`library(mlr3verse)`

# Scope

This is the third part of the practical tuning series. The other parts can be found here:

- Part I - Tune a Support Vector Machine
- Part II - Tune a Preprocessing Pipeline
- Part IV - Tuning and Parallel Processing

In this post, we implement a simple automated machine learning (AutoML) system which includes preprocessing, a switch between multiple learners and hyperparameter tuning. For this, we build a pipeline with the mlr3pipelines extension package. Additionally, we use nested resampling to get an unbiased performance estimate of our AutoML system.

# Prerequisites

We load the mlr3verse package which pulls in the most important packages for this example.

We initialize the random number generator with a fixed seed for reproducibility, and decrease the verbosity of the logger to keep the output clearly represented. The `lgr`

package is used for logging in all mlr3 packages. The mlr3 logger prints the logging messages from the base package, whereas the bbotk logger is responsible for logging messages from the optimization packages (e.g. mlr3tuning ).

```
set.seed(7832)
::get_logger("mlr3")$set_threshold("warn")
lgr::get_logger("bbotk")$set_threshold("warn") lgr
```

In this example, we use the Pima Indians Diabetes data set which is used to to predict whether or not a patient has diabetes. The patients are characterized by 8 numeric features and some have missing values.

`= tsk("pima") task `

# Branching

We use three popular machine learning algorithms: k-nearest-neighbors, support vector machines and random forests.

```
= list(
learners lrn("classif.kknn", id = "kknn"),
lrn("classif.svm", id = "svm", type = "C-classification"),
lrn("classif.ranger", id = "ranger")
)
```

The `PipeOpBranch`

allows us to specify multiple alternatives paths. In this graph, the paths lead to the different learner models. The `selection`

hyperparameter controls which path is executed i.e., which learner is used to fit a model. It is important to use the `PipeOpBranch`

after the branching so that the outputs are merged into one result object. We visualize the graph with branching below.

```
=
graph po("branch", options = c("kknn", "svm", "ranger")) %>>%
gunion(lapply(learners, po)) %>>%
po("unbranch")
$plot(html = FALSE) graph
```

Alternatively, we can use the `ppl()`

-shortcut to load a predefined graph from the `mlr_graphs`

dictionary. For this, the learner list must be named.

```
= list(
learners kknn = lrn("classif.kknn", id = "kknn"),
svm = lrn("classif.svm", id = "svm", type = "C-classification"),
ranger = lrn("classif.ranger", id = "ranger")
)
= ppl("branch", lapply(learners, po)) graph
```

# Preprocessing

The task has missing data in five columns.

`round(task$missings() / task$nrow, 2)`

```
diabetes age glucose insulin mass pedigree pregnant pressure triceps
0.00 0.00 0.01 0.49 0.01 0.00 0.00 0.05 0.30
```

The pipeline `"robustify"`

function creates a preprocessing pipeline based on our task. The resulting pipeline imputes missing values with `PipeOpImputeHist`

and creates a dummy column (`PipeOpMissInd`

) which indicates the imputed missing values. Internally, this creates two paths and the results are combined with `PipeOpFeatureUnion`

. In contrast to `PipeOpBranch`

, both paths are executed. Additionally, `"robustify"`

adds `PipeOpEncode`

to encode factor columns and `PipeOpRemoveConstants`

to remove features with a constant value.

```
= ppl("robustify", task = task, factors_to_numeric = TRUE) %>>%
graph
graphplot(graph, html = FALSE)
```

We could also create the preprocessing pipeline manually.

```
gunion(list(po("imputehist"),
po("missind", affect_columns = selector_type(c("numeric", "integer"))))) %>>%
po("featureunion") %>>%
po("encode") %>>%
po("removeconstants")
```

```
Graph with 5 PipeOps:
ID State sccssors prdcssors
imputehist <<UNTRAINED>> featureunion
missind <<UNTRAINED>> featureunion
featureunion <<UNTRAINED>> encode imputehist,missind
encode <<UNTRAINED>> removeconstants featureunion
removeconstants <<UNTRAINED>> encode
```

# Graph Learner

We use `as_learner()`

to create a `GraphLearner`

which encapsulates the pipeline and can be used like a learner.

`= as_learner(graph) graph_learner `

The parameter set of the graph learner includes all hyperparameters from all contained learners. The hyperparameter ids are prefixed with the corresponding learner ids. The hyperparameter `branch.selection`

controls which learner is used.

