mlsanityData to 7 Oct 2026

High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes

arXiv 1910.03002 ↗First posted 7 Oct 2019cs.LG stat.MLcited by 147

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Abstract (arXiv)

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

Key facts. Cited by 147 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Oct 2019.

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Citing papers per year: 2021: 19; 2022: 30; 2023: 31; 2024: 27; 2025: 21; 2026: 19.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 634
  3. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  4. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
  5. 2021Monash Time Series Forecasting Archivecited by 256
  6. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  7. 2025Chronos-2: From Univariate to Universal Forecastingcited by 158
  8. 2023Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecastingcited by 102
  9. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 89
  10. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 42
  11. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  12. 2022TACTiS: Transformer-Attentional Copulas for Time Seriescited by 38
38 more
  1. 2023ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizonscited by 35
  2. 2021Missing Value Imputation on Multidimensional Time Seriescited by 33
  3. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  4. 2021Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecastingcited by 32
  5. 2021Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecastingcited by 32
  6. 2024MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Processcited by 31
  7. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 28
  8. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  9. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 25
  10. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  11. 2023Pushing the Limits of Pre-training for Time Series Forecasting in the CloudOps Domaincited by 23
  12. 2022Multivariate Time Series Forecasting with Latent Graph Inferencecited by 20
  13. 2022Multivariate Quantile Function Forecastercited by 19
  14. 2021Adjusting for Autocorrelated Errors in Neural Networks for Time Seriescited by 18
  15. 2021Probabilistic Time Series Forecasting with Implicit Quantile Networkscited by 17
  16. 2024RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomaliescited by 17
  17. 2021RNN with Particle Flow for Probabilistic Spatio-temporal Forecastingcited by 16
  18. 2023pTSE: A Multi-model Ensemble Method for Probabilistic Time Series Forecastingcited by 16
  19. 2023Traffic Prediction using Artificial Intelligence: Review of Recent Advances and Emerging Opportunitiescited by 16
  20. 2022Robust Probabilistic Time Series Forecastingcited by 15
  21. 2021Online false discovery rate control for anomaly detection in time seriescited by 13
  22. 2022STGC-GNNs: A GNN-based traffic prediction framework with a spatial-temporal Granger causality graphcited by 12
  23. 2023Deep Learning based Forecasting: a case study from the online fashion industrycited by 12
  24. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  25. 2021Deep Time Series Forecasting with Shape and Temporal Criteriacited by 10
  26. 2022Diverse Counterfactual Explanations for Anomaly Detection in Time Seriescited by 10
  27. 2024Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Maskcited by 10
  28. 2021Hierarchically Regularized Deep Forecastingcited by 9
  29. 2024Variational Schr"odinger Diffusion Modelscited by 9
  30. 2024Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systemscited by 9
  31. 2025Probabilistic Forecasting via Autoregressive Flow Matchingcited by 9
  32. 2022Multi-Objective Model Selection for Time Series Forecastingcited by 8
  33. 2022Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanismscited by 8
  34. 2023Learning Informative Representation for Fairness-aware Multivariate Time-series Forecasting: A Group-based Perspectivecited by 8
  35. 2025Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Modelscited by 8
  36. 2025End-to-End Probabilistic Framework for Learning with Hard Constraintscited by 8
  37. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 8
  38. 2022Random Noise vs State-of-the-Art Probabilistic Forecasting Methods : A Case Study on CRPS-Sum Discrimination Abilitycited by 7

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