mlr3measures (version 1.0.0)

mbrier: Multiclass Brier Score

Description

Measure to compare true observed labels with predicted probabilities in multiclass classification tasks.

Usage

mbrier(truth, prob, ...)

Value

Performance value as numeric(1).

Arguments

truth

(factor())
True (observed) labels. Must have the same levels and length as response.

prob

(matrix())
Matrix of predicted probabilities, each column is a vector of probabilities for a specific class label. Columns must be named with levels of truth.

...

(any)
Additional arguments. Currently ignored.

Meta Information

• Type: "classif"

• Range: \([0, 2]\)

• Minimize: TRUE

• Required prediction: prob

Details

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

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

References

Brier GW (1950). “Verification of forecasts expressed in terms of probability.” Monthly Weather Review, 78(1), 1--3. tools:::Rd_expr_doi("10.1175/1520-0493(1950)078<0001:vofeit>2.0.co;2").

See Also

Other Classification Measures: acc(), bacc(), ce(), logloss(), mauc_aunu(), mcc(), zero_one()

Examples

set.seed(1)
lvls = c("a", "b", "c")
truth = factor(sample(lvls, 10, replace = TRUE), levels = lvls)
prob = matrix(runif(3 * 10), ncol = 3)
colnames(prob) = levels(truth)
mbrier(truth, prob)