`as.data.table(graph_learner$param_set)[, .(id, class, lower, upper, nlevels)]`

```
id class lower upper nlevels
1: removeconstants_prerobustify.ratio ParamDbl 0 1 Inf
2: removeconstants_prerobustify.rel_tol ParamDbl 0 Inf Inf
3: removeconstants_prerobustify.abs_tol ParamDbl 0 Inf Inf
4: removeconstants_prerobustify.na_ignore ParamLgl NA NA 2
5: removeconstants_prerobustify.affect_columns ParamUty NA NA Inf
6: imputehist.affect_columns ParamUty NA NA Inf
7: missind.which ParamFct NA NA 2
8: missind.type ParamFct NA NA 4
9: missind.affect_columns ParamUty NA NA Inf
10: imputesample.affect_columns ParamUty NA NA Inf
11: encode.method ParamFct NA NA 5
12: encode.affect_columns ParamUty NA NA Inf
13: removeconstants_postrobustify.ratio ParamDbl 0 1 Inf
14: removeconstants_postrobustify.rel_tol ParamDbl 0 Inf Inf
15: removeconstants_postrobustify.abs_tol ParamDbl 0 Inf Inf
16: removeconstants_postrobustify.na_ignore ParamLgl NA NA 2
17: removeconstants_postrobustify.affect_columns ParamUty NA NA Inf
18: kknn.k ParamInt 1 Inf Inf
19: kknn.distance ParamDbl 0 Inf Inf
20: kknn.kernel ParamFct NA NA 10
21: kknn.scale ParamLgl NA NA 2
22: kknn.ykernel ParamUty NA NA Inf
23: kknn.store_model ParamLgl NA NA 2
24: svm.cachesize ParamDbl -Inf Inf Inf
25: svm.class.weights ParamUty NA NA Inf
26: svm.coef0 ParamDbl -Inf Inf Inf
27: svm.cost ParamDbl 0 Inf Inf
28: svm.cross ParamInt 0 Inf Inf
29: svm.decision.values ParamLgl NA NA 2
30: svm.degree ParamInt 1 Inf Inf
31: svm.epsilon ParamDbl 0 Inf Inf
32: svm.fitted ParamLgl NA NA 2
33: svm.gamma ParamDbl 0 Inf Inf
34: svm.kernel ParamFct NA NA 4
35: svm.nu ParamDbl -Inf Inf Inf
36: svm.scale ParamUty NA NA Inf
37: svm.shrinking ParamLgl NA NA 2
38: svm.tolerance ParamDbl 0 Inf Inf
39: svm.type ParamFct NA NA 2
40: ranger.alpha ParamDbl -Inf Inf Inf
41: ranger.always.split.variables ParamUty NA NA Inf
42: ranger.class.weights ParamUty NA NA Inf
43: ranger.holdout ParamLgl NA NA 2
44: ranger.importance ParamFct NA NA 4
45: ranger.keep.inbag ParamLgl NA NA 2
46: ranger.max.depth ParamInt 0 Inf Inf
47: ranger.min.node.size ParamInt 1 Inf Inf
48: ranger.min.prop ParamDbl -Inf Inf Inf
49: ranger.minprop ParamDbl -Inf Inf Inf
50: ranger.mtry ParamInt 1 Inf Inf
51: ranger.mtry.ratio ParamDbl 0 1 Inf
52: ranger.num.random.splits ParamInt 1 Inf Inf
53: ranger.num.threads ParamInt 1 Inf Inf
54: ranger.num.trees ParamInt 1 Inf Inf
55: ranger.oob.error ParamLgl NA NA 2
56: ranger.regularization.factor ParamUty NA NA Inf
57: ranger.regularization.usedepth ParamLgl NA NA 2
58: ranger.replace ParamLgl NA NA 2
59: ranger.respect.unordered.factors ParamFct NA NA 3
60: ranger.sample.fraction ParamDbl 0 1 Inf
61: ranger.save.memory ParamLgl NA NA 2
62: ranger.scale.permutation.importance ParamLgl NA NA 2
63: ranger.se.method ParamFct NA NA 2
64: ranger.seed ParamInt -Inf Inf Inf
65: ranger.split.select.weights ParamUty NA NA Inf
66: ranger.splitrule ParamFct NA NA 3
67: ranger.verbose ParamLgl NA NA 2
68: ranger.write.forest ParamLgl NA NA 2
69: branch.selection ParamFct NA NA 3
id class lower upper nlevels
```

# Tune the pipeline

We will only tune one hyperparameter for each learner in this example. Additionally, we tune the branching parameter which selects one of the three learners. We have to specify that a hyperparameter is only valid for a certain learner by using `depends = branch.selection == <learner_id>`

