# Appendix A — Solutions to exercises

## A.1 Solutions to Chapter 2

1. Set the seed to `124` then train a classification tree model with `lrn("classif.rpart")` and default hyperparameters on 80% of the data in the predefined `"sonar"` task. Evaluate the model’s performance with the classification error measure on the remaining data. Also think about why we need to set the seed in this example.

Set the seed, load the `"sonar"` task, then the classification tree with `predict_type = "prob"` (needed for exercise 3), and the required measure.

``````set.seed(124)
learner = lrn("classif.rpart", predict_type = "prob")
measure = msr("classif.ce")``````

Use `partition()` to split the dataset then train the model. We set the seed because `partition()` introduces an element of randomness when splitting the data.

``````splits = partition(task, ratio = 0.8)

Once the model is trained, generate the predictions on the test set and score them.

``````prediction = learner\$predict(task, splits\$test)
prediction\$score(measure)``````
``````classif.ce
0.2195 ``````
1. Calculate the true positive, false positive, true negative, and false negative rates of the predictions made by the model in exercise 1.

Using `\$confusion`, generate a confusion matrix and extract the required statistics,

``prediction\$confusion``
``````        truth
response  M  R
M 20  7
R  2 12``````

Since the rows represent predictions (response) and the columns represent the ground truth values, the TP, FP, TN, and FN rates are as follows:

• True Positive (TP) = 20

• False Positive (FP) = 2

• True Negative (TN) = 12

• False Positive (FN) = 7

1. Since in this case we want the model to predict the negative class more often, we will raise the threshold (note the `predict_type` for the learner must be `prob` for this to work).
``````# raise threshold from 0.5 default to 0.6
prediction\$set_threshold(0.6)

prediction\$confusion``````
``````        truth
response  M  R
M 14  4
R  8 15``````

One reason we might want the false positive rate to be lower than the false negative rate is if we felt it was worse for a positive prediction to be incorrect (meaning the true label was the negative label) than it was for a negative prediction to be incorrect (meaning the true label was the positive label).

## A.2 Solutions to Chapter 3

1. Apply the “bootstrap” resampling strategy on `tsk("mtcars")` and evaluate the performance of `lrn("classif.rpart")`. Use 100 replicates and a sampling ratio of 80%. Calculate the MSE for each iteration and visualize the result. Finally, calculate the aggregated performance score.
``````set.seed(3)
learner = lrn("regr.rpart")
resampling = rsmp("bootstrap", repeats = 100, ratio = 0.8)

rr\$score(msr("regr.mse"))``````
``````     task_id learner_id resampling_id iteration regr.mse
1:  mtcars regr.rpart     bootstrap         1    17.53
2:  mtcars regr.rpart     bootstrap         2    15.71
3:  mtcars regr.rpart     bootstrap         3    31.63
4:  mtcars regr.rpart     bootstrap         4    22.59
5:  mtcars regr.rpart     bootstrap         5    36.64
---
96:  mtcars regr.rpart     bootstrap        96    18.79
97:  mtcars regr.rpart     bootstrap        97    19.10
98:  mtcars regr.rpart     bootstrap        98    18.72
99:  mtcars regr.rpart     bootstrap        99    33.32
100:  mtcars regr.rpart     bootstrap       100    25.87
Hidden columns: task, learner, resampling, prediction``````
``autoplot(rr)`` ``````# Alternatively: Histogram
autoplot(rr, type = "histogram")``````
```stat_bin()` using `bins = 30`. Pick better value with `binwidth`.`` ``rr\$aggregate(msr("regr.mse"))``
``````regr.mse
20.75 ``````
1. Use `tsk("spam")` and five-fold CV to benchmark Random forest (`lrn("classif.ranger")`), Logistic Regression (`lrn("classif.log_reg")`), and XGBoost (`lrn("classif.xgboost")`) with respect to AUC. Which learner appears to do best? How confident are you in your conclusion? How would you improve upon this?
``````set.seed(3)
design = benchmark_grid(
learners = lrns(c("classif.ranger", "classif.log_reg", "classif.xgboost"),
predict_type = "prob"),
resamplings = rsmp("cv", folds = 5)
)

bmr = benchmark(design)

mlr3viz::autoplot(bmr, measure = msr("classif.auc"))`````` This is only a small example for a benchmark workflow, but without tuning (see Chapter 4), the results are naturally not suitable to make any broader statements about the superiority of either learner for this task.

1. A colleague claims to have achieved a 93.1% classification accuracy using `lrn("classif.rpart")` on `tsk("penguins_simple")`. You want to reproduce their results and ask them about their resampling strategy. They said they used a custom three-fold CV with folds assigned as `factor(task\$row_ids %% 3)`. See if you can reproduce their results.
``````task = tsk("penguins_simple")
rsmp_cv = rsmp("custom_cv")

rr = resample(
learner = lrn("classif.rpart"),
resampling = rsmp_cv
)

rr\$aggregate(msr("classif.acc"))``````
``````classif.acc
0.9309 ``````

