Kriging Regression Learner

Kriging regression. Calls DiceKriging::km() from package DiceKriging.

• The predict type hyperparameter "type" defaults to "SK" (simple kriging).

• The additional hyperparameter nugget.stability is used to overwrite the hyperparameter nugget with nugget.stability * var(y) before training to improve the numerical stability. We recommend a value of 1e-8.

• The additional hyperparameter jitter can be set to add N(0, [jitter])-distributed noise to the data before prediction to avoid perfect interpolation. We recommend a value of 1e-12.

Dictionary

This mlr3::Learner can be instantiated via the dictionary mlr3::mlr_learners or with the associated sugar function mlr3::lrn():

mlr_learners$get("regr.km")
lrn("regr.km")

Meta Information

• Task type: “regr”

• Predict Types: “response”, “se”

• Feature Types: “logical”, “integer”, “numeric”

• Required Packages: mlr3, mlr3learners, DiceKriging

Parameters

Id	Type	Default	Levels	Range
bias.correct	logical	FALSE	TRUE, FALSE	-
checkNames	logical	TRUE	TRUE, FALSE	-
coef.cov	untyped	NULL		-
coef.trend	untyped	NULL		-
coef.var	untyped	NULL		-
control	untyped	NULL		-
cov.compute	logical	TRUE	TRUE, FALSE	-
covtype	character	matern5_2	gauss, matern5_2, matern3_2, exp, powexp	-
estim.method	character	MLE	MLE, LOO	-
gr	logical	TRUE	TRUE, FALSE	-
iso	logical	FALSE	TRUE, FALSE	-
jitter	numeric	0		\([0, \infty)\)
kernel	untyped	NULL		-
knots	untyped	NULL		-
light.return	logical	FALSE	TRUE, FALSE	-
lower	untyped	NULL		-
multistart	integer	1		\((-\infty, \infty)\)
noise.var	untyped	NULL		-
nugget	numeric	-		\((-\infty, \infty)\)
nugget.estim	logical	FALSE	TRUE, FALSE	-
nugget.stability	numeric	0		\([0, \infty)\)
optim.method	character	BFGS	BFGS, gen	-
parinit	untyped	NULL		-
penalty	untyped	NULL		-
scaling	logical	FALSE	TRUE, FALSE	-
se.compute	logical	TRUE	TRUE, FALSE	-
type	character	SK	SK, UK	-
upper	untyped	NULL		-

References

Roustant O, Ginsbourger D, Deville Y (2012). “DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization.” Journal of Statistical Software, 51(1), 1–55. doi:10.18637/jss.v051.i01 .

See also

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

• Package mlr3extralearners for more learners.

• 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).

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

• Extension packages for additional task types:

  • mlr3proba for probabilistic supervised regression and survival analysis.

  • mlr3cluster for unsupervised clustering.

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

Other Learner: mlr_learners_classif.cv_glmnet, mlr_learners_classif.glmnet, mlr_learners_classif.kknn, mlr_learners_classif.lda, mlr_learners_classif.log_reg, mlr_learners_classif.multinom, mlr_learners_classif.naive_bayes, mlr_learners_classif.nnet, mlr_learners_classif.qda, mlr_learners_classif.ranger, mlr_learners_classif.svm, mlr_learners_classif.xgboost, mlr_learners_regr.cv_glmnet, mlr_learners_regr.glmnet, mlr_learners_regr.kknn, mlr_learners_regr.lm, mlr_learners_regr.nnet, mlr_learners_regr.ranger, mlr_learners_regr.svm, mlr_learners_regr.xgboost

Super classes

mlr3::Learner -> mlr3::LearnerRegr -> LearnerRegrKM

Methods

Public methods

• LearnerRegrKM$new()

• LearnerRegrKM$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()

---

Method new()

Creates a new instance of this R6 class.

Usage

LearnerRegrKM$new()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerRegrKM$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Define the Learner and set parameter values
learner = lrn("regr.km")
print(learner)
#> 
#> ── <LearnerRegrKM> (regr.km): Kriging ──────────────────────────────────────────
#> • Model: -
#> • Parameters: list()
#> • Packages: mlr3, mlr3learners, and DiceKriging
#> • Predict Types: [response] and se
#> • Feature Types: logical, integer, and numeric
#> • Encapsulation: none (fallback: -)
#> • Properties:
#> • Other settings: use_weights = 'error'

