mlsanityData to 7 Oct 2026

Robust Probabilistic Time Series Forecasting

arXiv 2202.11910 ↗First posted 24 Feb 2022cs.LGcited by 15

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Abstract (arXiv)

Probabilistic time series forecasting has played critical role in decision-making processes due to its capability to quantify uncertainties. Deep forecasting models, however, could be prone to input perturbations, and the notion of such perturbations, together with that of robustness, has not even been completely established in the regime of probabilistic forecasting. In this work, we propose a framework for robust probabilistic time series forecasting. First, we generalize the concept of adversarial input perturbations, based on which we formulate the concept of robustness in terms of bounded Wasserstein deviation. Then we extend the randomized smoothing technique to attain robust probabilistic forecasters with theoretical robustness certificates against certain classes of adversarial perturbations. Lastly, extensive experiments demonstrate that our methods are empirically effective in enhancing the forecast quality under additive adversarial attacks and forecast consistency under supplement of noisy observations.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 42 of its 77 references that are in the map. First posted on arXiv 24 Feb 2022.

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42 of 77 references.

References · 42

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  6. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  7. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  8. 2016Adversarial Machine Learning at Scalecited by 934
  9. 2016Practical Black-Box Attacks against Machine Learningcited by 893
  10. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
  11. 2019Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecastingcited by 748
  12. 2015Generating Sentences from a Continuous Spacecited by 607
30 more
  1. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 606
  2. 2015Sequence Level Training with Recurrent Neural Networkscited by 568
  3. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  4. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 462
  5. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
  6. 2018Certified Defenses against Adversarial Examplescited by 305
  7. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  8. 2018Certified Adversarial Robustness with Additive Noisecited by 178
  9. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  10. 2019Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directionscited by 172
  11. 2019Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecastingcited by 161
  12. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  13. 2018Scaling provable adversarial defensescited by 141
  14. 2019Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like processcited by 123
  15. 2019Generalization in Generation: A closer look at Exposure Biascited by 123
  16. 2021Label Noise SGD Provably Prefers Flat Global Minimizerscited by 121
  17. 2019Deep Factors for Forecastingcited by 86
  18. 2016Reward Augmented Maximum Likelihood for Neural Structured Predictioncited by 80
  19. 2021Domain Adaptation for Time Series Forecasting via Attention Sharingcited by 68
  20. 2019Probabilistic Forecasting with Temporal Convolutional Neural Networkcited by 63
  21. 2019Adversarial Attacks on Deep Neural Networks for Time Series Classificationcited by 53
  22. 2018Training verified learners with learned verifierscited by 50
  23. 2020Detection as Regression: Certified Object Detection by Median Smoothingcited by 47
  24. 2019Adversarial Attacks on Time Seriescited by 40
  25. 2019Certifiably Robust Interpretation in Deep Learningcited by 35
  26. 2021Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecastingcited by 32
  27. 2020Interpretable Sequence Learning for COVID-19 Forecastingcited by 22
  28. 2020Adversarial Attacks on Probabilistic Autoregressive Forecasting Modelscited by 13
  29. 2021Variance Reduced Training with Stratified Sampling for Forecasting Modelscited by 13
  30. 2020Structured Policy Iteration for Linear Quadratic Regulatorcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 3; 2025: 4; 2026: 4.

15 papers.

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  1. 2024RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomaliescited by 17
  2. 2022Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanismscited by 8
  3. 2023A Co-training Approach for Noisy Time Series Learningcited by 8
  4. 2024FTS: A Framework to Find a Faithful TimeSievecited by 7
  5. 2024Denoising-Aware Contrastive Learning for Noisy Time Seriescited by 5
  6. 2023Adaptive Sampling for Probabilistic Forecasting under Distribution Shiftcited by 2
  7. 2023Non-parametric Probabilistic Time Series Forecasting via Innovations Representationcited by 2
  8. 2025Quantifying Robustness: A Benchmarking Framework for Deep Learning Forecasting in Cyber-Physical Systemscited by 1
  9. 2026SEER: Transformer-based Robust Time Series Forecasting via Automated Patch Enhancement and Replacementcited by 1
  10. 2026Adversarial Robustness of Deep State Space Models for Forecastingcited by 1
  11. 2026Exposure Bias as Epistemic Underidentification in Recursive Forecastingcited by 1
  12. 2025PA-RNet: Perturbation-Aware Residual Network for Robust Multimodal Time Series Forecastingcited by 0
3 more
  1. 2025Benchmarking M-LTSF: Frequency and Noise-Based Evaluation of Multivariate Long Time Series Forecasting Modelscited by 0
  2. 2025Contrastive Time Series Forecasting with Anomaliescited by 0
  3. 2026Towards Reliable Zero-Shot Crowd Forecasting: Evaluating Time Series Foundation Models for Special Event Pedestrian Forecastingcited by 0