.

```
# branch
$param_set$values$branch.selection =
graph_learnerto_tune(c("kknn", "svm", "ranger"))
# kknn
$param_set$values$kknn.k =
graph_learnerto_tune(p_int(3, 50, logscale = TRUE, depends = branch.selection == "kknn"))
# svm
$param_set$values$svm.cost =
graph_learnerto_tune(p_dbl(-1, 1, trafo = function(x) 10^x, depends = branch.selection == "svm"))
# ranger
$param_set$values$ranger.mtry =
graph_learnerto_tune(p_int(1, 8, depends = branch.selection == "ranger"))
# short learner id for printing
$id = "graph_learner" graph_learner
```

We define a tuning instance and select a random search which is stopped after 20 evaluated configurations.

```
= tune(
instance tuner = tnr("random_search"),
task = task,
learner = graph_learner,
resampling = rsmp("cv", folds = 3),
measure = msr("classif.ce"),
term_evals = 20
)
```

The following shows a quick way to visualize the tuning results.

```
autoplot(instance, type = "marginal",
cols_x = c("x_domain_kknn.k", "x_domain_svm.cost", "ranger.mtry"))
```

# Final Model

We add the optimized hyperparameters to the graph learner and train the learner on the full dataset.

```
= as_learner(graph)
learner $param_set$values = instance$result_learner_param_vals
learner$train(task) learner
```

The trained model can now be used to make predictions on new data. A common mistake is to report the performance estimated on the resampling sets on which the tuning was performed (`instance$result_y`

) as the model’s performance. Instead we have to use nested resampling to get an unbiased performance estimate.

# Nested Resampling

We use nested resampling to get an unbiased estimate of the predictive performance of our graph learner.

```
= as_learner(graph)
graph_learner $param_set$values$branch.selection =
graph_learnerto_tune(c("kknn", "svm", "ranger"))
$param_set$values$kknn.k =
graph_learnerto_tune(p_int(3, 50, logscale = TRUE, depends = branch.selection == "kknn"))
$param_set$values$svm.cost =
graph_learnerto_tune(p_dbl(-1, 1, trafo = function(x) 10^x, depends = branch.selection == "svm"))
$param_set$values$ranger.mtry =
graph_learnerto_tune(p_int(1, 8, depends = branch.selection == "ranger"))
$id = "graph_learner"
graph_learner
= rsmp("cv", folds = 3)
inner_resampling = AutoTuner$new(
at learner = graph_learner,
resampling = inner_resampling,
measure = msr("classif.ce"),
terminator = trm("evals", n_evals = 10),
tuner = tnr("random_search")
)
= rsmp("cv", folds = 3)
outer_resampling = resample(task, at, outer_resampling, store_models = TRUE) rr
```

We check the inner tuning results for stable hyperparameters. This means that the selected hyperparameters should not vary too much. We might observe unstable models in this example because the small data set and the low number of resampling iterations might introduce too much randomness. Usually, we aim for the selection of stable hyperparameters for all outer training sets.

`extract_inner_tuning_results(rr)`

Next, we want to compare the predictive performances estimated on the outer resampling to the inner resampling. Significantly lower predictive performances on the outer resampling indicate that the models with the optimized hyperparameters overfit the data.

`$score()[, .(iteration, task_id, learner_id, resampling_id, classif.ce)] rr`

```
iteration task_id learner_id resampling_id classif.ce
1: 1 pima graph_learner.tuned cv 0.2265625
2: 2 pima graph_learner.tuned cv 0.2382812
3: 3 pima graph_learner.tuned cv 0.2656250
```

The aggregated performance of all outer resampling iterations is essentially the unbiased performance of the graph learner with optimal hyperparameter found by random search.

`$aggregate() rr`

```
classif.ce
0.2434896
```

Applying nested resampling can be shortened by using the `tune_nested()`

-shortcut.

```
= as_learner(graph)
graph_learner $param_set$values$branch.selection =
graph_learnerto_tune(c("kknn", "svm", "ranger"))
$param_set$values$kknn.k =
graph_learnerto_tune(p_int(3, 50, logscale = TRUE, depends = branch.selection == "kknn"))
$param_set$values$svm.cost =
graph_learnerto_tune(p_dbl(-1, 1, trafo = function(x) 10^x, depends = branch.selection == "svm"))
$param_set$values$ranger.mtry =
graph_learnerto_tune(p_int(1, 8, depends = branch.selection == "ranger"))
$id = "graph_learner"
graph_learner
= tune_nested(
rr tuner = tnr("random_search"),
task = task,
learner = graph_learner,
inner_resampling = rsmp("cv", folds = 3),
outer_resampling = rsmp("cv", folds = 3),
measure = msr("classif.ce"),
term_evals = 10,
)
```

# Resources

The mlr3book includes chapters on pipelines and hyperparameter tuning. The mlr3cheatsheets contain frequently used commands and workflows of mlr3.