# 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)
#> 
#> optimisation start
#> ------------------
#> * estimation method   : MLE 
#> * optimisation method : BFGS 
#> * analytical gradient : used
#> * trend model : ~1
#> * covariance model : 
#>   - type :  matern5_2 
#>   - nugget : NO
#>   - parameters lower bounds :  1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 
#>   - parameters upper bounds :  2 14 8 801.8 4 4 566 10.82 2 7.822 
#>   - best initial criterion value(s) :  -59.07016 
#> 
#> N = 10, M = 5 machine precision = 2.22045e-16
#> At X0, 0 variables are exactly at the bounds
#> At iterate     0  f=        59.07  |proj g|=       1.5851
#> At iterate     1  f =        58.47  |proj g|=        1.4468
#> At iterate     2  f =       57.682  |proj g|=        1.1083
#> At iterate     3  f =        57.31  |proj g|=        1.4804
#> At iterate     4  f =       57.102  |proj g|=       0.22804
#> At iterate     5  f =       57.072  |proj g|=       0.12852
#> At iterate     6  f =       57.023  |proj g|=      0.092505
#> At iterate     7  f =       56.993  |proj g|=      0.082785
#> At iterate     8  f =       56.942  |proj g|=      0.078875
#> At iterate     9  f =       56.935  |proj g|=        0.3505
#> At iterate    10  f =       56.925  |proj g|=      0.075868
#> At iterate    11  f =       56.914  |proj g|=      0.071404
#> At iterate    12  f =       56.904  |proj g|=      0.065766
#> At iterate    13  f =       56.874  |proj g|=      0.056692
#> At iterate    14  f =       56.843  |proj g|=         0.183
#> At iterate    15  f =       56.834  |proj g|=      0.069327
#> At iterate    16  f =       56.816  |proj g|=      0.079876
#> At iterate    17  f =       56.791  |proj g|=       0.17252
#> At iterate    18  f =       56.741  |proj g|=       0.23101
#> At iterate    19  f =         56.7  |proj g|=      0.078292
#> At iterate    20  f =       56.699  |proj g|=       0.42973
#> At iterate    21  f =       56.692  |proj g|=           0.1
#> At iterate    22  f =       56.692  |proj g|=      0.020136
#> At iterate    23  f =       56.692  |proj g|=      0.019801
#> At iterate    24  f =       56.691  |proj g|=      0.016019
#> At iterate    25  f =       56.691  |proj g|=      0.012699
#> At iterate    26  f =        56.69  |proj g|=     0.0086906
#> At iterate    27  f =        56.69  |proj g|=      0.020358
#> At iterate    28  f =        56.69  |proj g|=     0.0095171
#> At iterate    29  f =        56.69  |proj g|=     0.0014117
#> At iterate    30  f =        56.69  |proj g|=     0.0011036
#> At iterate    31  f =        56.69  |proj g|=     0.0007854
#> At iterate    32  f =        56.69  |proj g|=    0.00059486
#> At iterate    33  f =        56.69  |proj g|=    0.00059486
#> At iterate    34  f =        56.69  |proj g|=     0.0041266
#> At iterate    35  f =        56.69  |proj g|=     0.0029411
#> At iterate    36  f =        56.69  |proj g|=     0.0039306
#> At iterate    37  f =        56.69  |proj g|=     0.0052101
#> At iterate    38  f =        56.69  |proj g|=      0.005922
#> At iterate    39  f =       56.689  |proj g|=      0.042845
#> At iterate    40  f =       56.689  |proj g|=      0.037171
#> At iterate    41  f =       56.688  |proj g|=       0.20109
#> At iterate    42  f =       56.685  |proj g|=      0.068051
#> At iterate    43  f =       56.682  |proj g|=      0.052802
#> At iterate    44  f =        56.68  |proj g|=      0.077905
#> At iterate    45  f =       56.674  |proj g|=       0.11328
#> At iterate    46  f =       56.662  |proj g|=        0.3624
#> At iterate    47  f =        56.64  |proj g|=       0.13956
#> At iterate    48  f =       56.631  |proj g|=       0.11137
#> At iterate    49  f =       56.623  |proj g|=      0.082252
#> At iterate    50  f =       56.619  |proj g|=       0.41233
#> At iterate    51  f =       56.611  |proj g|=      0.096519
#> At iterate    52  f =       56.609  |proj g|=      0.057431
#> At iterate    53  f =       56.609  |proj g|=      0.078522
#> At iterate    54  f =       56.607  |proj g|=       0.11328
#> At iterate    55  f =       56.606  |proj g|=      0.026921
#> At iterate    56  f =       56.606  |proj g|=     0.0044438
#> At iterate    57  f =       56.606  |proj g|=     0.0020148
#> At iterate    58  f =       56.606  |proj g|=     0.0021817
#> At iterate    59  f =       56.606  |proj g|=     0.0077769
#> At iterate    60  f =       56.606  |proj g|=     0.0017723
#> At iterate    61  f =       56.606  |proj g|=    0.00017898
#> At iterate    62  f =       56.606  |proj g|=    0.00018164
#> 
#> iterations 62
#> function evaluations 68
#> segments explored during Cauchy searches 63
#> BFGS updates skipped 0
#> active bounds at final generalized Cauchy point 4
#> norm of the final projected gradient 0.000181643
#> final function value 56.6056
#> 
#> F = 56.6056
#> final  value 56.605601 
#> converged

# Print the model
print(learner$model)
#> 
#> Call:
#> DiceKriging::km(design = data, response = truth, control = pv$control)
#> 
#> Trend  coeff.:
#>                Estimate
#>  (Intercept)    20.9518
#> 
#> Covar. type  : matern5_2 
#> Covar. coeff.:
#>                Estimate
#>    theta(am)     1.3090
#>  theta(carb)    14.0000
#>   theta(cyl)     8.0000
#>  theta(disp)   801.8000
#>  theta(drat)     2.3370
#>  theta(gear)     2.3296
#>    theta(hp)   565.1725
#>  theta(qsec)     1.1729
#>    theta(vs)     2.0000
#>    theta(wt)     2.4287
#> 
#> Variance estimate: 41.95229

# Importance method
if ("importance" %in% learner$properties) print(learner$importance())

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

# Score the predictions
predictions$score()
#> regr.mse 
#> 4.053721