mlr_measures_regr.rqr: R-Squared for Quantile Regression

In mlr3: Machine Learning in R - Next Generation

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

Measure -> MeasureRegr -> MeasureRegrRQR

Active bindings

pred_set_mean

(logical(1))
Whether the empirical quantile is calculated on the prediction set. Set during construction.

Methods

Public methods

• MeasureRegrRQR$new()

• MeasureRegrRQR$clone()

Inherited methods

• Measure$aggregate()
• Measure$format()
• Measure$help()
• Measure$obs_loss()
• Measure$print()
• Measure$score()

---

MeasureRegrRQR$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.

---

MeasureRegrRQR$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

• Chapter in the mlr3book: https://mlr3book.mlr-org.com/chapters/chapter2/data_and_basic_modeling.html#sec-eval

• Package mlr3measures for the scoring functions. Dictionary of Measures: mlr_measures as.data.table(mlr_measures) for a table of available Measures in the running session (depending on the loaded packages).

• Extension packages for additional task types:

  • mlr3proba for probabilistic supervised regression and survival analysis.

  • mlr3cluster for unsupervised clustering.

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 June 11, 2026, 5:08 p.m.