Measure to compare true observed response with predicted quantiles in regression tasks.
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")
Task type: “regr”
Range: \((-\infty, 1]\)
Minimize: FALSE
Average: macro
Required Prediction: “quantiles”
Required Packages: mlr3
| Id | Type | Default | Range |
| alpha | numeric | - | \([0, 1]\) |
mlr3::Measure -> mlr3::MeasureRegr -> MeasureRQR
new()Creates a new instance of this R6 class.
MeasureRegrRQR$new(alpha = 0.5, pred_set_mean = TRUE)alphanumeric(1)
The quantile for which to compute the measure.
Must be one of the quantiles that the Learner was trained on.
pred_set_meanlogical(1)
If TRUE, the mean of the true values is calculated on the prediction set.
If FALSE, the mean of the true values is calculated on the training set.
clone()The objects of this class are cloneable with this method.
MeasureRegrRQR$clone(deep = FALSE)deepWhether to make a deep clone.
\(R^1(\alpha)\) 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 \(t\).
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. tools:::Rd_expr_doi("10.1080/01621459.1999.10473882").
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