mlsanityData to 7 Oct 2026

Deep Time Series Forecasting with Shape and Temporal Criteria

arXiv 2104.04610 ↗First posted 9 Apr 2021stat.ML cs.AI cs.LGcited by 10

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Abstract (arXiv)

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic forEcasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 43 of its 86 references that are in the map. First posted on arXiv 9 Apr 2021.

Builds on

43 of 86 references.

References · 43

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31 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 0; 2023: 3; 2024: 1; 2025: 2; 2026: 3.

10 papers.

  1. 2021Unsupervised Domain Adaptation for Constraining Star Formation Historiescited by 8
  2. 2023TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecastingcited by 4
  3. 2026Deep Time-series Forecasting Needs Kernelized Moment Balancingcited by 2
  4. 2023Curricular and Cyclical Loss for Time Series Learning Strategycited by 1
  5. 2024Real-time respiratory motion forecasting with online learning of recurrent neural networks for accurate targeting in externally guided radiotherapycited by 1
  6. 2023Time Series Forecasting via Semi-Asymmetric Convolutional Architecture with Global Atrous Sliding Windowcited by 0
  7. 2025PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Modelscited by 0
  8. 2025Error Adjustment Based on Spatiotemporal Correlation Fusion for Traffic Forecastingcited by 0
  9. 2026From Static Spectra to Operando Infrared Dynamics: Physics Informed Flow Modeling and a Benchmarkcited by 0
  10. 2026Deep Time-Series Forecasting in 10 Years: A Surveycited by 0