基于签名核的鲁棒概率与尾事件预测评估指标

Probabilistic forecasting is increasingly vital in high-stakes fields such as finance, epidemiology, and climate science. Current evaluation frameworks lack a consensus metric and exhibit two significant flaws: they often assume independence across time steps or variables, and they lack sensitivity to tail events, which are crucial for real-world decision-making. To address these issues, two kernel-based metrics are proposed: the signature maximum mean discrepancy (Sig-MMD) and the novel censored signature maximum mean discrepancy (CSig-MMD). By leveraging the signature kernel, these metrics capture complex inter-variable and inter-temporal dependencies while remaining robust to missing data. Furthermore, CSig-MMD demonstrates enhanced sensitivity in evaluating tail events, thereby better supporting high-risk decision-making.