## A.3 Solutions to Chapter 4

1. Tune the `mtry`, `sample.fraction`, `num.trees` hyperparameters of a random forest model (`lrn("regr.ranger")`) on the `"mtcars"` task. Use a simple random search with 50 evaluations and select a suitable batch size. Evaluate with a three-fold CV and the root mean squared error.
``````set.seed(4)
learner = lrn("regr.ranger",
mtry.ratio      = to_tune(0, 1),
sample.fraction = to_tune(1e-1, 1),
num.trees       = to_tune(1, 2000)
)

instance = ti(
learner = learner,
resampling = rsmp("cv", folds = 3),
measures = msr("regr.rmse"),
terminator = trm("evals", n_evals = 50)
)

tuner = tnr("random_search", batch_size = 10)

tuner\$optimize(instance)``````
``````   mtry.ratio sample.fraction num.trees learner_param_vals  x_domain
1:     0.2764          0.9772       556          <list> <list>
1 variable not shown: [regr.rmse]``````
1. Evaluate the performance of the model created in Question 1 with nested resampling. Use a holdout validation for the inner resampling and a three-fold CV for the outer resampling. Print the unbiased performance estimate of the model.
``````set.seed(4)
learner = lrn("regr.ranger",
mtry.ratio      = to_tune(0, 1),
sample.fraction = to_tune(1e-1, 1),
num.trees       = to_tune(1, 2000)
)

at = auto_tuner(
tuner = tnr("random_search", batch_size = 10),
learner = learner,
resampling = rsmp("holdout"),
measure = msr("regr.rmse"),
terminator = trm("evals", n_evals = 50)
)

outer_resampling = rsmp("cv", folds = 3)
rr = resample(task, at, outer_resampling, store_models = TRUE)

rr\$aggregate()``````
``````regr.mse
8.322 ``````
1. Tune and benchmark an XGBoost model against a logistic regression model on the `"spam"` task and determine which has the best Brier score. Use mlr3tuningspaces and nested resampling.
``library(mlr3tuningspaces)``
``Loading required package: mlr3tuning``
``````lrn_xgboost = lts(lrn("classif.xgboost", predict_type = "prob"))

at_xgboost = auto_tuner(
tuner = tnr("random_search", batch_size = 1),
learner = lrn_xgboost,
resampling = rsmp("cv", folds = 3),
measure = msr("classif.bbrier"),
term_evals = 2,
)

lrn_logreg = lrn("classif.log_reg", predict_type = "prob")

at_logreg = auto_tuner(
tuner = tnr("random_search", batch_size = 1),
learner = lrn_logreg,
resampling = rsmp("cv", folds = 3),
measure = msr("classif.bbrier"),
term_evals = 2,
)

outer_resampling = rsmp("cv", folds = 3)

design = benchmark_grid(
learners = list(at_xgboost, at_logreg),
resamplings = outer_resampling
)

bmr = benchmark(design, store_models = TRUE)``````
``````Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred``````
``bmr``
``````<BenchmarkResult> of 6 rows with 2 resampling runs
nr task_id            learner_id resampling_id iters warnings errors
1    spam classif.xgboost.tuned            cv     3        0      0
2    spam classif.log_reg.tuned            cv     3        0      0``````

## A.4 Solutions to Chapter 5

1. We first construct the objective function and optimization instance:
``````library(bbotk)
library(mlr3mbo)

rastrigin = function(xdt) {
D = ncol(xdt)
y = 10 * D + rowSums(xdt^2 - (10 * cos(2 * pi * xdt)))
data.table(y = y)
}

objective = ObjectiveRFunDt\$new(
fun = rastrigin,
domain = ps(x1 = p_dbl(lower = -5.12, upper = 5.12),
x2 = p_dbl(lower = -5.12, upper = 5.12)),
codomain = ps(y = p_dbl(tags = "minimize")),
id = "rastrigin2D")

instance = OptimInstanceSingleCrit\$new(
objective = objective,
terminator = trm("evals", n_evals = 40))``````

Based on the different surrogate models, we can construct two optimizers:

``````library(mlr3mbo)

surrogate_gp = srlrn(lrn("regr.km", covtype = "matern5_2",
optim.method = "BFGS", control = list(trace = FALSE)))

surrogate_rf = srlrn(lrn("regr.ranger", num.trees = 10L, keep.inbag = TRUE,
se.method = "jack"))

acq_function = acqf("cb", lambda = 1)

acq_optimizer = acqo(opt("nloptr", algorithm = "NLOPT_GN_ORIG_DIRECT"),
terminator = trm("stagnation", iters = 100, threshold = 1e-5))

optimizer_gp = opt("mbo",
loop_function = bayesopt_ego,
surrogate = surrogate_gp,
acq_function = acq_function,
acq_optimizer = acq_optimizer)

optimizer_rf = opt("mbo",
loop_function = bayesopt_ego,
surrogate = surrogate_rf,
acq_function = acq_function,
acq_optimizer = acq_optimizer)``````

We then evaluate the given initial design on the instance and optimize it with the first BO algorithm using a Gaussian Process as surrogate model:

``````initial_design = data.table(
x1 = c(-3.95, 1.16, 3.72, -1.39, -0.11, 5.00, -2.67, 2.44),
x2 = c(1.18, -3.93, 3.74, -1.37, 5.02, -0.09, -2.65, 2.46))

instance\$eval_batch(initial_design)

optimizer_gp\$optimize(instance)

gp_data = instance\$archive\$data
gp_data[, y_min := cummin(y)]
gp_data[, nr_eval := seq_len(.N)]
gp_data[, surrogate := "Gaussian Process"]``````

Afterwards, we clear the instance, evaluate the initial design again and optimize the instance with the second BO algorithm using a random forest as surrogate model:

``````instance\$archive\$clear()

instance\$eval_batch(initial_design)

optimizer_rf\$optimize(instance)

rf_data = instance\$archive\$data
rf_data[, y_min := cummin(y)]
rf_data[, nr_eval := seq_len(.N)]
rf_data[, surrogate := "Random forest"]``````

We collect all data and visualize the anytime performance:

