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The squared error is indeed a proper scoring rule, it is however important to note that it is not strictly proper, meaning that if you have two different probab
by deng 11y ago
The squared error is indeed a proper scoring rule, it is however important to note that it is not strictly proper, meaning that if you have two different probabilistic forecasts generating the same mean, they will perform the same. Outside the linear context, this is often not what you want, and you should look into alternatives like the logarithmic scoring rule.
- shoyer 11y agoNo, squared error (the Brier score) is absolutely a strictly proper scoring rule for classification, which is the claim made in the article. See the linked Wikipedia article: https://en.wikipedia.org/wiki/Scoring_rule#Brier.2Fquadratic_scoring_rule https://en.wikipedia.org/wiki/Scoring_rule#Brier.2Fquadratic... Perhaps you are thinking of probabilistic regression problems, for which mean squared error is indeed not strictly proper. My favorite scoring rule for continuous variables is the continuous ranked probability score, which is actually a generalization of mean absolute error (for non-probabilistic regression).
- deng 11y agoYou are right, I was thinking of probabilistic problems.