# mlrCPO Core

#### Martin Binder

#### 2020-04-06

#### CPO Vignette Navigation

1. First Steps (compact version)
2. mlrCPO Core (compact version)
3. CPOs Built Into mlrCPO (compact version)
4. Building Custom CPOs (compact version)

## Table of Contents

## Introduction

This vignette is supposed to be a short reference of the primitives and tools supplied by the `mlrCPO` package.

## Lifecycle of a CPO

CPOs are first-class objects in R that represent data manipulation. They can be combined to form networks of operation, they can be attached to `mlr` `Learner`s, and they have tunable Hyperparameters that influence their behaviour. `CPO`s go through a lifecycle from construction to `CPO` to a `CPOTrained` “retrafo” or “inverter” object. The different stages of a `CPO` related object can be distinguished using `getCPOClass()`, which takes one of five values:

    getCPOClass(cpoPca)
    #> [1] "CPOConstructor"
    getCPOClass(cpoPca())
    #> [1] "CPO"
    getCPOClass(pid.task %>|% cpoPca())
    #> [1] "CPORetrafo"
    getCPOClass(inverter(bh.task %>>% cpoLogTrafoRegr()))
    #> [1] "CPOInverter"
    getCPOClass(NULLCPO)
    #> [1] "NULLCPO"

### CPOConstructor

`CPO`s are created using `CPOConstructor`s. These are R functions with a print function and many parameters in common.

    print(cpoAsNumeric)  # example CPOConstructor
    #> <<CPO as.numeric()>>
    print(cpoAsNumeric, verbose = TRUE)  # alternative: !cpoAsNumeric
    #> <<CPO as.numeric()>>
    #>
    #> cpo.retrafo:
    #> function (data)
    #> {
    #>     as.data.frame(lapply(data, as.numeric), row.names = rownames(data))
    #> }
    #> <environment: namespace:mlrCPO>
    class(cpoAsNumeric)
    #> [1] "CPOConstructor" "function"
    getCPOName(cpoPca)  # same as getCPOName() of the *constructed* CPO
    #> [1] "pca"
    getCPOClass(cpoPca)
    #> [1] "CPOConstructor"

The function parameters of a `CPOConstructor`

- set the `CPO` Hyperparameters
- set the `CPO` `id` (default to the `CPO`’s `name`)
- resetrict the data columns a CPO operates on (`affect.*` parameters)
- control which of the `CPO`’s hyperparameters are “exported”, i.e. can late be manipulated using `setHyperPars()`.

    names(formals(cpoPca))
    #>  [1] "center"                     "scale"
    #>  [3] "tol"                        "rank"
    #>  [5] "id"                         "export"
    #>  [7] "affect.type"                "affect.index"
    #>  [9] "affect.names"               "affect.pattern"
    #> [11] "affect.invert"              "affect.pattern.ignore.case"
    #> [13] "affect.pattern.perl"        "affect.pattern.fixed"

### CPO

    (cpo = cpoScale()) # construct CPO with default Hyperparameter values
    #> scale(center = TRUE, scale = TRUE)
    print(cpo, verbose = TRUE)  # detailed printing. Alternative: !cpo
    #> Trafo chain of 1 cpos:
    #> scale(center = TRUE, scale = TRUE)
    #> Operating: feature
    #> ParamSet:
    #>                 Type len  Def Constr Req Tunable Trafo
    #> scale.center logical   - TRUE      -   -    TRUE     -
    #> scale.scale  logical   - TRUE      -   -    TRUE     -
    class(cpo)  # CPOs that are not compound are "CPOPrimitive"
    #> [1] "CPOPrimitive" "CPO"
    getCPOClass(cpo)
    #> [1] "CPO"

#### Functions that work on CPOs

The inner “state” of a `CPO` can be inspected and manipulated using various getters and setters.

    getParamSet(cpo)
    #>                 Type len  Def Constr Req Tunable Trafo
    #> scale.center logical   - TRUE      -   -    TRUE     -
    #> scale.scale  logical   - TRUE      -   -    TRUE     -
    getHyperPars(cpo)
    #> $scale.center
    #> [1] TRUE
    #>
    #> $scale.scale
    #> [1] TRUE
    setHyperPars(cpo, scale.center = FALSE)
    #> scale(center = FALSE, scale = TRUE)
    getCPOId(cpo)
    #> [1] "scale"
    setCPOId(cpo, "MYID")
    #> MYID<scale>(center = TRUE, scale = TRUE)
    getCPOName(cpo)
    #> [1] "scale"
    getCPOAffect(cpo)  # empty, since no affect set
    #> named list()
    getCPOAffect(cpoPca(affect.pattern = "Width$"))
    #> $pattern
    #> [1] "Width$"
    getCPOConstructor(cpo)  # the constructor used to create the CPO
    #> <<CPO scale(center = TRUE, scale = TRUE)>>
    getCPOProperties(cpo)  # see properties explanation below
    #> $handling
    #>  [1] "numerics"   "factors"    "ordered"    "missings"   "cluster"
    #>  [6] "classif"    "multilabel" "regr"       "surv"       "oneclass"
    #> [11] "twoclass"   "multiclass" "prob"       "se"
    #>
    #> $adding
    #> character(0)
    #>
    #> $needed
    #> character(0)
    getCPOPredictType(cpo)
    #>   response       prob         se
    #> "response"     "prob"       "se"
    getCPOClass(cpo)
    #> [1] "CPO"
    getCPOOperatingType(cpo)  # Operating on feature, target, retrafoless?
    #> [1] "feature"