``````library(ggplot2)
library(viridisLite)
all_data = rbind(gp_data, rf_data)
ggplot(aes(x = nr_eval, y = y_min, colour = surrogate), data = all_data) +
geom_step() +
scale_colour_manual(values = viridis(2, end = 0.8)) +
labs(y = "Best Observed Function Value", x = "Number of Function Evaluations",
colour = "Surrogate Model") +
theme_minimal() +
theme(legend.position = "bottom")`````` 1. We first construct the non-parallelized objective function and the optimization instance:
``````schaffer1 = function(xss) {
evaluations = lapply(xss, FUN = function(xs) {
Sys.sleep(5)
list(y1 = xs\$x, y2 = (xs\$x - 2)^2)
})
rbindlist(evaluations)
}

objective = ObjectiveRFunMany\$new(
fun = schaffer1,
domain = ps(x = p_dbl(lower = -10, upper = 10)),
codomain = ps(y1 = p_dbl(tags = "minimize"), y2 = p_dbl(tags = "minimize")),
id = "schaffer1")

instance = OptimInstanceMultiCrit\$new(
objective = objective,
terminator = trm("run_time", secs = 60))``````

Using the surrogate, acquisition function and acquisition function optimizer that are provided, we can proceed to optimize the instance via ParEGO:

``````surrogate = srlrn(lrn("regr.ranger", num.trees = 10L, keep.inbag = TRUE,
se.method = "jack"))

acq_function = acqf("ei")

acq_optimizer = acqo(opt("random_search", batch_size = 100),
terminator = trm("evals", n_evals = 100))

optimizer = opt("mbo",
loop_function = bayesopt_parego,
surrogate = surrogate,
acq_function = acq_function,
acq_optimizer = acq_optimizer,
args = list(q = 4))``````
``optimizer\$optimize(instance)``

We observe that 12 points were evaluated in total (which makes sense as the objective function evaluation is not yet parallelized and the overhead of each function evaluation is given by 5 seconds). While the points are appropriately evaluated in batches of size `q = 4` (with the initial design automatically constructed as the first batch), we do not experience any acceleration of the optimization process unless the function evaluation is explicitly parallelized.

``nrow(instance\$archive\$data)``
`` 12``
``instance\$archive\$data[, c("x", "timestamp", "batch_nr")]``
``````           x           timestamp batch_nr
1:  0.03433 2023-07-12 09:16:13        1
2: -9.96567 2023-07-12 09:16:13        1
3: -4.96567 2023-07-12 09:16:13        1
4:  5.03433 2023-07-12 09:16:13        1
5:  7.34464 2023-07-12 09:16:34        2
---
8: -8.50644 2023-07-12 09:16:34        2
9: -2.22408 2023-07-12 09:16:54        3
10: -6.44530 2023-07-12 09:16:54        3
11:  0.90963 2023-07-12 09:16:54        3
12: -2.21318 2023-07-12 09:16:54        3``````

We now parallelize the evaluation of the objective function and proceed to optimize the instance again:

``````library(future)
library(future.apply)
plan("multisession", workers = 4)

schaffer1_parallel = function(xss) {
evaluations = future_lapply(xss, FUN = function(xs) {
Sys.sleep(5)
list(y1 = xs\$x, y2 = (xs\$x - 2)^2)
})
rbindlist(evaluations)
}

objective_parallel = ObjectiveRFunMany\$new(
fun = schaffer1_parallel,
domain = ps(x = p_dbl(lower = -10, upper = 10)),
codomain = ps(y1 = p_dbl(tags = "minimize"), y2 = p_dbl(tags = "minimize")),
id = "schaffer1_parallel")

instance_parallel = OptimInstanceMultiCrit\$new(
objective = objective_parallel,
terminator = trm("run_time", secs = 60))``````
``optimizer\$optimize(instance_parallel)``

By parallelizing the evaluation of the objective function we used our compute resources much more efficiently and evaluated many more points:

``nrow(instance_parallel\$archive\$data)``
`` 44``
``instance_parallel\$archive\$data[, c("x", "timestamp", "batch_nr")]``
``````         x           timestamp batch_nr
1: -8.010 2023-07-12 09:17:01        1
2:  1.990 2023-07-12 09:17:01        1
3: -3.010 2023-07-12 09:17:01        1
4:  6.990 2023-07-12 09:17:01        1
5:  9.454 2023-07-12 09:17:07        2
---
40:  6.300 2023-07-12 09:17:52       10
41: -8.767 2023-07-12 09:17:57       11
42: -9.546 2023-07-12 09:17:57       11
43:  3.432 2023-07-12 09:17:57       11
44:  3.917 2023-07-12 09:17:57       11``````

## A.5 Solutions to Chapter 6

1. Calculate a correlation filter on the `"mtcars"` task.
``````library(mlr3verse)
filter = flt("correlation")

as.data.table(filter)``````
``````    feature  score
1:      wt 0.8677
2:     cyl 0.8522
3:    disp 0.8476
4:      hp 0.7762
5:    drat 0.6812
6:      vs 0.6640
7:      am 0.5998
8:    carb 0.5509
9:    gear 0.4803
10:    qsec 0.4187``````
1. Use the filter from the first exercise to select the five best features in the `mtcars` dataset.
``````keep = names(head(filter\$scores, 5))
`` "cyl"  "disp" "drat" "hp"   "wt"  ``
1. Apply a backward selection to `tsk("penguins")` with `lrn("classif.rpart")` and holdout resampling by the measure classification accuracy. Compare the results with those in Section 6.2.1.
``library(mlr3fselect)``
``````
Attaching package: 'mlr3fselect'``````
``````The following object is masked from 'package:mlr3tuning':

