Measure to compare true observed response with predicted response in regression tasks.
Details
R Squared is defined as $$ 1 - \frac{\sum_{i=1}^n w_i \left( t_i - r_i \right)^2}{\sum_{i=1}^n w_i \left( t_i - \bar{t} \right)^2}, $$ where \(\bar{t} = \frac{1}{n} \sum_{i=1}^n t_i\) and \(w_i\) are weights.
Also known as coefficient of determination or explained variation. It compares the squared error of the predictions relative to a naive model predicting the mean.
Note that weights are used to scale the squared error of individual predictions (both in the numerator and in the denominator), but the "plug in" value \(\bar{t}\) is computed without weights.
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():
Meta Information
Task type: “regr”
Range: \((-\infty, 1]\)
Minimize: FALSE
Average: macro
Required Prediction: “response”
Required Packages: mlr3
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_selected_features
Super classes
mlr3::Measure -> mlr3::MeasureRegr -> MeasureRSQ
Methods
Method new()
Creates a new instance of this R6 class.
Usage
MeasureRegrRSQ$new(pred_set_mean = TRUE)