Compare the predict type and operating type of a TOCPO or ROCPO:

    getCPOPredictType(cpoResponseFromSE())
    #> response       se
    #>     "se"     "se"
    getCPOOperatingType(cpoResponseFromSE())
    #> [1] "target"
    getCPOOperatingType(cpoSample())
    #> [1] "retrafoless"

The `identicalCPO()` function is used to check whether the underlying operation of two `CPO`s is identical. For this understanding, `CPO`s with different hyperparameters can still be “identical”.

    identicalCPO(cpoScale(scale = TRUE), cpoScale(scale = FALSE))
    #> [1] TRUE
    identicalCPO(cpoScale(), cpoPca())
    #> [1] FALSE

#### CPO Application

`CPO`s can be applied to `data.frame` and `Task` objects using `%>>%` or `applyCPO`.

    head(iris) %>>% cpoPca()
    #>   Species        PC1          PC2         PC3           PC4
    #> 1  setosa -0.1634147  0.017230444 -0.11038321 -0.0231625616
    #> 2  setosa  0.3324970 -0.189351624 -0.08152883  0.0005612917
    #> 3  setosa  0.3268659  0.101103375 -0.02238439  0.0464537730
    #> 4  setosa  0.4202367  0.005523981  0.17106514 -0.0222757931
    #> 5  setosa -0.1768684  0.140149101 -0.04185224 -0.0194870755
    #> 6  setosa -0.7393165 -0.074655279  0.08508352  0.0179103657
    task = applyCPO(cpoPca(), iris.task)
    head(getTaskData(task))
    #>   Species       PC1        PC2         PC3          PC4
    #> 1  setosa -2.684126 -0.3193972  0.02791483  0.002262437
    #> 2  setosa -2.714142  0.1770012  0.21046427  0.099026550
    #> 3  setosa -2.888991  0.1449494 -0.01790026  0.019968390
    #> 4  setosa -2.745343  0.3182990 -0.03155937 -0.075575817
    #> 5  setosa -2.728717 -0.3267545 -0.09007924 -0.061258593
    #> 6  setosa -2.280860 -0.7413304 -0.16867766 -0.024200858

#### CPO Composition

`CPO` composition can be done using `%>>%` or `composeCPO`. It results in a new CPO which mostly behaves like a primitive CPO. Exceptions are:

- Compound CPOs have no `id`
- Affect of compound CPOs cannot be retrieved

    scale = cpoScale()
    pca = cpoPca()

    compound = scale %>>% pca
    composeCPO(scale, pca)  # same
    #> (scale >> pca)(scale.center = TRUE, scale.scale = TRUE, pca.center = TRUE, pca.scale = FALSE)
    class(compound)
    #> [1] "CPOPipeline" "CPO"
    !compound
    #> Trafo chain of 2 cpos:
    #> scale(center = TRUE, scale = TRUE)
    #> Operating: feature
    #> ParamSet:
    #>                 Type len  Def Constr Req Tunable Trafo
    #> scale.center logical   - TRUE      -   -    TRUE     -
    #> scale.scale  logical   - TRUE      -   -    TRUE     -
    #>   ====>
    #> pca(center = TRUE, scale = FALSE)[not exp'd: tol = <NULL>, rank = <NULL>]
    #> Operating: feature
    #> ParamSet:
    #>               Type len   Def Constr Req Tunable Trafo
    #> pca.center logical   -  TRUE      -   -    TRUE     -
    #> pca.scale  logical   - FALSE      -   -    TRUE     -
    getCPOName(compound)
    #> [1] "pca.scale"
    getHyperPars(compound)
    #> $scale.center
    #> [1] TRUE
    #>
    #> $scale.scale
    #> [1] TRUE
    #>
    #> $pca.center
    #> [1] TRUE
    #>
    #> $pca.scale
    #> [1] FALSE
    setHyperPars(compound, scale.center = TRUE, pca.center = FALSE)
    #> (scale >> pca)(scale.center = TRUE, scale.scale = TRUE, pca.center = FALSE, pca.scale = FALSE)

    getCPOId(compound)  # error: no ID for compound CPOs
    #> Error in getCPOId.CPO(compound): Compound CPOs have no IDs.
    getCPOAffect(compound)  # error: no affect for compound CPOs
    #> Error in getCPOAffect.CPO(compound): Compound CPOs have no affect arguments.

