MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting
This work addresses robustness issues in probabilistic forecasting for applications like finance or weather prediction, but it is incremental as it extends an existing univariate method to multivariate settings.
The paper tackled the problem of sensitivity to outliers in multivariate probabilistic forecasting by proposing MVG-CRPS, a robust loss function based on the continuous ranked probability score, which improved robustness, accuracy, and uncertainty quantification in experiments on real-world datasets.
Multivariate Gaussian (MVG) distributions are central to modeling correlated continuous variables in probabilistic forecasting. Neural forecasting models typically parameterize the mean vector and covariance matrix of the distribution using neural networks, optimizing with the log-score (negative log-likelihood) as the loss function. However, the sensitivity of the log-score to outliers can lead to significant errors in the presence of anomalies. Drawing on the continuous ranked probability score (CRPS) for univariate distributions, we propose MVG-CRPS, a strictly proper scoring rule for MVG distributions. MVG-CRPS admits a closed-form expression in terms of neural network outputs, thereby integrating seamlessly into deep learning frameworks. Experiments on real-world datasets across multivariate autoregressive and univariate sequence-to-sequence (Seq2Seq) forecasting tasks show that MVG-CRPS improves robustness, accuracy, and uncertainty quantification in probabilistic forecasting.