mlsanityData to 14 Oct 2026

Taming the Long Tail of Deep Probabilistic Forecasting

arXiv 2202.13418 ↗First posted 27 Feb 2022cs.LGcited by 7

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Abstract (arXiv)

Deep probabilistic forecasting is gaining attention in numerous applications ranging from weather prognosis, through electricity consumption estimation, to autonomous vehicle trajectory prediction. However, existing approaches focus on improvements on the most common scenarios without addressing the performance on rare and difficult cases. In this work, we identify a long tail behavior in the performance of state-of-the-art deep learning methods on probabilistic forecasting. We present two moment-based tailedness measurement concepts to improve performance on the difficult tail examples: Pareto Loss and Kurtosis Loss. Kurtosis loss is a symmetric measurement as the fourth moment about the mean of the loss distribution. Pareto loss is asymmetric measuring right tailedness, modeling the loss using a generalized Pareto distribution (GPD). We demonstrate the performance of our approach on several real-world datasets including time series and spatiotemporal trajectories, achieving significant improvements on the tail examples.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 31 of its 53 references that are in the map. First posted on arXiv 27 Feb 2022.

Builds on

31 of 53 references.

References · 31

  1. 2019nuScenes: A multimodal dataset for autonomous drivingcited by 4,523
  2. 2019Class-Balanced Loss Based on Effective Number of Samplescited by 1,245
  3. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  4. 2019Learning Imbalanced Datasets with Label-Distribution-Aware Margin Losscited by 989
  5. 2019Argoverse: 3D Tracking and Forecasting with Rich Mapscited by 732
  6. 2019Large-Scale Long-Tailed Recognition in an Open Worldcited by 705
  7. 2018Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networkscited by 690
  8. 2020Long-tail learning via logit adjustmentcited by 618
  9. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 607
  10. 2020What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimationcited by 497
  11. 2019Does Learning Require Memorization? A Short Tale about a Long Tailcited by 460
  12. 2021Deep Long-Tailed Learning: A Surveycited by 417
19 more
  1. 2019BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognitioncited by 403
  2. 2020Balanced Meta-Softmax for Long-Tailed Visual Recognitioncited by 400
  3. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
  4. 2017DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agentscited by 310
  5. 2016Large-Margin Softmax Loss for Convolutional Neural Networkscited by 296
  6. 2020Long-tailed Recognition by Routing Diverse Distribution-Aware Expertscited by 271
  7. 2020Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effectcited by 256
  8. 2019Multiple Futures Predictioncited by 178
  9. 2021Delving into Deep Imbalanced Regressioncited by 158
  10. 2020Overcoming Classifier Imbalance for Long-tail Object Detection with Balanced Group Softmaxcited by 152
  11. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  12. 2019Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Predictioncited by 96
  13. 2019Deep Factors for Forecastingcited by 86
  14. 2019NAOMI: Non-Autoregressive Multiresolution Sequence Imputationcited by 59
  15. 2021On Exposing the Challenging Long Tail in Future Prediction of Traffic Actorscited by 48
  16. 2021On Model Calibration for Long-Tailed Object Detection and Instance Segmentationcited by 39
  17. 2021Towards Calibrated Model for Long-Tailed Visual Recognition from Prior Perspectivecited by 39
  18. 2020Probabilistic Multi-modal Trajectory Prediction with Lane Attention for Autonomous Vehiclescited by 28
  19. 2021RNN with Particle Flow for Probabilistic Spatio-temporal Forecastingcited by 16

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 3; 2026: 1.

7 papers.

  1. 2025Position: Model Collapse Does Not Mean What You Thinkcited by 33
  2. 2024ReFine: Boosting Time Series Prediction of Extreme Events by Reweighting and Fine-tuningcited by 2
  3. 2024Critical Example Mining for Vehicle Trajectory Prediction using Flow-based Generative Modelscited by 1
  4. 2026EVEREST: An Evidential, Tail-Aware Transformer for Rare-Event Time-Series Forecastingcited by 1
  5. 2023A Comparative Study of Loss Functions: Traffic Predictions in Regular and Congestion Scenarioscited by 0
  6. 2025Ensemble of Pre-Trained Models for Long-Tailed Trajectory Predictioncited by 0
  7. 2025AdaSports-Traj: Role- and Domain-Aware Adaptation for Multi-Agent Trajectory Modeling in Sportscited by 0