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

By David Salinas, Michael Bohlke-Schneider, Laurent Callot, Roberto Medico, Jan Gasthaus. 2019

278 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Signal Processing, Time-Series & Forecasting

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Science and Operations Research

In Signal Processing

In Time-Series & Forecasting

Citations in the corpus

Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models (2022, methodology): “Similarly, diverse methods significantly contributed to the literature such as GP-Copula [42], Transformer MAF [39], and TLAE [37].”
Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion (2024, unknown): “In Appendix E, we show that DF is competitive with prior diffusion [49] and transformer-based [50] work on multivariate time series forecasting, following the experimental setup of [53].”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, methodology): “Neural methods have recently become widely-used for solving the prediction problem with univariate point forecasting methods [172] or univariate probabilistic methods [205].”
Deep Learning on Traffic Prediction: Methods, Analysis, and Future Directions (2021, methodology): “…[25] Traditional machine learning methods Feature-based models Flow [30] Demand [28], [29] Gaussian process models Flow [31] Speed [33] Demand [32] Occupancy [32] State space models Flow [34], [35], [38]–[40], [45]–[48] Speed [36], [42], [43] Demand [37] Travel time [44] Occupancy [41], [44]…”
Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting (2021, methodology): “…forecasting meth-ods (Lai et al., 2018; Li et al., 2019) as well as probabilistic methods, like this method, which explicitly model the data distribution using Gaussian copulas (Salinas et al., 2019a), GANs (Yoon et al., 2019), or normalizing ﬂows (de B´ezenac et al., 2020; Rasul et al., 2021).”
CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation (2021, methodology): “We use the same prediction steps as previous studies [34, 37].”
Forecasting: theory and practice (2020, methodology): “…complex real-world forecasting situations such as data sparsity and cold-starts (Chen et al., 2020), include exogenous covariates such as promotional information and keyword search indices (Law et al., 2019), and allow for different choices of distributional assumptions (Salinas et al., 2019a).”
Deep Learning for Forecasting (2020, methodology): “In this virtual workshop, we aim at covering neural forecasting methods from ground up, starting from the very basics of deep learning up to recent forecasting model improvements such as [5].”