`getCPOOperatingType()` always considers the operating type of the whole `CPO` chain and may return multiple values:

    getCPOOperatingType(NULLCPO)
    #> character(0)
    getCPOOperatingType(cpoScale())
    #> [1] "feature"
    getCPOOperatingType(cpoScale() %>>% cpoLogTrafoRegr() %>>% cpoSample())
    #> [1] "feature"     "target"      "retrafoless"

#### Compound CPO Chaining and Decomposition

Composite `CPO` objects can be broken into their constituent primitive `CPO`s using `as.list()`. The inverse of this operation is `pipeCPO()`, which composes a list of `CPO`s in the given order.

    as.list(compound)
    #> [[1]]
    #> scale(center = TRUE, scale = TRUE)
    #>
    #> [[2]]
    #> pca(center = TRUE, scale = FALSE)[not exp'd: tol = <NULL>, rank = <NULL>]
    pipeCPO(as.list(compound))  # chainCPO: (list of CPO) -> CPO
    #> (scale >> pca)(scale.center = TRUE, scale.scale = TRUE, pca.center = TRUE, pca.scale = FALSE)
    pipeCPO(list())
    #> NULLCPO

### CPOLearner

CPO-Learner attachment works using `%>>%` or `attachCPO`.

    lrn = makeLearner("classif.logreg")
    (cpolrn = cpo %>>% lrn)  # the new learner has the CPO hyperparameters
    #> Learner classif.logreg.scale from package stats
    #> Type: classif
    #> Name: ; Short name:
    #> Class: CPOLearner
    #> Properties: numerics,factors,twoclass,prob
    #> Predict-Type: response
    #> Hyperparameters: model=FALSE
    attachCPO(compound, lrn)  # attaching compound CPO
    #> Learner classif.logreg.pca.scale from package stats
    #> Type: classif
    #> Name: ; Short name:
    #> Class: CPOLearner
    #> Properties: numerics,factors,twoclass,prob
    #> Predict-Type: response
    #> Hyperparameters: model=FALSE

The new object is a `CPOLearner`, which performs the operation given by the `CPO` before trainign the `Learner`.

    class(lrn)
    #> [1] "classif.logreg"  "RLearnerClassif" "RLearner"        "Learner"

The work performed by a `CPOLearner` can also be performed manually:

    lrn = cpoLogTrafoRegr() %>>% makeLearner("regr.lm")
    model = train(lrn, subsetTask(bh.task, 1:300))
    predict(model, subsetTask(bh.task, 301:500))
    #> Prediction: 200 observations
    #> predict.type: response
    #> threshold:
    #> time: 0.00
    #>     id truth response
    #> 301  1  24.8 28.69715
    #> 302  2  22.0 27.89821
    #> 303  3  26.4 28.33370
    #> 304  4  33.1 33.80868
    #> 305  5  36.1 34.93957
    #> 306  6  28.4 28.77130
    #> ... (#rows: 200, #cols: 3)

is equivalent to

    trafo = subsetTask(bh.task, 1:300) %>>% cpoLogTrafoRegr()
    model = train("regr.lm", trafo)

    newdata = subsetTask(bh.task, 301:500) %>>% retrafo(trafo)
    pred = predict(model, newdata)
    invert(inverter(newdata), pred)
    #> Prediction: 200 observations
    #> predict.type: response
    #> threshold:
    #> time: 0.00
    #>     id truth response
    #> 301  1  24.8 28.69715
    #> 302  2  22.0 27.89821
    #> 303  3  26.4 28.33370
    #> 304  4  33.1 33.80868
    #> 305  5  36.1 34.93957
    #> 306  6  28.4 28.77130
    #> ... (#rows: 200, #cols: 3)

#### CPOLearner Decomposition

It is possible to obtain both the underlying `Learner` and the attached `CPO` from a `CPOLearner`. Note that if a `CPOLearner` is wrapped by some method (e.g. a `TuneWrapper`), this does not work, since `CPO` can not probe below the first wrapping layer.

    getLearnerCPO(cpolrn)  # the CPO
    #> scale(center = TRUE, scale = TRUE)
    getLearnerBare(cpolrn)  # the Learner
    #> Learner classif.logreg from package stats
    #> Type: classif
    #> Name: Logistic Regression; Short name: logreg
    #> Class: classif.logreg
    #> Properties: twoclass,numerics,factors,prob,weights
    #> Predict-Type: response
    #> Hyperparameters: model=FALSE

### CPOTrained

CPOs perform data-dependent operation. However, when this operation becomes part of a machine-learning process, the operation on predict-data must depend only on the training data. A `CPORetrafo` object represents the re-application of a trained CPO. A `CPOInverter` object represents the transformation of a prediction made on a transformed task back to the form of the original data.

The `CPOTrained` objects generated by application of a `CPO` (or application of another `CPOTrained`) can be retrieved using the `retrafo()` or the `inverter()` function.

    transformed = iris %>>% cpoScale()
    head(transformed)
    #>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
    #> 1   -0.8976739  1.01560199    -1.335752   -1.311052  setosa
    #> 2   -1.1392005 -0.13153881    -1.335752   -1.311052  setosa
    #> 3   -1.3807271  0.32731751    -1.392399   -1.311052  setosa
    #> 4   -1.5014904  0.09788935    -1.279104   -1.311052  setosa
    #> 5   -1.0184372  1.24503015    -1.335752   -1.311052  setosa
    #> 6   -0.5353840  1.93331463    -1.165809   -1.048667  setosa
    (ret = retrafo(transformed))
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]

    head(getTaskTargets(bh.task))
    #> [1] 24.0 21.6 34.7 33.4 36.2 28.7
    transformed = bh.task %>>% cpoLogTrafoRegr()
    head(getTaskTargets(transformed))
    #> [1] 3.178054 3.072693 3.546740 3.508556 3.589059 3.356897
    (inv = inverter(transformed))
    #> CPO Inverter chain {type:regr} (able to predict 'response', 'se')
    #> [INVERTER fun.apply.regr.target(){type:regr}]
    head(invert(inv, getTaskTargets(transformed)))
    #> [1] 24.0 21.6 34.7 33.4 36.2 28.7

