Brier score for binary classification problems defined as $$ \frac{1}{n} \sum_{i=1}^n (I_i - p_i)^2. $$ \(I_{i}\) is 1 if observation \(i\) belongs to the positive class, and 0 otherwise.

Note that this (more common) definition of the Brier score is equivalent to the original definition of the multi-class Brier score (see mbrier()) divided by 2.

Note

The score function calls mlr3measures::bbrier() 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("bbrier")
msr("bbrier")

Meta Information

  • Type: "binary"

  • Range: \([0, 1]\)

  • Minimize: TRUE

  • Required prediction: prob

See also