ContextEval``````
``````instance = fselect(
fselector = fs("sequential", strategy = "sbs"),
learner = lrn("classif.rpart"),
resampling = rsmp("holdout"),
measure = msr("classif.acc")
)
as.data.table(instance\$result)[, .(bill_depth, bill_length, body_mass, classif.acc)]``````
``````   bill_depth bill_length body_mass classif.acc
1:       TRUE        TRUE      TRUE      0.9565``````
``instance\$result_feature_set``
`````` "bill_depth"  "bill_length" "body_mass"   "island"      "sex"
 "year"       ``````

1. Do the selected features differ?

Yes, the backward selection selects more features.

1. Which feature selection method achieves a higher classification accuracy?

In this example, the backwards example performs slightly better, but this depends heavily on the random seed and could look different in another run.

1. Are the accuracy values in b) directly comparable? If not, what has to be changed to make them comparable?

No, they are not comparable because the holdout sampling called with `rsmp("holdout")` creates a different holdout set for the two runs. A fair comparison would create a single resampling instance and use it for both feature selections (see Chapter 3 for details):

``````resampling = rsmp("holdout")
resampling\$instantiate(tsk("penguins"))

instance_sfs = fselect(
fselector = fs("sequential", strategy = "sfs"),
learner = lrn("classif.rpart"),
resampling = resampling,
measure = msr("classif.acc")
)
instance_sbs = fselect(
fselector = fs("sequential", strategy = "sbs"),
learner = lrn("classif.rpart"),
resampling = resampling,
measure = msr("classif.acc")
)
as.data.table(instance_sfs\$result)[, .(bill_depth, bill_length, body_mass, classif.acc)]``````
``````   bill_depth bill_length body_mass classif.acc
1:      FALSE        TRUE     FALSE      0.9304``````
``as.data.table(instance_sbs\$result)[, .(bill_depth, bill_length, body_mass, classif.acc)]``
``````   bill_depth bill_length body_mass classif.acc
1:      FALSE        TRUE      TRUE      0.9565``````

Alternatively, one could automate the feature selection and perform a benchmark between the two wrapped learners.

1. Automate the feature selection as in Section 6.2.6 with `tsk("spam")` and `lrn("classif.log_reg")`.
``````library(mlr3fselect)
library(mlr3learners)

at = auto_fselector(
fselector = fs("random_search"),
learner = lrn("classif.log_reg"),
resampling = rsmp("holdout"),
measure = msr("classif.acc"),
terminator = trm("evals", n_evals = 50)
)

design = benchmark_grid(
learner = list(at, lrn("classif.log_reg")),
resampling = rsmp("cv", folds = 3)
)

bmr = benchmark(design)

aggr = bmr\$aggregate(msrs(c("classif.acc", "time_train")))
as.data.table(aggr)[, .(learner_id, classif.acc, time_train)]``````
``````                  learner_id classif.acc time_train
1: classif.log_reg.fselector      0.9226     15.666
2:           classif.log_reg      0.9268      0.372``````

## A.6 Solutions to Chapter 7

1. Concatenate the named PipeOps using `%>>%`. To get a `Learner` object, use `as_learner()`
``````library(mlr3pipelines)
library(mlr3learners)

graph = po("imputeoor") %>>% po("scale") %>>% lrn("classif.log_reg")
graph_learner = as_learner(graph)``````
1. After training, the underlying `lrn("classif.log_reg")` can be accessed through the `\$base_learner()` method. Alternatively, the learner can be accessed explicitly using `po("learner")`.
``````graph_learner\$train(tsk("pima"))

# access the learner through the \$base_learner() method
model = graph_learner\$base_learner()\$model
coef(model)``````
``````(Intercept)         age     glucose     insulin        mass    pedigree
-0.88835     0.15584     1.13631    -0.17477     0.74383     0.32121
pregnant    pressure     triceps
0.39594    -0.24967     0.05599 ``````
``````# access the learner explicitly through the PipeOp
pipeop = graph_learner\$graph_model\$pipeops\$classif.log_reg
model = pipeop\$learner_model\$model
coef(model)``````
``````(Intercept)         age     glucose     insulin        mass    pedigree
-0.88835     0.15584     1.13631    -0.17477     0.74383     0.32121
pregnant    pressure     triceps
0.39594    -0.24967     0.05599 ``````
1. Set the `\$keep_results` flag of the Graph to `TRUE` to keep the results of the individual PipeOps. Afterwards, the input of the `lrn("classif.log_reg")` can be accessed through the `\$.result` field of its predecessor, the `po("scale")`. Note that the `\$.result` is a `list`, we want to access its only element, named `\$output`.
``````graph_learner\$graph\$keep_results = TRUE
graph_learner\$train(tsk("pima"))

# access the input of the learner
scale_result = graph_learner\$graph_model\$pipeops\$scale\$.result

# check if the age column is standardized:
# 1. does it have mean 0? -- almost, up to numerical precision!
mean(age_column)``````
`` 1.988e-16``
``````# 2. does it have standard deviation 1? -- yes!
sd(age_column)``````
`` 1``

## A.7 Solutions to Chapter 8

1. To use `po("select")` to remove, instead of keep, a feature based on a pattern, use `selector_invert` together with `selector_grep`. To remove the “`R`” class columns in Section 8.3.2, the following `po("select")` could be used:
``po("select", selector = selector_invert(selector_grep("\\.R")))``
``````PipeOp: <select> (not trained)
values: <selector=<Selector>>
Input channels <name [train type, predict type]>:
Output channels <name [train type, predict type]>:

which would have the benefit that it would keep the columns pertaining to all other classes, even if the `"sonar"` task had more target classes.