Retrafos and inverters are stored as attributes:

    attributes(transformed)
    #> $names
    #> [1] "type"        "env"         "weights"     "blocking"    "coordinates"
    #> [6] "task.desc"
    #>
    #> $class
    #> [1] "RegrTask"       "SupervisedTask" "Task"
    #>
    #> $retrafo
    #> CPO Retrafo / Inverter chain {type:regr} (able to predict 'response', 'se')
    #> [RETRAFO fun.apply.regr.target(){type:regr}]
    #>
    #> $inverter
    #> CPO Inverter chain {type:regr} (able to predict 'response', 'se')
    #> [INVERTER fun.apply.regr.target(){type:regr}]

It is possible to set the `"retrafo"` and `"inverter"` attributes of an object using `retrafo()` and `inverter()`. This can be useful for writing elegant scripts, especially since CPOTrained are automatically chained. To delete the `CPOTrained` attribute of an object, set it to `NULL` or `NULLCPO`, or use `clearRI()`.

    bh2 = bh.task
    retrafo(bh2) = ret
    attributes(bh2)
    #> $names
    #> [1] "type"        "env"         "weights"     "blocking"    "coordinates"
    #> [6] "task.desc"
    #>
    #> $class
    #> [1] "RegrTask"       "SupervisedTask" "Task"
    #>
    #> $retrafo
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]

    retrafo(bh2) = NULLCPO
    # equivalent:
    # retrafo(bh2) = NULL
    attributes(bh2)
    #> $names
    #> [1] "type"        "env"         "weights"     "blocking"    "coordinates"
    #> [6] "task.desc"
    #>
    #> $class
    #> [1] "RegrTask"       "SupervisedTask" "Task"

    # clearRI returns the object without retrafo or inverter attributes
    bh3 = clearRI(transformed)
    attributes(bh3)
    #> $names
    #> [1] "type"        "env"         "weights"     "blocking"    "coordinates"
    #> [6] "task.desc"
    #>
    #> $class
    #> [1] "RegrTask"       "SupervisedTask" "Task"

#### Functions that work on CPOTrained

General methods that work on `CPOTrained` object to inspect its object properties. Many methods that work on a `CPO` also work on a `CPOTrained` and give the same result.

    getCPOName(ret)
    #> [1] "scale"
    getParamSet(ret)
    #>           Type len  Def Constr Req Tunable Trafo
    #> center logical   - TRUE      -   -    TRUE     -
    #> scale  logical   - TRUE      -   -    TRUE     -
    getHyperPars(ret)
    #> $center
    #> [1] TRUE
    #>
    #> $scale
    #> [1] TRUE
    getCPOProperties(ret)
    #> $handling
    #>  [1] "numerics"   "factors"    "ordered"    "missings"   "cluster"
    #>  [6] "classif"    "multilabel" "regr"       "surv"       "oneclass"
    #> [11] "twoclass"   "multiclass" "prob"       "se"
    #>
    #> $adding
    #> character(0)
    #>
    #> $needed
    #> character(0)
    getCPOPredictType(ret)
    #>   response       prob         se
    #> "response"     "prob"       "se"
    getCPOOperatingType(ret)  # Operating on feature, target, both?
    #> [1] "feature"
    getCPOOperatingType(inv)
    #> [1] "target"

A `CPOTrained` has information about whether it can be used as a `CPORetrafo` object (and be applied to new data using `%>>%`), or as a `CPOInverter` object (and used by `invert()`), or possibly both. This is given by `getCPOTrainedCapability()`, which returns a `1` if the object has an effect in the given role, `0` if the object has no effect (but can be used), or `-1` if the object can not be used in the role.

    getCPOTrainedCapability(ret)
    #> retrafo  invert
    #>       1       0
    getCPOTrainedCapability(inv)
    #> retrafo  invert
    #>      -1       1
    getCPOTrainedCapability(NULLCPO)
    #> retrafo  invert
    #>       0       0

The “`CPO` class” of a `CPOTrained` is determined by this as well. A pure inverter is `CPOInverter`, an object that can be used for retrafo is a `CPORetrafo`.

    getCPOClass(ret)
    #> [1] "CPORetrafo"
    getCPOClass(inv)
    #> [1] "CPOInverter"

The `CPO` and the `CPOConstructor` used to create the `CPOTrained can be queried.

    getCPOTrainedCPO(ret)
    #> scale(center = TRUE, scale = TRUE)
    getCPOConstructor(ret)
    #> <<CPO scale(center = TRUE, scale = TRUE)>>

#### CPOTrained Inspection

`CPOTrained` objects can be inspected using `getCPOTrainedState()`. The state contains the hyperparameters, the `control` object (CPO dependent data representing the data information needed to re-apply the operation), and information about the `Task` / `data.frame` layout used for training (column names, column types) in `data$shapeinfo.input` and `data$shapeinfo.output`.

The state can be manipulated and used to create new `CPOTrained`s, using `makeCPOTrainedFromState()`.

