Definition: Proper scoring rule
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Machine learning ▷
Scoring rules ▷
Proper scoring rule
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Metadata: ID: D193 | shortcut: psr | author: KarahanS | date: 2024-02-28, 20:50.
Definition: A scoring rule $\mathbf{S}$ is called a proper scoring rule, if and only if
\[\label{eq:psr} \max_{Q \in \mathcal{Q}} \mathbb{E}_{Y \sim P}[\mathbf{S}(Q, Y)] = \mathbb{E}_{Y \sim P}[\mathbf{S}(P, Y)] \; .\]In other words, score function $\mathbf{S}$ is a proper scoring rule, if it is maximized when the forecaster gives exactly the ground truth distribution $P(Y)$ as its probabilistic forecast $Q \in \mathcal{Q}$.
- Bálint Mucsányi, Michael Kirchhof, Elisa Nguyen, Alexander Rubinstein, Seong Joon Oh (2023): "Proper/Strictly Proper Scoring Rule"; in: Trustworthy Machine Learning; URL: https://trustworthyml.io/; DOI: 10.48550/arXiv.2310.08215.
Metadata: ID: D193 | shortcut: psr | author: KarahanS | date: 2024-02-28, 20:50.