1. A solution that does not need to specify the target classes at all is to use a custom `Selector`, as was shown in Section 8.3.1:
``````selector_remove_one_prob_column = function(task) {
selector_use = selector_invert(selector_grep(paste0("\\.", class_removing)))

}``````

Using this selector in Section 8.3.2, one could use the resulting stacking learner on any classification task with arbitrary target classes.

1. As the first hint states, two `po("imputelearner")` objects are necessary: one to impute missing values in factor columns using a classification learner, and another to impute missing values in numeric columns using a regression learner. Additionally, `ppl("robustify")` is used along with the `ranger`-based learners inside `po("imputelearner")` because the data passed to the imputation learners still contains missing values, which `ranger::ranger` cannot handle.
``````gr_impute_factors = po("imputelearner", id = "impute_factors",
learner = ppl("robustify", learner = lrn("classif.ranger")) %>>%
lrn("classif.ranger"),
affect_columns = selector_type("factor")
)
gr_impute_numerics = po("imputelearner", id = "impute_numerics",
learner = ppl("robustify", learner = lrn("regr.ranger")) %>>%
lrn("regr.ranger"),
affect_columns = selector_type(c("numeric", "integer"))
)

gr_impute = gr_impute_numerics %>>% gr_impute_factors

imputed = gr_impute\$train(tsk("penguins"))[]

# e.g. see how row 4 was imputed
# original:
tsk("penguins")\$data(rows = 4)``````
``````   species bill_depth bill_length body_mass flipper_length    island
1:  Adelie         NA          NA        NA             NA Torgersen
sex
1: <NA>
1 variable not shown: [year]``````
``````# imputed:
imputed\$data(rows = 4)``````
``````   species    island year bill_depth bill_length body_mass
1:  Adelie Torgersen 2007         19       41.67      4278
2 variables not shown: [flipper_length, sex]``````

## A.8 Solutions for Chapter 9

We will consider a similar prediction problem as throughout this section, using the King County Housing data instead (available with `tsk("kc_housing")`). To evaluate the models, we again use 10-fold cv and the mean absolute error. The learner we want to use is a elastic-net regression by `lrn("regr.glmnet")`. For now we will ignore the `date` column and simply remove it:

``````kc_housing = tsk("kc_housing")
kc_housing\$select(setdiff(kc_housing\$feature_names, "date"))``````
1. Have a look at the features, are there any features which might be problematic? If so, change or remove them.
``summary(kc_housing)``
``````     price           bathrooms       bedrooms       condition
Min.   :  75000   Min.   :0.00   Min.   : 0.00   Min.   :1.00
1st Qu.: 321950   1st Qu.:1.75   1st Qu.: 3.00   1st Qu.:3.00
Median : 450000   Median :2.25   Median : 3.00   Median :3.00
Mean   : 540088   Mean   :2.12   Mean   : 3.37   Mean   :3.41
3rd Qu.: 645000   3rd Qu.:2.50   3rd Qu.: 4.00   3rd Qu.:4.00
Max.   :7700000   Max.   :8.00   Max.   :33.00   Max.   :5.00

Min.   :1.00   Min.   : 1.00   Min.   :47.2   Min.   :-123
1st Qu.:1.00   1st Qu.: 7.00   1st Qu.:47.5   1st Qu.:-122
Median :1.50   Median : 7.00   Median :47.6   Median :-122
Mean   :1.49   Mean   : 7.66   Mean   :47.6   Mean   :-122
3rd Qu.:2.00   3rd Qu.: 8.00   3rd Qu.:47.7   3rd Qu.:-122
Max.   :3.50   Max.   :13.00   Max.   :47.8   Max.   :-121

sqft_above   sqft_basement    sqft_living    sqft_living15
Min.   : 290   Min.   :  10    Min.   :  290   Min.   : 399
1st Qu.:1190   1st Qu.: 450    1st Qu.: 1427   1st Qu.:1490
Median :1560   Median : 700    Median : 1910   Median :1840
Mean   :1788   Mean   : 742    Mean   : 2080   Mean   :1987
3rd Qu.:2210   3rd Qu.: 980    3rd Qu.: 2550   3rd Qu.:2360
Max.   :9410   Max.   :4820    Max.   :13540   Max.   :6210
NA's   :13126
sqft_lot         sqft_lot15          view       waterfront
Min.   :    520   Min.   :   651   Min.   :0.000   Mode :logical
1st Qu.:   5040   1st Qu.:  5100   1st Qu.:0.000   FALSE:21450
Median :   7618   Median :  7620   Median :0.000   TRUE :163
Mean   :  15107   Mean   : 12768   Mean   :0.234
3rd Qu.:  10688   3rd Qu.: 10083   3rd Qu.:0.000
Max.   :1651359   Max.   :871200   Max.   :4.000

yr_built     yr_renovated      zipcode
Min.   :1900   Min.   :1934    Min.   :98001
1st Qu.:1951   1st Qu.:1987    1st Qu.:98033
Median :1975   Median :2000    Median :98065
Mean   :1971   Mean   :1996    Mean   :98078
3rd Qu.:1997   3rd Qu.:2007    3rd Qu.:98118
Max.   :2015   Max.   :2015    Max.   :98199
NA's   :20699                  ``````

`zipcode` should not really be interpreted as a numeric value, so we cast it to a factor. We could argue to remove `lat` and `long` as handling them as linear effects is not necessarily a suitable, but we will keep them since `glmnet` performs internal feature selection anyways.

``zipencode = po("mutate", mutation = list(zipcode = ~ as.factor(zipcode)), id = "zipencode")``
1. Check the dataset and learner properties to understand which preprocessing steps you need to do.
``print(kc_housing)``
``````<TaskRegr:kc_housing> (21613 x 19): King County House Sales
* Target: price
* Properties: -
* Features (18):
- int (13): bedrooms, condition, grade, sqft_above,
sqft_basement, sqft_living, sqft_living15, sqft_lot,
sqft_lot15, view, yr_built, yr_renovated, zipcode
- dbl (4): bathrooms, floors, lat, long
- lgl (1): waterfront``````
``kc_housing\$missings()``
``````        price     bathrooms      bedrooms     condition        floors
0             0             0             0             0
0             0             0             0         13126
sqft_living sqft_living15      sqft_lot    sqft_lot15          view
0             0             0             0             0
waterfront      yr_built  yr_renovated       zipcode
0             0         20699             0 ``````

The data has missings and a categorical feature (since we are encoding the zipcode as a factor).

