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arXiv · 2602.10182

Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting

Benjamin R. Redhead·Thomas L. Lee·Peng Gu·Víctor Elvira·Amos Storkey
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Abstract

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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Benjamin R. Redhead, Thomas L. Lee, Peng Gu, Víctor Elvira, Amos Storkey. 2026-02-10. Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting. https://arxiv.org/abs/2602.10182

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