mlsanityData to 7 Oct 2026

TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series

arXiv 2310.01327 ↗First posted 2 Oct 2023cs.LG cs.AI stat.MLcited by 25

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Abstract (arXiv)

We introduce a new model for multivariate probabilistic time series prediction, designed to flexibly address a range of tasks including forecasting, interpolation, and their combinations. Building on copula theory, we propose a simplified objective for the recently-introduced transformer-based attentional copulas (TACTiS), wherein the number of distributional parameters now scales linearly with the number of variables instead of factorially. The new objective requires the introduction of a training curriculum, which goes hand-in-hand with necessary changes to the original architecture. We show that the resulting model has significantly better training dynamics and achieves state-of-the-art performance across diverse real-world forecasting tasks, while maintaining the flexibility of prior work, such as seamless handling of unaligned and unevenly-sampled time series. Code is made available at https://github.com/ServiceNow/TACTiS.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 39 of its 73 references that are in the map. First posted on arXiv 2 Oct 2023.

Builds on

39 of 73 references.

References · 39

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2021On the Opportunities and Risks of Foundation Modelscited by 3,961
  6. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  7. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  8. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  9. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  10. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  11. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  12. 2020Time Series Forecasting With Deep Learning: A Surveycited by 457
27 more
  1. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
  2. 2021Monash Time Series Forecasting Archivecited by 256
  3. 2018Neural Autoregressive Flowscited by 207
  4. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  5. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  6. 2022ETSformer: Exponential Smoothing Transformers for Time-series Forecastingcited by 146
  7. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 142
  8. 2018Temporal Pattern Attention for Multivariate Time Series Forecastingcited by 125
  9. 2022Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Timecited by 85
  10. 2019Discrete Flows: Invertible Generative Models of Discrete Datacited by 68
  11. 2019Latent Normalizing Flows for Discrete Sequencescited by 66
  12. 2019Probabilistic Forecasting with Temporal Convolutional Neural Networkcited by 63
  13. 2020A Survey on Principles, Models and Methods for Learning from Irregularly Sampled Time Seriescited by 42
  14. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  15. 2022TACTiS: Transformer-Attentional Copulas for Time Seriescited by 38
  16. 2020Time Series Data Imputation: A Survey on Deep Learning Approachescited by 34
  17. 2022WOODS: Benchmarks for Out-of-Distribution Generalization in Time Seriescited by 29
  18. 2019Copulas as High-Dimensional Generative Models: Vine Copula Autoencoderscited by 20
  19. 2019Deep Generative Quantile-Copula Models for Probabilistic Forecastingcited by 18
  20. 2019Copula & Marginal Flows: Disentangling the Marginal from its Jointcited by 17
  21. 2021Implicit Generative Copulascited by 17
  22. 2018Learning Sparse Latent Representations with the Deep Copula Information Bottleneckcited by 9
  23. 2019Neural Gaussian Copula for Variational Autoencodercited by 9
  24. 2013Semi-Supervised Domain Adaptation with Non-Parametric Copulascited by 8
  25. 2023Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecastscited by 7
  26. 2020Stanza: A Nonlinear State Space Model for Probabilistic Inference in Non-Stationary Time Seriescited by 6
  27. 2019Copula-like Variational Inferencecited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 10; 2026: 8.

25 papers.

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  1. 2024UniTS: A Unified Multi-Task Time Series Modelcited by 93
  2. 2025SciTS: Scientific Time Series Understanding and Generation with LLMscited by 13
  3. 2024Your copula is a classifier in disguise: classification-based copula density estimationcited by 8
  4. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 8
  5. 2024Multivariate Probabilistic Time Series Forecasting with Correlated Errorscited by 6
  6. 2024Quasi-Bayes meets Vinescited by 5
  7. 2024MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecastingcited by 5
  8. 2025Winner-takes-all for Multivariate Probabilistic Time Series Forecastingcited by 4
  9. 2025RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecastingcited by 4
  10. 2025Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Modelscited by 4
  11. 2025Neural Mutual Information Estimation with Vector Copulascited by 4
  12. 2024Strada-LLM: Graph LLM for traffic predictioncited by 3
13 more
  1. 2025TimePre: Bridging Accuracy, Efficiency, and Stability in Probabilistic Time-Series Forecastingcited by 3
  2. 2026CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networkscited by 3
  3. 2024Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesiscited by 1
  4. 2026A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Predictioncited by 1
  5. 2026Probabilistic Circuits for Irregular Multivariate Time Series Forecastingcited by 1
  6. 2025A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixingcited by 0
  7. 2025How Patterns Dictate Learnability in Sequential Datacited by 0
  8. 2025Foundation Model Forecasts: Form and Functioncited by 0
  9. 2026Probabilistic Multivariate Time Series Forecasting with Diffusion Copulascited by 0
  10. 2026Gaussian Mixture Copula Processes for Irregular Time Seriescited by 0
  11. 2026TSCoNet: A Two-Stage Copula CNN-LSTM for Uncertainty-Aware Spatio-Temporal Forecastingcited by 0
  12. 2026SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecastingcited by 0
  13. 2026STRIDE: State-Transition Representation via Increment Dynamics and Evolutioncited by 0