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Is the squared error a proper score?
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.
What is a proper score?
Proper scoring rules are used in meteorology, finance, and pattern classification where a forecaster or algorithm will attempt to minimize the average score to yield refined, calibrated probabilities (i.e. accurate probabilities).
What is the value of the Brier score?
Brier score is a evaluation metric that is used to check the goodness of a predicted probability score. This is very similar to the mean squared error, but only applied for prediction probability scores, whose values range between 0 and 1.
When to use the Brier score for uni dimensional predictions?
For uni dimensional predictions, it is strictly equivalent to the mean squared error as applied to predicted probabilities. The Brier score is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive discrete outcomes or classes.
How is the Brier score used in machine learning?
Brier score is a type of evaluation metric for classification tasks, where you predict outcomes such as win/lose, spam/ham, click/no-click etc. It is similar in spirit to the log-loss evaluation metric, but the only difference is that it is gentler than log loss in penalizing inaccurate predictions.
How are the your classes chosen for the Brier score?
As Glenn Brier, the score’s originator, put it in his 1950 Monthly Weather Review article outlining the formula, “The R classes are chosen to be mutually exclusive and exhaustive….” This means that for a given event, the R outcomes considered in the calculation of the Brier score should cover all possible outcomes of the event.