Polynomial Regression Learner

Polynomial regression without interactions between features. Calls stats::lm() from base package 'stats' on a model formula in which every feature is expanded with stats::poly(). For polynomial regression that also includes interaction terms, see regr.polyFit.

Initial parameter values

• degree

  • Actual default: 1

  • Adjusted default: 2

  • Reason for change: A degree of 1 is plain linear regression, so the lowest degree that makes this learner differ from stats::lm() is the more useful default.

Polynomial degree

stats::poly() requires the degree of the polynomial to be smaller than the number of distinct values of a feature. To keep the learner usable inside resampling, where individual folds may contain features with few distinct values, the degree is capped per feature at min(degree, <number of distinct values> - 1). Features that are constant in the training data enter the formula untransformed.

Dictionary

This Learner can be instantiated via lrn():

lrn("regr.polynomial")

Meta Information

• Task type: “regr”

• Predict Types: “response”, “se”

• Feature Types: “integer”, “numeric”

• Required Packages: mlr3, mlr3extralearners, 'stats'

Parameters

Id	Type	Default	Levels	Range
degree	integer	1		\([1, \infty)\)
raw	logical	FALSE	TRUE, FALSE	-

References

Hastie, Trevor, Tibshirani, Robert, Friedman, Jerome (2009). The Elements of Statistical Learning, series Springer Series in Statistics, 2 edition. Springer, New York. doi:10.1007/978-0-387-84858-7 .

See also

• Dictionary of Learners: mlr3::mlr_learners.

• as.data.table(mlr_learners) for a table of available Learners in the running session (depending on the loaded packages).

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

• mlr3learners for a selection of recommended learners.

• mlr3cluster for unsupervised clustering learners.

• mlr3pipelines to combine learners with pre- and postprocessing steps.

• mlr3tuning for tuning of hyperparameters, mlr3tuningspaces for established default tuning spaces.

Author

imanechadli2003

Super classes

mlr3::Learner -> mlr3::LearnerRegr -> LearnerRegrPolynomial

Methods

Public methods

• LearnerRegrPolynomial$new()

• LearnerRegrPolynomial$clone()

Inherited methods

• mlr3::Learner$base_learner()
• mlr3::Learner$configure()
• mlr3::Learner$encapsulate()
• mlr3::Learner$format()
• mlr3::Learner$help()
• mlr3::Learner$predict()
• mlr3::Learner$predict_newdata()
• mlr3::Learner$print()
• mlr3::Learner$reset()
• mlr3::Learner$selected_features()
• mlr3::Learner$train()
• mlr3::LearnerRegr$predict_newdata_fast()

---

LearnerRegrPolynomial$new()

Creates a new instance of this R6 class.

Usage

LearnerRegrPolynomial$new()

---

LearnerRegrPolynomial$clone()

The objects of this class are cloneable with this method.

Usage

LearnerRegrPolynomial$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Define the Learner
learner = lrn("regr.polynomial")
print(learner)
#> 
#> ── <LearnerRegrPolynomial> (regr.polynomial): Polynomial Regression ────────────
#> • Model: -
#> • Parameters: degree=2
#> • Packages: mlr3, mlr3extralearners, and stats
#> • Predict Types: [response] and se
#> • Feature Types: integer and numeric
#> • Encapsulation: none (fallback: -)
#> • Properties: weights
#> • Other settings: use_weights = 'use', predict_raw = 'FALSE'

# Define a Task
task = tsk("mtcars")

# Create train and test set
ids = partition(task)

# Train the learner on the training ids
learner$train(task, row_ids = ids$train)

print(learner$model)
#> 
#> Call:
#> stats::lm(formula = formula, data = data, weights = private$.get_weights(task))
#> 
#> Coefficients:
#>                          (Intercept)     poly(am, degree = 1, raw = FALSE)  
#>                               19.581                                 5.901  
#> poly(carb, degree = 2, raw = FALSE)1  poly(carb, degree = 2, raw = FALSE)2  
#>                               -1.552                                -9.264  
#>  poly(cyl, degree = 2, raw = FALSE)1   poly(cyl, degree = 2, raw = FALSE)2  
#>                               11.388                                -1.374  
#> poly(disp, degree = 2, raw = FALSE)1  poly(disp, degree = 2, raw = FALSE)2  
#>                                3.027                                 8.333  
#> poly(drat, degree = 2, raw = FALSE)1  poly(drat, degree = 2, raw = FALSE)2  
#>                               -3.880                                -4.924  
#> poly(gear, degree = 2, raw = FALSE)1  poly(gear, degree = 2, raw = FALSE)2  
#>                                8.728                                 6.738  
#>   poly(hp, degree = 2, raw = FALSE)1    poly(hp, degree = 2, raw = FALSE)2  
#>                                3.802                                 3.229  
#> poly(qsec, degree = 2, raw = FALSE)1  poly(qsec, degree = 2, raw = FALSE)2  
#>                               23.356                                 2.530  
#>    poly(vs, degree = 1, raw = FALSE)    poly(wt, degree = 2, raw = FALSE)1  
#>                               -6.116                               -33.407  
#>   poly(wt, degree = 2, raw = FALSE)2  
#>                               -2.658  
#> 


# Make predictions for the test rows
predictions = learner$predict(task, row_ids = ids$test)

# Score the predictions
predictions$score()
#> regr.mse 
#> 57.09187