``````glmnet = lrn("regr.glmnet")
glmnet\$properties``````
`` "weights"``
``glmnet\$feature_types``
`` "logical" "integer" "numeric"``

`glmnet` does not support factors or missing values. So our pipeline needs to handle both.

1. Build a suitable pipeline that allows glmnet to be trained on the dataset.
``````glmnet_preproc = GraphLearner\$new(
zipencode %>>%
po("fixfactors") %>>%
po("encodeimpact") %>>%
list(
po("missind",
type = "integer",
affect_columns = selector_type("integer")
),
po("imputehist",
affect_columns = selector_type("integer")
)) %>>%
po("featureunion") %>>%
po("imputeoor",
affect_columns = selector_type("factor")
) %>>%
glmnet,
id = "regr.glmnet_preproc")

log_glmnet_preproc = ppl("targettrafo", graph = glmnet_preproc)
log_glmnet_preproc\$param_set\$values\$targetmutate.trafo = function(x) log(x)
log_glmnet_preproc\$param_set\$values\$targetmutate.inverter = function(x) list(response = exp(x\$response))
log_glmnet_preproc = GraphLearner\$new(log_glmnet_preproc, id = "regr.log_glmnet_preproc")``````

First we fix the factor levels to ensure that all 70 zipcodes are fixed. We can consider 70 levels high cardinality, so we use impact encoding. We use the same imputation strategy as in Chapter 9. Since the target is highly skewed, we also apply a log-transformation of the target.

1. As a comparison, apply `pipeline_robustify` to glmnet and compare the results with your pipeline.
``````glmnet_robustify = GraphLearner\$new(
zipencode %>>%
mlr3pipelines::pipeline_robustify() %>>%
glmnet,
id = "regr.glmnet_robustify"
)

log_glmnet_robustify = ppl("targettrafo", graph = glmnet_robustify)
log_glmnet_robustify\$param_set\$values\$targetmutate.trafo = function(x) log(x)
log_glmnet_robustify\$param_set\$values\$targetmutate.inverter = function(x) list(response = exp(x\$response))
log_glmnet_robustify = GraphLearner\$new(log_glmnet_robustify, id = "regr.log_glmnet_robustify")

learners = list(
lrn("regr.featureless", robust = TRUE),
glmnet_preproc,
log_glmnet_preproc,
glmnet_robustify,
log_glmnet_robustify
)

set.seed(123L)
cv10 = rsmp("cv")
cv10\$instantiate(kc_housing)

design = benchmark_grid(kc_housing, learners = learners, cv10)
bmr = benchmark(design)
bmr\$aggregate(measure = msr("regr.mae"))[, .(learner_id, regr.mae)]``````
``````                  learner_id regr.mae
1:          regr.featureless   221817
2:       regr.glmnet_preproc   101229
3:   regr.log_glmnet_preproc    84477
4:     regr.glmnet_robustify    96478
5: regr.log_glmnet_robustify    84958``````

The log-transformed `glmnet` with impact encoding results in the best model, although only by a very small margin.

1. Consider the `date` feature: How can you extract information from this feature that `glmnet` can use? Check how much this improves your pipeline. Also consider the spatial nature of the dataset: Can you extract an additional feature from the lat/long coordinates? (Hint: Downtown Seattle has lat/long coordinates `47.605`/`-122.334`).
``````extractors = po("mutate", mutation = list(
date = ~ as.numeric(date),
distance_downtown = ~ sqrt((lat - 47.605)^2 + (long  + 122.334)^2)))

kc_housing_full = extractors\$train(list(tsk("kc_housing")))[]
kc_housing_full\$id = "kc_housing_feat_extr"

design_ext = benchmark_grid(kc_housing_full, learners = learners, cv10)
bmr_ext = benchmark(design_ext)
bmr\$combine(bmr_ext)
bmr\$aggregate(measure = msr("regr.mae"))[, .(learner_id, task_id, regr.mae)]``````
``````                   learner_id              task_id regr.mae
1:          regr.featureless           kc_housing   221817
2:       regr.glmnet_preproc           kc_housing   101229
3:   regr.log_glmnet_preproc           kc_housing    84477
4:     regr.glmnet_robustify           kc_housing    96478
5: regr.log_glmnet_robustify           kc_housing    84958
6:          regr.featureless kc_housing_feat_extr   221817
7:       regr.glmnet_preproc kc_housing_feat_extr   100228
8:   regr.log_glmnet_preproc kc_housing_feat_extr    82832
9:     regr.glmnet_robustify kc_housing_feat_extr    95458
10: regr.log_glmnet_robustify kc_housing_feat_extr    84444``````

We simply convert the `date` feature into a numeric timestamp so that `glmnet` can handle the feature. We create one additional feature as the distance to downtown Seattle. This improves the average error of our model by a further 1600\$.

## A.9 Solutions to Chapter 13

1. Run a benchmark experiment on the `"german_credit"` task with algorithms: `lrn("classif.featureless")`, `lrn("classif.log_reg")`, `lrn("classif.ranger")`. Tune the `lrn("classif.featureless")` model using `tunetreshold` and `learner_cv`. Use two-fold CV and evaluate with `msr("classif.costs", costs = costs)` where you should make the parameter `costs` so that the cost of a true positive is -10, the cost of a true negative is -1, the cost of a false positive is 2, and the cost of a false negative is 3. Use `set.seed(11)` to make sure you get the same results as us. Are your results surprising?
``````library(mlr3verse)
set.seed(11)

costs = matrix(c(-10, 3, 2, -1), nrow = 2, dimnames =
msr_costs = msr("classif.costs", costs = costs)

