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Multiclass AUC Scores

Source: R/classif_auc.R
mauc_aunu.Rd

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

Usage

mauc_aunu(truth, prob, na_value = NaN, ...)

mauc_aunp(truth, prob, na_value = NaN, ...)

mauc_au1u(truth, prob, na_value = NaN, ...)

mauc_au1p(truth, prob, na_value = NaN, ...)

mauc_mu(truth, prob, na_value = NaN, ...)

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.

na_value

(numeric(1))
Value that should be returned if the measure is not defined for the input (as described in the note). Default is NaN.

...

(any)
Additional arguments. Currently ignored.

Value

Performance value as numeric(1).

Details

Multiclass AUC measures.

  • AUNU: AUC of each class against the rest, using the uniform class distribution. Computes the AUC treating a c-dimensional classifier as c two-dimensional 1-vs-rest classifiers, where classes are assumed to have uniform distribution, in order to have a measure which is independent of class distribution change (Fawcett 2001).

  • AUNP: AUC of each class against the rest, using the a-priori class distribution. Computes the AUC treating a c-dimensional classifier as c two-dimensional 1-vs-rest classifiers, taking into account the prior probability of each class (Fawcett 2001).

  • AU1U: AUC of each class against each other, using the uniform class distribution. Computes something like the AUC of c(c - 1) binary classifiers (all possible pairwise combinations). See Hand (2001) for details.

  • AU1P: AUC of each class against each other, using the a-priori class distribution. Computes something like AUC of c(c - 1) binary classifiers while considering the a-priori distribution of the classes as suggested in Ferri (2009). Note we deviate from the definition in Ferri (2009) by a factor of c.

  • MU: Multiclass AUC as defined in Kleinman and Page (2019). This measure is an average of the pairwise AUCs between all classes. The measure was tested against the Python implementation by Ross Kleinman.

Meta Information

  • Type: "classif"

  • Range: \([0, 1]\)

  • Minimize: FALSE

  • Required prediction: prob

References

Fawcett, Tom (2001). “Using rule sets to maximize ROC performance.” In Proceedings 2001 IEEE international conference on data mining, 131–138. IEEE.

Ferri, César, Hernández-Orallo, José, Modroiu, R (2009). “An experimental comparison of performance measures for classification.” Pattern Recognition Letters, 30(1), 27–38. doi:10.1016/j.patrec.2008.08.010 .

Hand, J D, Till, J R (2001). “A simple generalisation of the area under the ROC curve for multiple class classification problems.” Machine learning, 45(2), 171–186.

Kleiman R, Page D (2019). “AUC mu: A Performance Metric for Multi-Class Machine Learning Models.” In Chaudhuri, Kamalika, Salakhutdinov, Ruslan (eds.), Proceedings of the 36th International Conference on Machine Learning, volume 97 series Proceedings of Machine Learning Research, 3439–3447. PMLR.

See also

Other Classification Measures: acc(), bacc(), ce(), logloss(), mbrier(), 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)
mauc_aunu(truth, prob)
#> [1] 0.4047619