    (state = getCPOTrainedState(retrafo(iris %>>% cpoScale())))
    #> $center
    #> [1] TRUE
    #>
    #> $scale
    #> [1] TRUE
    #>
    #> $control
    #> $control$center
    #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width
    #>     5.843333     3.057333     3.758000     1.199333
    #>
    #> $control$scale
    #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width
    #>    0.8280661    0.4358663    1.7652982    0.7622377
    #>
    #>
    #> $data
    #> $data$shapeinfo.input
    #> <ShapeInfo (input) Sepal.Length: num, Sepal.Width: num, Petal.Length: num, Petal.Width: num, Species: fac>
    #>
    #> $data$shapeinfo.output
    #> <ShapeInfo (output)>:
    #> numeric:
    #> <ShapeInfo Sepal.Length: num, Sepal.Width: num, Petal.Length: num, Petal.Width: num>
    #> factor:
    #> <ShapeInfo Species: fac>
    #> other:
    #> <ShapeInfo (empty)>
    state$control$center[1] = 1000  # will now subtract 1000 from the first column
    new.retrafo = makeCPOTrainedFromState(cpoScale, state)
    head(iris %>>% new.retrafo)
    #>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
    #> 1    -1201.474  1.01560199    -1.335752   -1.311052  setosa
    #> 2    -1201.716 -0.13153881    -1.335752   -1.311052  setosa
    #> 3    -1201.957  0.32731751    -1.392399   -1.311052  setosa
    #> 4    -1202.078  0.09788935    -1.279104   -1.311052  setosa
    #> 5    -1201.595  1.24503015    -1.335752   -1.311052  setosa
    #> 6    -1201.112  1.93331463    -1.165809   -1.048667  setosa

#### CPOTrained are Automatically Chained

When executing `data %>>% CPO`, the result has an associated `CPORetrafo` and `CPOInverter` object. When applying another `CPO`, the `CPORetrafo` and `CPOInverter` will be chained automatically. This is to make `(data %>>% CPO1) %>>% CPO2` work the same as `data %>>% (CPO1 %>>% CPO2)`.

    data = head(iris) %>>% cpoPca()
    retrafo(data)
    #> CPO Retrafo chain
    #> [RETRAFO pca(center = TRUE, scale = FALSE)]
    data2 = data %>>% cpoScale()

`retrafo(data2)` is the same as `retrafo(data %>>% pca %>>% scale)`:

    retrafo(data2)
    #> CPO Retrafo chain
    #> [RETRAFO pca(center = TRUE, scale = FALSE)] =>
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]

To interrupt this chain, set retrafo to `NULL` either explicitly, or using `clearRI()`.

    data = clearRI(data)
    data2 = data %>>% cpoScale()
    retrafo(data2)
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]

this is equivalent to

    retrafo(data) = NULL
    inverter(data) = NULL
    data3 = data %>>% cpoScale()
    retrafo(data3)
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]

#### CPOTrained Composition, Decomposition, and Chaining

`CPOTrained` can be composed using `%>>%` and `pipeCPO()`, just like `CPO`s. They can also be split apart into primitive parts using `as.list`. It is recommended to only chain `CPOTrained` objects if they were created in the given order by preprocessing operations, since `CPOTrained`s are very dependent on their position within a preprocessing pipeline.

    compound.retrafo = retrafo(head(iris) %>>% compound)
    compound.retrafo
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)] =>
    #> [RETRAFO pca(center = TRUE, scale = FALSE)]

    (retrafolist = as.list(compound.retrafo))
    #> [[1]]
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)]
    #>
    #> [[2]]
    #> CPO Retrafo chain
    #> [RETRAFO pca(center = TRUE, scale = FALSE)]

    retrafolist[[1]] %>>% retrafolist[[2]]
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)] =>
    #> [RETRAFO pca(center = TRUE, scale = FALSE)]
    pipeCPO(retrafolist)
    #> CPO Retrafo chain
    #> [RETRAFO scale(center = TRUE, scale = TRUE)] =>
    #> [RETRAFO pca(center = TRUE, scale = FALSE)]

#### Application of CPOTrained

Similarly to `CPO`s, `CPOTrained` objects can be applied to data using `%>>%`, `applyCPO`, or `predict`. This only works with objects that have the `"retrafo"` capability and hence the `CPORetrafo` class.

    transformed = iris %>>% cpoScale()
    head(iris) %>>% retrafo(transformed)
    #>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
    #> 1   -0.8976739  1.01560199    -1.335752   -1.311052  setosa
    #> 2   -1.1392005 -0.13153881    -1.335752   -1.311052  setosa
    #> 3   -1.3807271  0.32731751    -1.392399   -1.311052  setosa
    #> 4   -1.5014904  0.09788935    -1.279104   -1.311052  setosa
    #> 5   -1.0184372  1.24503015    -1.335752   -1.311052  setosa
    #> 6   -0.5353840  1.93331463    -1.165809   -1.048667  setosa

Should in general give the same as `head(transformed)`, since the same data was used:

    head(transformed)
    #>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
    #> 1   -0.8976739  1.01560199    -1.335752   -1.311052  setosa
    #> 2   -1.1392005 -0.13153881    -1.335752   -1.311052  setosa
    #> 3   -1.3807271  0.32731751    -1.392399   -1.311052  setosa
    #> 4   -1.5014904  0.09788935    -1.279104   -1.311052  setosa
    #> 5   -1.0184372  1.24503015    -1.335752   -1.311052  setosa
    #> 6   -0.5353840  1.93331463    -1.165809   -1.048667  setosa