gr = po("learner_cv", lrn("classif.featureless", predict_type = "prob")) %>>%
po("tunethreshold", measure = msr_costs)
learners = list(as_learner(gr), lrn("classif.log_reg"), lrn("classif.ranger"))
bmr = benchmark(benchmark_grid(task, learners, rsmp("cv", folds = 2)))
bmr\$aggregate(msr_costs)[, c(4, 7)]``````
``````                          learner_id classif.costs
1: classif.featureless.tunethreshold        -6.400
2:                   classif.log_reg        -5.420
3:                    classif.ranger        -5.923``````
1. Train and predict a survival forest using `rfsrc` (from `mlr3extralearners`). Run this experiment using `task = tsk("rats"); split = partition(task)`. Evaluate your model with the RCLL measure.
``````library(mlr3verse)
library(mlr3proba)
library(mlr3extralearners)
set.seed(11)

lrn("surv.rfsrc")\$
score(msr("surv.rcll"))``````
``````surv.rcll
4.031 ``````
1. Estimate the density of the `tsk("precip")` data using `lrn("dens.logspline")` (from `mlr3extralearners`). Run this experiment using `task = tsk("precip"); split = partition(task)`. Evaluate your model with the logloss measure.
``````library(mlr3verse)
library(mlr3proba)
library(mlr3extralearners)
set.seed(11)

lrn("dens.logspline")\$
score(msr("dens.logloss"))``````
``````dens.logloss
3.979 ``````
1. Run a benchmark clustering experiment on the `wine` dataset without a label column. Compare the performance of `"clust.kmeans"` learner with `k` equal to 2, 3 and 4 using the silhouette measure. Use insample resampling technique. What value of `k` would you choose based on the silhouette scores?
``````library(mlr3)
library(mlr3cluster)
set.seed(11)
learners = list(
lrn("clust.kmeans", centers = 2L, id = "k-means, k=2"),
lrn("clust.kmeans", centers = 3L, id = "k-means, k=3"),
lrn("clust.kmeans", centers = 4L, id = "k-means, k=4")
)

measure = msr("clust.silhouette")
bmr\$aggregate(measure)[, c(4, 7)]``````
``````     learner_id clust.silhouette
1: k-means, k=2           0.6569
2: k-means, k=3           0.5711
3: k-means, k=4           0.5606``````

Based on the silhouette score, we can choose `k = 2`.

1. Run a (spatially) unbiased classification benchmark experiment on the `"ecuador"` task with a featureless learner and xgboost, evaluate with the binary Brier score.

You can use any resampling method from `mlr3spatiotempcv`, in this solution we use 4-fold spatial environmental blocking.

``````library(mlr3verse)
library(mlr3spatial)
library(mlr3spatiotempcv)``````
``````
Attaching package: 'mlr3spatiotempcv'``````
``````The following objects are masked from 'package:mlr3spatial':

``````set.seed(11)
learners = lrns(paste0("classif.", c("xgboost", "featureless")),
predict_type = "prob")
rsmp_sp = rsmp("spcv_env", folds = 4)
bmr = benchmark(design)
bmr\$aggregate(msr("classif.bbrier"))[, c(4, 7)]``````
``````            learner_id classif.bbrier
1:     classif.xgboost         0.2303
2: classif.featureless         0.2413``````

## A.10 Solutions to Chapter 10

1. Consider the following example where you resample a learner (debug learner, sleeps for 3 seconds during train) on 4 workers using the multisession backend:
``````task = tsk("penguins")
learner = lrn("classif.debug", sleep_train = function() 3)
resampling = rsmp("cv", folds = 6)

future::plan("multisession", workers = 4)
1. Assuming that the learner would actually calculate something and not just sleep: Would all CPUs be busy?
2. Prove your point by measuring the elapsed time, e.g., using `system.time()`.
3. What would you change in the setup and why?

Not all CPUs would be utilized in the example. All 4 of them are occupied for the first 4 iterations of the cross validation. The 5th iteration, however, only runs in parallel to the 6th fold, leaving 2 cores idle. This is supported by the elapsed time of roughly 6 seconds for 6 jobs compared to also roughly 6 seconds for 8 jobs:

``````task = tsk("penguins")
learner = lrn("classif.debug", sleep_train = function() 3)

future::plan("multisession", workers = 4)

resampling = rsmp("cv", folds = 6)

resampling = rsmp("cv", folds = 8)

If possible, the number of resampling iterations should be an integer multiple of the number of workers. Therefore, a simple adaptation either increases the number of folds for improved accuracy of the error estimate or reduces the number of folds for improved runtime.

1. Create a new custom classification measure (either using methods demonstrated in Section 10.5 or with `msr("classif.costs")` which scores predictions using the mean over the following classification costs:
• If the learner predicted label “A” and the truth is “A”, assign score 0
• If the learner predicted label “B” and the truth is “B”, assign score 0
• If the learner predicted label “A” and the truth is “B”, assign score 1
• If the learner predicted label “B” and the truth is “A”, assign score 10

The rules can easily be translated to R code where we expect `truth` and `prediction` to be factor vectors of the same length with levels `"A"` and `"B"`:

``````costsens = function(truth, prediction) {
score = numeric(length(truth))
score[truth == "A" & prediction == "B"] = 10
score[truth == "B" & prediction == "A"] = 1

mean(score)
}``````

This function can be embedded in the `Measure` class accordingly.

