提出两种新评估指标，更精准衡量预测模型对极端事件的捕捉能力。
Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting
- 基于签名核设计评估指标，捕捉变量与时间间的复杂依赖关系。
- 新指标对极端事件敏感，且在缺失数据下仍保持稳定性能。
- 适合高风险领域如金融、气候预测中模型评估，尤其关注极端事件表现。
概率预测在金融、流行病学和气候科学等高风险领域日益重要。然而，现有评估框架缺乏统一标准，存在两大缺陷：通常假设时间步或变量间独立，且对尾部事件不敏感——而这正是实际决策中最关键的部分。为此，我们提出两种基于核的度量方法：签名最大均值差异（Sig-MMD）和新型截断式Sig-MMD（CSig-MMD）。通过利用签名核，这些度量能有效捕捉变量间与时间上的复杂依赖，并对缺失数据具有鲁棒性。此外，CSig-MMD引入截断机制，在严格保证评分规则合理性的同时，强调预测尾部事件的能力。该方法可实现更可靠的多步直接概率预测评估，推动更稳健的概率算法发展。
原文摘要 · Abstract (English)
Probabilistic forecasting is increasingly critical across high-stakes domains, from finance and epidemiology to climate science. However, current evaluation frameworks lack a consensus metric and suffer from two critical flaws: they often assume independence across time steps or variables, and they demonstrably lack sensitivity to tail events, the very occurrences that are most pivotal in real-world decision-making. To address these limitations, we propose two kernel-based metrics: the signature maximum mean discrepancy (Sig-MMD) and our novel censored Sig-MMD (CSig-MMD). By leveraging the signature kernel, these metrics capture complex inter-variate and inter-temporal dependencies and remain robust to missing data. Furthermore, CSig-MMD introduces a censoring scheme that prioritizes a forecaster's capability to predict tail events while strictly maintaining properness, a vital property for a good scoring rule. These metrics enable a more reliable evaluation of direct multi-step forecasting, facilitating the development of more robust probabilistic algorithms.
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