Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts

Étienne Marcotte, Valentina Zantedeschi, Alexandre Drouin, Nicolas Chapados (2022). Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts. International Conference on Machine Learning (ICML 2023).

[Paper]

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

Contents

All results reported in the paper can be reproduced using the provided notebooks. Some of these require our raw experimental data, which can be found attached to the releases.

• calibrate_experiments.ipynb: calibration of the difficulty of the test cases based on the power of the negative log likelihood.
• optimize_solar.ipynb: real data experiments using the solar dataset.
• plot_power_vs_epsilon_covariance.ipynb: produces Figure 9 of the paper.
• plot_ror_results.ipynb: plot a single region of reliability heatmap (e.g., Figure 2).
• plot_ror_results_all.ipynb: plot all region of reliability heatmaps, produce the aggregated results (Figure 8), and generate Table 3.

Citing this work

Please use the following Bibtex entry:

@inproceedings{marcotte2023regions,
  title     = {Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts},
  author    = {\'{E}tienne Marcotte and Valentina Zantedeschi and Alexandre Drouin and Nicolas Chapados},
  booktitle = {40th International Conference on Machine Learning},
  year      = {2023},
  url       = {https://arxiv.org/abs/2304.09836}
}