`applyCPO()` and `predict()` are synonyms of `%>>%` when used for `CPORetrafo` objects:

    applyCPO(retrafo(transformed), head(iris))
    predict(retrafo(transformed), head(iris))

#### Inversion using CPOTrained

To use `CPOTrained` objects for inversion, the `invert()` function is used. Besides the `CPOTrained`, it takes the data to invert, and optionally the `predict.type`. Typically `CPOTrained` objects that were retrieved using `inverter()` from a transformed dataset should be used for inversion. Retrafo `CPOTrained` objects retrieved from a transformed data set using `retrafo()` sometimes have both the `"retrafo"` as well as the `"invert"` capability (precisely when all TOCPOs used had the `constant.invert` flag set, see Building Custom CPOs) and can then also be used for inversion. In that case, however, the `"truth"` column of an inverted prediction is dropped.

    transformed = bh.task %>>% cpoLogTrafoRegr()
    prediction = predict(train("regr.lm", transformed), transformed)
    inv = inverter(transformed)
    invert(inv, prediction)
    #> Prediction: 506 observations
    #> predict.type: response
    #> threshold:
    #> time: 0.00
    #>   id truth response
    #> 1  1  24.0 29.46569
    #> 2  2  21.6 24.65039
    #> 3  3  34.7 30.48177
    #> 4  4  33.4 28.91454
    #> 5  5  36.2 27.40745
    #> 6  6  28.7 25.77416
    #> ... (#rows: 506, #cols: 3)

    ret = retrafo(transformed)
    invert(ret, prediction)
    #> Prediction: 506 observations
    #> predict.type: response
    #> threshold:
    #> time: 0.00
    #>   id response
    #> 1  1 29.46569
    #> 2  2 24.65039
    #> 3  3 30.48177
    #> 4  4 28.91454
    #> 5  5 27.40745
    #> 6  6 25.77416
    #> ... (#rows: 506, #cols: 2)

Inversion can be done on both predictions given by `mlr` `Learner`s, as well as plain vectors, `data.frame`s, and `matrix` objects.

Note that the prediction being inverted must have the form of a prediction done with the `predict.type` that an inverter expects as input for the `predict.type` given to `invert()` as an argument. This can be queried using the `getCPOPredictType()` function. If `invert()` is called with `predict.type = p`, then the prediction must be one made with a `Learner` that has `predict.type` set to `getCPOPredictType(cpo)[p]`.

## NULLCPO

`NULLCPO` is the neutral element of `%>>%` and the operations it represents (`composeCPO()`, `applyCPO()`, and `attachCPO()`), i.e. when it is used as an argument of these functions, the data, `Learner` or `CPO` is not changed. `NULLCPO` is also the result `pipeCPO()` called with the empty list, and of `retrafo()` and `inverter()` when they are called for objects with no `CPOTrained` objects attached.

    pipeCPO(list())
    #> NULLCPO
    as.list(NULLCPO)  # the inverse of pipeCPO
    #> list()
    retrafo(bh.task)
    #> NULLCPO
    inverter(bh.task %>>% cpoPca())  # cpoPca is a TOCPO, so no inverter is created
    #> NULLCPO

Many getters give characteristic results for `NULLCPO`.

    getCPOClass(NULLCPO)
    #> [1] "NULLCPO"
    getCPOName(NULLCPO)
    #> [1] "NULLCPO"
    getCPOId(NULLCPO)
    #> [1] "NULLCPO"
    getHyperPars(NULLCPO)
    #> named list()
    getParamSet(NULLCPO)
    #> [1] "Empty parameter set."
    getCPOAffect(NULLCPO)
    #> named list()
    getCPOOperatingType(NULLCPO)  # operates neither on features nor on targets.
    #> character(0)
    getCPOProperties(NULLCPO)
    #> $handling
    #>  [1] "numerics"   "factors"    "ordered"    "missings"   "cluster"
    #>  [6] "classif"    "multilabel" "regr"       "surv"       "oneclass"
    #> [11] "twoclass"   "multiclass" "prob"       "se"
    #>
    #> $adding
    #> character(0)
    #>
    #> $needed
    #> character(0)
    # applying NULLCPO leads to a retrafo() of NULLCPO, so it is its own CPOTrainedCPO
    getCPOTrainedCPO(NULLCPO)
    #> NULLCPO
    # NULLCPO has no effect on applyCPO and invert, so NULLCPO's capabilities are 0.
    getCPOTrainedCapability(NULLCPO)
    #> retrafo  invert
    #>       0       0
    getCPOTrainedState(NULLCPO)
    #> NULL

Some helper functions convert `NULLCPO` to `NULL` and back, while leaving other values as they are.

    nullToNullcpo(NULL)
    #> NULLCPO
    nullcpoToNull(NULLCPO)
    #> NULL
    nullToNullcpo(10) # not changed
    #> [1] 10
    nullcpoToNull(10) # ditto
    #> [1] 10

