Brier score for multi-class classification problems with \(r\) labels defined as $$ \frac{1}{n} \sum_{i=1}^n \sum_{j=1}^r (I_{ij} - p_{ij})^2. $$ \(I_{ij}\) is 1 if observation \(i\) has true label \(j\), and 0 otherwise.

Note that there also is the more common definition of the Brier score for binary classification problems in bbrier().

Note

The score function calls mlr3measures::mbrier() from package mlr3measures.

If the measure is undefined for the input, NaN is returned. This can be customized by setting the field na_value.

Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

mlr_measures$get("mbrier")
msr("mbrier")

Meta Information

  • Type: "classif"

  • Range: \([0, 2]\)

  • Minimize: TRUE

  • Required prediction: prob

See also