    Kyunghyun Cho, Bart Van Merriënboer, Ça˘glar Gulçehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder– decoder for statistical machine translation. InProceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), pages 1724–1734, 2014

    work page 2014

  17. [17]

    Temporal convolutional networks for action segmentation and detection

    Colin Lea, Michael D Flynn, Rene Vidal, Austin Reiter, and Gregory D Hager. Temporal convolutional networks for action segmentation and detection. Inproceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 156–165, 2017. 10

    work page 2017

  18. [18]

    An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling

    Shaojie Bai, J Zico Kolter, and Vladlen Koltun. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling.arXiv preprint arXiv:1803.01271, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting.Advances in neural information processing systems, 32, 2019

    Shiyang Li, Xiaoyong Jin, Yao Xuan, Xiyou Zhou, Wenhu Chen, Yu-Xiang Wang, and Xifeng Yan. Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting.Advances in neural information processing systems, 32, 2019

    work page 2019

  20. [20]

    Informer: Beyond efficient transformer for long sequence time-series forecasting

    Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 11106–11115, 2021

    work page 2021

  21. [21]

    Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting.Advances in neural information processing systems, 34:22419–22430, 2021

    Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting.Advances in neural information processing systems, 34:22419–22430, 2021

    work page 2021

  22. [22]

    Time-LLM: Time Series Forecasting by Reprogramming Large Language Models

    Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, et al. Time-llm: Time series forecasting by reprogramming large language models.arXiv preprint arXiv:2310.01728, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  23. [23]

    Large language models are zero-shot time series forecasters.Advances in neural information processing systems, 36:19622– 19635, 2023

    Nate Gruver, Marc Finzi, Shikai Qiu, and Andrew G Wilson. Large language models are zero-shot time series forecasters.Advances in neural information processing systems, 36:19622– 19635, 2023

    work page 2023

  24. [24]

    Autotimes: Au- toregressive time series forecasters via large language models.Advances in Neural Information Processing Systems, 37:122154–122184, 2024

    Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, and Mingsheng Long. Autotimes: Au- toregressive time series forecasters via large language models.Advances in Neural Information Processing Systems, 37:122154–122184, 2024

    work page 2024

  25. [25]

    CRC press, 1994

    Gennady Samorodnitsky and Murad S Taqqu.Stable non-Gaussian random processes: stochas- tic models with infinite variance, volume 1. CRC press, 1994

    work page 1994

  26. [26]

    Least absolute deviation estimation for regression with arma errors.Journal of Theoretical Probability, 10(2):481–497, 1997

    Richard A Davis and William TM Dunsmuir. Least absolute deviation estimation for regression with arma errors.Journal of Theoretical Probability, 10(2):481–497, 1997

    work page 1997

  27. [27]

    Lade-based inferences for autore- gressive models with heavy-tailed g-garch (1, 1) noise.Journal of Econometrics, 227(1):228– 240, 2022

    Xingfa Zhang, Rongmao Zhang, Yuan Li, and Shiqing Ling. Lade-based inferences for autore- gressive models with heavy-tailed g-garch (1, 1) noise.Journal of Econometrics, 227(1):228– 240, 2022

    work page 2022

  28. [28]

    Least absolute deviation estimation for all-pass time series models.Annals of statistics, pages 919–946, 2001

    F Jay Breidt, Richard A Davis, and A Alexandre Trindade. Least absolute deviation estimation for all-pass time series models.Annals of statistics, pages 919–946, 2001

    work page 2001

  29. [29]

    Shiqing Ling. Self-weighted least absolute deviation estimation for infinite variance autore- gressive models.Journal of the Royal Statistical Society Series B: Statistical Methodology, 67(3):381–393, 2005

    work page 2005

  30. [30]

    A generalized least absolute deviation method for parame- ter estimation of autoregressive signals.IEEE Transactions on Neural Networks, 19(1):107–118, 2008

    Youshen Xia and Mohamed S Kamel. A generalized least absolute deviation method for parame- ter estimation of autoregressive signals.IEEE Transactions on Neural Networks, 19(1):107–118, 2008

    work page 2008

  31. [31]

    Least absolute deviation estimation for general autore- gressive moving average time-series models.Journal of Time Series Analysis, 31(2):98–112, 2010

    Rongning Wu and Richard A Davis. Least absolute deviation estimation for general autore- gressive moving average time-series models.Journal of Time Series Analysis, 31(2):98–112, 2010

    work page 2010

  32. [32]

    Least absolute deviations estimation for uncertain regression with imprecise observations.Fuzzy Optimization and Decision Making, 19(1):33–52, 2020

    Zhe Liu and Ying Yang. Least absolute deviations estimation for uncertain regression with imprecise observations.Fuzzy Optimization and Decision Making, 19(1):33–52, 2020

    work page 2020

  33. [33]

    Robust estimation of a location parameter

    Peter J Huber. Robust estimation of a location parameter. InBreakthroughs in statistics: Methodology and distribution, pages 492–518. Springer, 1992

    work page 1992

  34. [34]