## CPO Name and ID

A `CPO` has a “name” which identifies the general operation done by this `CPO`. For example, it is `"pca"` for a `CPO` created using `cpoPca()`. Furthermore, a `CPO` has an “ID” which is associated with the particular `CPO` object at hand. For primitive `CPO`s, it can be queried and set using `getCPOId()` and `setCPOId()`, and it can be set during construction, but it defaults to the `CPO`’s name. The ID will also be prefixed to the `CPO`’s hyperparameters after construction, if they are exported. This can help prevent hyperparameter name clashes when composing `CPO`s with otherwise identical hyperparameter names. It is possible to set the ID to `NULL` to have no prefix for hyperparameter names.

    cpo = cpoPca()
    getCPOId(cpo)
    #> [1] "pca"

    getParamSet(cpo)
    #>               Type len   Def Constr Req Tunable Trafo
    #> pca.center logical   -  TRUE      -   -    TRUE     -
    #> pca.scale  logical   - FALSE      -   -    TRUE     -

    getParamSet(setCPOId(cpo, "my.id"))
    #>                 Type len   Def Constr Req Tunable Trafo
    #> my.id.center logical   -  TRUE      -   -    TRUE     -
    #> my.id.scale  logical   - FALSE      -   -    TRUE     -

    getParamSet(setCPOId(cpo, NULL))
    #>           Type len   Def Constr Req Tunable Trafo
    #> center logical   -  TRUE      -   -    TRUE     -
    #> scale  logical   - FALSE      -   -    TRUE     -

In the following (silly) example an error is thrown because of hyperparameter name clash. This can be avoided by setting the ID of one of the constituents to a different value.

    cpo %>>% cpo
    #> Error in parameterClashAssert(cpo1, cpo2, cpo1$debug.name, cpo2$debug.name): Parameters "pca.center", "pca.scale" occur in both pca and pca
    #> Use the id parameter when constructing, or setCPOId, to prevent name collisions.

    cpo %>>% setCPOId(cpo, "two")
    #> (pca >> two<pca>)(pca.center = TRUE, pca.scale = FALSE, two.center = TRUE, two.scale = FALSE)

## CPO Properties

CPOs contain information about the kind of data they can work with, and what kind of data they produce. `getCPOProperties` returns a list with the slots `handling`, `adding`, `needed`. `properties$handling` indicates the kind of data a CPO can handle, `properties$needed` indicates the kind of data it needs the data receiver (e.g. attached learner) to have, and `properties$adding` lists the properties it adds to a given learner. An example is `cpoDummyEncode()`, a CPO that converts factors to numerics: The receiving learner needs to handle numerics, so `properties$needed == "numerics"`, but it adds the ability to handle factors (since they are converted), so `properties$adding = c("factors", "ordered")`.

    getCPOProperties(cpoDummyEncode())
    #> $handling
    #>  [1] "numerics"   "factors"    "ordered"    "missings"   "cluster"
    #>  [6] "classif"    "multilabel" "regr"       "surv"       "oneclass"
    #> [11] "twoclass"   "multiclass" "prob"       "se"
    #>
    #> $adding
    #> [1] "factors" "ordered"
    #>
    #> $needed
    #> [1] "numerics"

As a result, `cpoDummyEncode` endows a `Learner` with the ability to train on data with factor variables:

    train("classif.geoDA", bc.task)  # gives an error
    #> Error in checkLearnerBeforeTrain(task, learner, weights): Task 'BreastCancer-example' has factor inputs in 'Cl.thickness, Cell.size, Cell.shape, Marg.adhes...', but learner 'classif.geoDA' does not support that!

    train(cpoDummyEncode(reference.cat = TRUE) %>>% makeLearner("classif.geoDA"), bc.task)
    #> Model for learner.id=classif.geoDA.dummyencode; learner.class=CPOLearner
    #> Trained on: task.id = BreastCancer-example; obs = 683; features = 9
    #> Hyperparameters: validation=NULL

    getLearnerProperties("classif.geoDA")
    #> [1] "twoclass"   "multiclass" "numerics"

    getLearnerProperties(cpoDummyEncode(TRUE) %>>% makeLearner("classif.geoDA"))
    #> [1] "numerics"   "factors"    "ordered"    "twoclass"   "multiclass"

### `.sometimes`-Properties

As described in more detail in the Building Custom CPOs vignette, `CPO`s can have properties that are considered only when composing `CPO`s, or only when checking data returned by `CPO`s. In short, consider a `CPO` that does imputation, but only for factorial features. This `CPO` would need to have `"missings"` in its `$adding` properties slot, since it enables `Learner` to handle (some) `Tasks` that have missing values. However, this `CPO` may under certain circumstances still return data that has missing values. This discrepancy is recorded internally by having two “hidden” sets of properties that can be retrieved with `getCPOProperties()` with `get.internal` set to `TRUE`. These properties are `adding.min`, the minimal set of properties added, and `needed.max`, the maximal set of properties needed by consecutive operators. These can be understood as a description of the “worst case” behaviour of the `CPO`, since behaviour that is out of bounds of these sets causes an error by the `mlrCPO`-framework.

