Title: MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting
Primary area: learning on time series and dynamical systems
Keywords: probabilistic forecasting, scoring rules, robust optimization

Abstract: Multivariate probabilistic forecasting typically leverages neural network-based distributional regression, often employing Gaussian assumptions to simplify computation. While the standard negative log-likelihood provides analytical convenience, its sensitivity to outliers can severely degrade forecasting accuracy. Conversely, robust alternatives like the Energy Score, although less sensitive to extreme values, rely heavily on computationally expensive sampling approximations, limiting scalability in neural network training. To bridge this gap, we introduce the MVG-CRPS, a novel, strictly proper scoring rule for multivariate Gaussian distributions that maintains robustness to outliers while providing a closed-form expression, enabling efficient training and evaluation. Our approach leverages a whitening transformation, decorrelating multivariate outputs and reducing the multivariate scoring task to tractable univariate CRPS computations. Experiments on real-world datasets for both multivariate autoregressive and univariate sequence-to-sequence (Seq2Seq) forecasting tasks demonstrate that MVG-CRPS enhances robustness and predictive performance.

TL;DR: We introduce a robust loss function for multivariate probabilistic forecasting that enhances the robustness of deep learning models and outperforms traditional scoring rules.