mlr_measures_regr.rqr: R-Squared for Quantile Regression

mlr_measures_regr.rqrR Documentation

R-Squared for Quantile Regression

Description

Measure to compare true observed response with predicted quantiles in regression tasks.

Details

R^1(\alpha) is defined as

1 - \frac{\sum_{i=1}^n \rho_\alpha \left( t_i - r_i(\alpha) \right)}{\sum_{i=1}^n \rho_\alpha \left( t_i - q_{\alpha} \right)},

where for a quantile \alpha, \rho_\alpha is the pinball function, r_i(\alpha) are the predictions for the quantile and q_{\alpha} is the empirical \alpha-quantile of the test or training data.

R^1(\alpha) is analogous to R^2 for regression tasks. It compares the pinball function of the predictions relative to a naive model predicting the empirical quantile.

This measure is undefined for constant t.

Dictionary

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

mlr_measures$get("regr.rqr")
msr("regr.rqr")

Meta Information

  • Task type: “regr”

  • Range: (-\infty, 1]

  • Minimize: FALSE

  • Average: macro

  • Required Prediction: “quantiles”

  • Required Packages: mlr3

Parameters

Id Type Default Range
alpha numeric - [0, 1]

Super classes

mlr3::Measure -> mlr3::MeasureRegr -> MeasureRQR

Methods

Public methods

Inherited methods

Method new()

Creates a new instance of this R6 class.

Usage
MeasureRegrRQR$new(alpha = 0.5, pred_set_mean = TRUE)
Arguments
alpha

numeric(1)
The quantile for which to compute the measure. Must be one of the quantiles that the Learner was trained on.

pred_set_mean

logical(1)
If TRUE, the mean of the true values is calculated on the prediction set. If FALSE, the mean of the true values is calculated on the training set.


Method clone()

The objects of this class are cloneable with this method.

Usage
MeasureRegrRQR$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

References

Koenker, Roger, Machado, F. JA (1999). “Goodness of Fit and Related Inference Processes for Quantile Regression.” Journal of the American Statistical Association, 94(448), 1296–1310. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1999.10473882")}.

See Also

Other Measure: Measure, MeasureClassif, MeasureRegr, MeasureSimilarity, mlr_measures, mlr_measures_aic, mlr_measures_bic, mlr_measures_classif.costs, mlr_measures_debug_classif, mlr_measures_elapsed_time, mlr_measures_internal_valid_score, mlr_measures_oob_error, mlr_measures_regr.pinball, mlr_measures_regr.rsq, mlr_measures_selected_features


mlr3 documentation built on Sept. 14, 2025, 1:08 a.m.