An example is the `cpoApplyFun` `CPO`: When it is constructed, it is not known what kind of properties will be added or needed, so `adding.min` is empty while `needed.max` is the set of all data properties. When composing `CPO`s, this `CPO` is handled as if it magically does exactly the data conversion necessary to make the `CPO`s or `Learner` coming after it work with the data. If this ends up not being the case, an error is thrown during application or training by the following `CPO` or `Learner`.

    getCPOProperties(cpoApplyFun(export = "export.all"), get.internal = TRUE)
    #> $handling
    #>  [1] "numerics"   "factors"    "ordered"    "missings"   "cluster"
    #>  [6] "classif"    "multilabel" "regr"       "surv"       "oneclass"
    #> [11] "twoclass"   "multiclass" "prob"       "se"
    #>
    #> $adding
    #> [1] "numerics" "factors"  "ordered"  "missings"
    #>
    #> $needed
    #> character(0)
    #>
    #> $adding.min
    #> character(0)
    #>
    #> $needed.max
    #> [1] "numerics" "factors"  "ordered"  "missings"

## CPO Affect

When constructing a `CPO`, it is possible to restrict the columns on which the `CPO` operates using the `affect.*` parameters of the `CPOConstructor`. These parameters are:

- `affect.index`: Identify affected columns by a vector of column indices.
- `affect.names`: Identify affected columns by a vector of column names.
- `affect.pattern`: Match column names against a `grep()` style regex pattern.
- `affect.pattern.ignore.case`: Ignore case when matching by pattern.
- `affect.pattern.perl`: Use “perl” syntax in `affect.pattern`.
- `affect.pattern.fixed`: Use fixed pattern instead of regex in `affect.pattern`.
- `affect.invert`: Invert the columns to affect: Only columns not matched by any of the other `affect.*` parameters are affected.

    # onlhy PCA columns that have '.Length' in their name
    cpo = cpoPca(affect.pattern = ".Length")
    getCPOAffect(cpo)
    #> $pattern
    #> [1] ".Length"

    triris = iris %>>% cpo
    head(triris)
    #>   Sepal.Width Petal.Width Species       PC1         PC2
    #> 1         3.5         0.2  setosa -2.460241 -0.24479165
    #> 2         3.0         0.2  setosa -2.538962 -0.06093579
    #> 3         3.2         0.2  setosa -2.709611  0.08355948
    #> 4         3.1         0.2  setosa -2.565116  0.25420858
    #> 5         3.6         0.2  setosa -2.499602 -0.15286372
    #> 6         3.9         0.4  setosa -2.066375 -0.40249369

## CPO Parameter Export

Sometimes when using many CPOs, their hyperparameters may get messy. `mlrCPO` enables the user to control which hyperparameter get exported. The parameter “export” can be one of `"export.default"`, `"export.set"`, `"export.unset"`, `"export.default.set"`, `"export.default.unset"`, `"export.all"`, `"export.none"`. “all” and “none” do what one expects; “default” exports the “recommended” parameters; “set” and “unset” export the values that have not been set, or only the values that were set (and are not left as default). “default.set” and “default.unset” work as “set” and “unset”, but restricted to the default exported parameters.

    !cpoScale()
    #> Trafo chain of 1 cpos:
    #> scale(center = TRUE, scale = TRUE)
    #> Operating: feature
    #> ParamSet:
    #>                 Type len  Def Constr Req Tunable Trafo
    #> scale.center logical   - TRUE      -   -    TRUE     -
    #> scale.scale  logical   - TRUE      -   -    TRUE     -

    !cpoScale(export = "export.none")
    #> Trafo chain of 1 cpos:
    #> scale()[not exp'd: center = TRUE, scale = TRUE]
    #> Operating: feature
    #> ParamSet:
    #> [1] "Empty parameter set."

    !cpoScale(scale = FALSE, export = "export.unset")
    #> Trafo chain of 1 cpos:
    #> scale(center = TRUE)[not exp'd: scale = FALSE]
    #> Operating: feature
    #> ParamSet:
    #>                 Type len  Def Constr Req Tunable Trafo
    #> scale.center logical   - TRUE      -   -    TRUE     -

## Syntactic Sugar

There are some `%>>%`-related operators that perform similar operations but may be more concise in certain applications. In general these operators are left-assiciative, i.e. they are evaluated after the expressions to their left were evaluated. Therefore, for example, `a %>>% b %<<% c` is equivalent to `(a %>>% b) %<<% c`. Exceptions are the assignment operators, `%<>>%` and `%<<<%`, as well as the `%>|%` operator, see below.

The operators are:

- `%>>%`: The application, composition or attachment operator.
- `%<<%`: The above with exchanged arguments. `a %<<% b` is equivalent to `b %>>% a`
- `%<>>%`: `%>>%`, followed with assignment to the left. This operator evaluates the arguments to its right before being evaluated itself. `a %<>>% b %>>% c` is equivalent to `a = (a %>>% b %>>% c)`.
- `%<<<%`: `%<<%`, followed with assignment to the left. Note this is not the `%<>>%` operator with its arguments flipped. This operator evaluates the arguments to its right before being evaluated itself. `a %<<<% b %>>% c` is equivalent to `a = (a %<<% (b %>>% c))`.
- `%>|%`: `%>>%`, followed by application of `retrafo()`. This operator evaluates the arguments to its right before being evaluated itself. `a %>|% b %<<% c` is equivalent to `retrafo(a %>>% (b %<<% c))`.
- `%|<%`: The above with exchanged arguments. Like most R operators, this one evaluates arguments to its left before being evaluated itself. `a %>>% b %|<% c` is equivalent to `retrafo((a %>>% b) %<<% c)`.