    John Wiley & Sons, 2019

    Ricardo A Maronna, R Douglas Martin, Victor J Yohai, and Matías Salibián-Barrera.Robust statistics: theory and methods (with R). John Wiley & Sons, 2019

    work page 2019

  35. [35]

    Adaptive huber regression.Journal of the American Statistical Association, 115(529):254–265, 2020

    Qiang Sun, Wen-Xin Zhou, and Jianqing Fan. Adaptive huber regression.Journal of the American Statistical Association, 115(529):254–265, 2020. 11

    work page 2020

  36. [36]

    Adaptive huber regression on markov-dependent data.Stochastic processes and their applications, 150:802–818, 2022

    Jianqing Fan, Yongyi Guo, and Bai Jiang. Adaptive huber regression on markov-dependent data.Stochastic processes and their applications, 150:802–818, 2022

    work page 2022

  37. [37]

    Quantile regression.Journal of economic perspectives, 15(4):143–156, 2001

    Roger Koenker and Kevin F Hallock. Quantile regression.Journal of economic perspectives, 15(4):143–156, 2001

    work page 2001

  38. [38]

    Quantile autoregression.Journal of the American statistical association, 101(475):980–990, 2006

    Roger Koenker and Zhijie Xiao. Quantile autoregression.Journal of the American statistical association, 101(475):980–990, 2006

    work page 2006

  39. [39]

    Spatial quantile autoregressive model: A review.Journal of Economics and Administrative Sciences, 31(146):141–155, 2025

    Sawsan Qassim Hadi and Omar Abdulmohsin Ali. Spatial quantile autoregressive model: A review.Journal of Economics and Administrative Sciences, 31(146):141–155, 2025

    work page 2025

  40. [40]

    A quantile autoregression analysis of price volatility in agricultural markets.Agricultural Economics, 51(2):273–289, 2020

    Jean-Paul Chavas and Jian Li. A quantile autoregression analysis of price volatility in agricultural markets.Agricultural Economics, 51(2):273–289, 2020

    work page 2020

  41. [41]

    Spatial quantile autoregression for season within year daily maximum temperature data.The Annals of Applied Statistics, 17(3):2305–2325, 2023

    Jorge Castillo-Mateo, Jesús Asín, Ana C Cebrián, Alan E Gelfand, and Jesús Abaurrea. Spatial quantile autoregression for season within year daily maximum temperature data.The Annals of Applied Statistics, 17(3):2305–2325, 2023

    work page 2023

  42. [42]

    Robust regression computation using iteratively reweighted least squares

    Dianne P O’Leary. Robust regression computation using iteratively reweighted least squares. SIAM Journal on Matrix Analysis and Applications, 11(3):466–480, 1990

    work page 1990

  43. [43]

    Ingrid Daubechies, Ronald DeV ore, Massimo Fornasier, and C Sinan Güntürk. Iteratively reweighted least squares minimization for sparse recovery.Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 63(1):1–38, 2010

    work page 2010

  44. [44]

    Global linear and local superlinear convergence of IRLS for non-smooth robust regression.Advances in neural information processing systems, 35:28972–28987, 2022

    Liangzu Peng, Christian Kümmerle, and René Vidal. Global linear and local superlinear convergence of IRLS for non-smooth robust regression.Advances in neural information processing systems, 35:28972–28987, 2022

    work page 2022

  45. [45]

    Majorization-minimization algorithms in signal processing, communications, and machine learning.IEEE Transactions on Signal Processing, 65(3):794–816, 2016

    Ying Sun, Prabhu Babu, and Daniel P Palomar. Majorization-minimization algorithms in signal processing, communications, and machine learning.IEEE Transactions on Signal Processing, 65(3):794–816, 2016

    work page 2016

  46. [46]

    Interpretable time series autoregression for periodicity quantification.arXiv preprint arXiv:2506.22895, 2025

    Xinyu Chen, Vassilis Digalakis Jr, Lijun Ding, Dingyi Zhuang, and Jinhua Zhao. Interpretable time series autoregression for periodicity quantification.arXiv preprint arXiv:2506.22895, 2025

    work page arXiv 2025

  47. [47]

    Ingrid Daubechies, Michel Defrise, and Christine De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 57(11):1413– 1457, 2004

    work page 2004

  48. [48]

    A fast iterative shrinkage-thresholding algorithm for linear inverse problems.SIAM Journal on Imaging Sciences, 2(1):183–202, 2009

    Amir Beck and Marc Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems.SIAM Journal on Imaging Sciences, 2(1):183–202, 2009

    work page 2009

  49. [49]

    Cambridge university press, 2004

    Stephen Boyd and Lieven Vandenberghe.Convex optimization. Cambridge university press, 2004

    work page 2004

  50. [50]

    " " 10Download p ag ev ie ws files 11

    IBM ILOG CPLEX. Cplex optimization studio cplex user’s manual, version 12 release 6.https: //www.engineering.iastate.edu/~jdm/ee458/CPLEX-UsersManual2015.pdf, 2015. 12 Supplementary Material for TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification A Benchmark Datasets Figure 6 shows the histogram plots of 8 be...

    work page 2015