MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting

Vincent Zhihao Zheng, Lijun Sun

Keywords: Probabilistic forecasting, scoring rules, time series

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.

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.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 6053