Learning with the Nash-Sutcliffe loss
The Nash-Sutcliffe efficiency ($\text{NSE}$) is a widely used, positively oriented relative measure for evaluating forecasts across multiple time series. However, it lacks a decision-theoretic foundation for this purpose. To address this, we examine its negatively oriented counterpart, which we refer to as Nash-Sutcliffe loss, defined as $L_{\text{NS}} = 1 - \text{NSE}$. We prove that $L_{\text{NS}}$ is strictly consistent for an elicitable and identifiable multi-dimensional functional, which we name the Nash-Sutcliffe functional. This functional is a data-weighted component-wise mean. The common practice of maximizing the average $\text{NSE}$ across multiple series is the sample analog o...
| Authors | Hristos Tyralis, Georgia Papacharalampous |
|---|---|
| Primary category | stat.ML |
| Published | 1 March 2026 |
| Last updated at source | 3 July 2026 |
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