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

---

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

if (requireNamespace("DiceKriging", quietly = TRUE)) {
# Define the Learner and set parameter values
learner = lrn("regr.km")
print(learner)

# 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 the model
print(learner$model)

# 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()
}
#> <LearnerRegrKM:regr.km>: Kriging
#> * Model: -
#> * Parameters: list()
#> * Packages: mlr3, mlr3learners, DiceKriging
#> * Predict Types:  [response], se
#> * Feature Types: logical, integer, numeric
#> * Properties: -
#> 
#> 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 4.34 4 566 16.8 2 7.618 
#>   - best initial criterion value(s) :  -58.39364 
#> 
#> N = 10, M = 5 machine precision = 2.22045e-16
#> At X0, 0 variables are exactly at the bounds
#> At iterate     0  f=       58.394  |proj g|=      0.65458
#> At iterate     1  f =       58.174  |proj g|=       0.78365
#> At iterate     2  f =       58.053  |proj g|=       0.20068
#> At iterate     3  f =       58.003  |proj g|=       0.17351
#> At iterate     4  f =       57.483  |proj g|=       0.14905
#> At iterate     5  f =       57.466  |proj g|=      0.070431
#> At iterate     6  f =       57.453  |proj g|=       0.12724
#> At iterate     7  f =       57.414  |proj g|=      0.063327
#> At iterate     8  f =        57.38  |proj g|=      0.058924
#> At iterate     9  f =       57.199  |proj g|=       0.20806
#> At iterate    10  f =       57.171  |proj g|=       0.16029
#> At iterate    11  f =       57.161  |proj g|=      0.051045
#> At iterate    12  f =       57.155  |proj g|=      0.098034
#> At iterate    13  f =       57.149  |proj g|=      0.076632
#> At iterate    14  f =       57.146  |proj g|=      0.023702
#> At iterate    15  f =       57.143  |proj g|=      0.072994
#> At iterate    16  f =       57.136  |proj g|=       0.15658
#> At iterate    17  f =       57.117  |proj g|=       0.26162
#> At iterate    18  f =       57.077  |proj g|=       0.33895
#> At iterate    19  f =       57.018  |proj g|=       0.17888
#> At iterate    20  f =       57.009  |proj g|=       0.12259
#> At iterate    21  f =       57.008  |proj g|=       0.04601
#> At iterate    22  f =       57.007  |proj g|=        0.0161
#> At iterate    23  f =       57.007  |proj g|=      0.016285
#> At iterate    24  f =       57.006  |proj g|=       0.04721
#> At iterate    25  f =       57.004  |proj g|=       0.10892
#> At iterate    26  f =       56.999  |proj g|=       0.22179
#> At iterate    27  f =        56.99  |proj g|=       0.29589
#> At iterate    28  f =       56.985  |proj g|=       0.18398
#> At iterate    29  f =        56.98  |proj g|=       0.01533
#> At iterate    30  f =        56.98  |proj g|=       0.02337
#> At iterate    31  f =       56.979  |proj g|=      0.068303
#> At iterate    32  f =       56.976  |proj g|=       0.12392
#> At iterate    33  f =       56.969  |proj g|=       0.20846
#> At iterate    34  f =       56.953  |proj g|=       0.31837
#> At iterate    35  f =       56.907  |proj g|=       0.39657
#> At iterate    36  f =       56.785  |proj g|=        0.5768
#> At iterate    37  f =       56.616  |proj g|=       0.69008
#> At iterate    38  f =       56.357  |proj g|=       0.50184
#> At iterate    39  f =       56.286  |proj g|=       0.22707
#> At iterate    40  f =       56.242  |proj g|=       0.50681
#> At iterate    41  f =        56.14  |proj g|=        1.1696
#> At iterate    42  f =       56.018  |proj g|=        1.5842
#> At iterate    43  f =       55.983  |proj g|=       0.73268
#> At iterate    44  f =       55.902  |proj g|=       0.44156
#> At iterate    45  f =       55.855  |proj g|=       0.40828
#> At iterate    46  f =       55.842  |proj g|=      0.037859
#> At iterate    47  f =       55.838  |proj g|=      0.080262
#> At iterate    48  f =       55.833  |proj g|=        0.1956
#> At iterate    49  f =        55.82  |proj g|=       0.27206
#> At iterate    50  f =       55.802  |proj g|=       0.21758
#> At iterate    51  f =       55.796  |proj g|=      0.050006
#> At iterate    52  f =       55.795  |proj g|=      0.061304
#> At iterate    53  f =       55.793  |proj g|=       0.11254
#> At iterate    54  f =       55.787  |proj g|=       0.25647
#> At iterate    55  f =       55.772  |proj g|=       0.46121
#> At iterate    56  f =       55.743  |proj g|=       0.77069
#> At iterate    57  f =       55.718  |proj g|=       0.58626
#> At iterate    58  f =       55.685  |proj g|=       0.06202
#> At iterate    59  f =       55.684  |proj g|=       0.02268
#> At iterate    60  f =       55.684  |proj g|=      0.083878
#> At iterate    61  f =       55.683  |proj g|=      0.024401
#> At iterate    62  f =       55.682  |proj g|=     0.0016686
#> At iterate    63  f =       55.682  |proj g|=     0.0016702
#> At iterate    64  f =       55.682  |proj g|=     0.0016726
#> At iterate    65  f =       55.682  |proj g|=     0.0065732
#> At iterate    66  f =       55.682  |proj g|=     0.0067642
#> At iterate    67  f =       55.682  |proj g|=      0.008156
#> At iterate    68  f =       55.682  |proj g|=      0.011045
#> At iterate    69  f =       55.682  |proj g|=      0.044371
#> At iterate    70  f =       55.681  |proj g|=      0.043548
#> At iterate    71  f =       55.677  |proj g|=       0.04273
#> At iterate    72  f =       55.668  |proj g|=        0.2078
#> At iterate    73  f =       55.651  |proj g|=       0.28109
#> At iterate    74  f =       55.603  |proj g|=       0.58369
#> At iterate    75  f =       55.541  |proj g|=        0.3966
#> At iterate    76  f =       55.418  |proj g|=         0.539
#> At iterate    77  f =       55.381  |proj g|=       0.51935
#> At iterate    78  f =       55.361  |proj g|=      0.053448
#> At iterate    79  f =        55.36  |proj g|=      0.005173
#> At iterate    80  f =        55.36  |proj g|=    0.00028756
#> At iterate    81  f =        55.36  |proj g|=    8.3708e-05
#> 
#> iterations 81
#> function evaluations 90
#> segments explored during Cauchy searches 84
#> BFGS updates skipped 0
#> active bounds at final generalized Cauchy point 7
#> norm of the final projected gradient 8.37075e-05
#> final function value 55.3604
#> 
#> F = 55.3604
#> final  value 55.360421 
#> converged
#> 
#> Call:
#> DiceKriging::km(design = data, response = task$truth(), control = pv$control)
#> 
#> Trend  coeff.:
#>                Estimate
#>  (Intercept)    20.5212
#> 
#> Covar. type  : matern5_2 
#> Covar. coeff.:
#>                Estimate
#>    theta(am)     0.0000
#>  theta(carb)    14.0000
#>   theta(cyl)     8.0000
#>  theta(disp)   801.8000
#>  theta(drat)     1.0804
#>  theta(gear)     4.0000
#>    theta(hp)   566.0000
#>  theta(qsec)     1.3130
#>    theta(vs)     2.0000
#>    theta(wt)     3.2168
#> 
#> Variance estimate: 31.82454
#> regr.mse 
#> 16.72725