提出一种更抗异常的多变量概率预测损失函数，提升模型鲁棒性。
MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting
- 基于连续排序概率得分设计多变量高斯分布的严格正确损失函数
- 在真实数据集上显著提升预测准确率与不确定性量化能力
- 适合处理含异常值的多变量时间序列预测任务
多变量高斯（MVG）分布是建模相关连续变量在概率预测中的核心工具。神经预测模型通常使用神经网络参数化分布的均值向量和协方差矩阵，并以负对数似然（log-score）作为损失函数进行优化。然而，log-score 对异常值敏感，易导致显著误差。受单变量连续排序概率得分（CRPS）启发，本文提出 MVG-CRPS，一种适用于多变量高斯分布的严格正确评分规则。MVG-CRPS 可以用神经网络输出表示闭式表达式，从而无缝集成至深度学习框架。在多变量自回归与单变量序列到序列（Seq2Seq）预测任务的真实数据集上实验表明，MVG-CRPS 显著提升了概率预测的鲁棒性、准确性和不确定性量化性能。
原文摘要 · Abstract (English)
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.
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