``````MeasureCustom = R6::R6Class("MeasureCustom",
inherit = mlr3::MeasureClassif, # classification measure
public = list(
initialize = function() { # initialize class
super\$initialize(
id = "custom", # unique ID
packages = character(), # no dependencies
properties = character(), # no special properties
predict_type = "response", # measures response prediction
range = c(0, Inf), # results in values between (0, 1)
minimize = TRUE # smaller values are better
)
}
),

private = list(
.score = function(prediction, ...) { # define score as private method
# define loss
costsens = function(truth, prediction) {
score = numeric(length(truth))
score[truth == "A" & prediction == "B"] = 10
score[truth == "B" & prediction == "A"] = 1

mean(score)
}

# call loss function
costsens(prediction\$truth, prediction\$response)
}
)
)``````

An alternative (as pointed to by the hint) can be constructed by first translating the rules to a matrix of misclassification costs, and then feeding this matrix to the constructor of `msr("classif.costs")`:

``````# truth in columns, prediction in rows
C = matrix(c(0, 10, 1, 0), nrow = 2)
rownames(C) = colnames(C) = c("A", "B")
C``````
``````   A B
A  0 1
B 10 0``````
``msr("classif.costs", costs = C)``
``````<MeasureClassifCosts:classif.costs>: Cost-sensitive Classification
* Packages: mlr3
* Range: [0, Inf]
* Minimize: TRUE
* Average: macro
* Parameters: normalize=TRUE
* Properties: -
* Predict type: response``````

## A.11 Solutions to Chapter 11

1. Load the OpenML collection with ID 269, which contains regression tasks from the AutoML benchmark .

We access the AutoML benchmark suite with ID 269 using the `ocl()` function.

``````library(mlr3oml)
automl_suite = ocl(id = 269)
``````  167210 233211 233212 233213 233214 233215 317614 359929 359930
 359931 359932 359933 359934 359935 359936 359937 359938 359939
 359940 359941 359942 359943 359944 359945 359946 359948 359949
 359950 359951 359952 360932 360933 360945``````
1. Find all tasks with less than 4000 observations and convert them to `mlr3` tasks.

We can find all tasks with less than 4000 observations by specifying this constraint in `list_oml_tasks()`.

``````tbl = list_oml_tasks(
)``````

This returns a table which only contains matching tasks from the AutoML benchmark.

``tbl[, .(task_id, data_id, name, NumberOfInstances)]``
``````    task_id data_id                 name NumberOfInstances
1:  167210   41021            Moneyball              1232
2:  359930     550                quake              2178
3:  359931     546              sensory               576
4:  359932     541               socmob              1156
5:  359933     507             space_ga              3107
6:  359934     505              tecator               240
7:  359945   42730             us_crime              1994
8:  359950     531               boston               506
9:  359951   42563 house_prices_nominal              1460
10:  360945   43071  MIP-2016-regression              1090``````

We can create `mlr3` tasks from these OpenML IDs using `tsk("oml")`.

``tasks = lapply(tbl\$task_id, function(id) tsk("oml", task_id = id))``
1. Create an experimental design that compares `regr.ranger` to `regr.rpart`, use the robustify pipeline for both learners and a featureless fallback learner. Use three-fold cross-validation instead of the OpenML resamplings.

Below, we define the robustified learners with a featureless fallback learner.

``````lrn_ranger = as_learner(
ppl("robustify", learner = lrn("regr.ranger")) %>>%
po("learner", lrn("regr.ranger"))
)
lrn_ranger\$id = "ranger"
lrn_ranger\$fallback = lrn("regr.featureless")

lrn_rpart = as_learner(
ppl("robustify", learner = lrn("regr.rpart")) %>>%
po("learner", lrn("regr.rpart"))
)
lrn_rpart\$id = "rpart"
lrn_rpart\$fallback = lrn("regr.featureless")

learners = list(lrn_ranger, lrn_rpart)``````

Finally, we create the experimental design using `benchmark_grid()`.

``````# we set the seed, as benchmark_grid instantiates the resamplings
set.seed(123)
resampling = rsmp("cv", folds = 3)
design``````
``````                    task learner resampling
1:            Moneyball  ranger         cv
2:            Moneyball   rpart         cv
3:                quake  ranger         cv
4:                quake   rpart         cv
5:              sensory  ranger         cv
---
16:               boston   rpart         cv
17: house_prices_nominal  ranger         cv
18: house_prices_nominal   rpart         cv
19:  MIP-2016-regression  ranger         cv
20:  MIP-2016-regression   rpart         cv``````
1. Create a registry and populate it with the experiments. Optionally: change the cluster function to either “Socket” or “Multicore” (the latter does not work on Windows).

We start with loading the relevant libraries and creating a registry. By specifying the registry’s `file.dir` to `NA` we are using a temporary directory.

``````library(mlr3batchmark)
library(batchtools)

reg = makeExperimentRegistry(
file.dir = NA,
seed = 1,
packages = "mlr3verse"
)``````
``No readable configuration file found``
``Created registry in '/tmp/RtmpNVR0BP/registry375d443618bb' using cluster functions 'Interactive'``

Then, we change the cluster function to “Multicore” (or “Socket” if you are on Windows).

``````# Mac and Linux
reg\$cluster.functions = makeClusterFunctionsMulticore()``````
``Auto-detected 2 CPUs``
``````# Windows:
reg\$cluster.functions = makeClusterFunctionsSocket()``````
``Auto-detected 2 CPUs``
``saveRegistry(reg)``
`` TRUE``
1. Submit the jobs and once they are finished, collect the results.

The next two steps are to populate the registry with the experiments using `batchmark()` and to submit them. By specifying no IDs in `submitJobs()`, all jobs returned by `findNotSubmitted()` are queued, which in this case are all existing jobs.

``````batchmark(design, reg = reg)
submitJobs(reg = reg)
waitForJobs(reg = reg)``````

After the execution of the experiment finished, we can collect the results like below.

``````bmr = reduceResultsBatchmark(reg = reg)
bmr``````
``````<BenchmarkResult> of 60 rows with 20 resampling runs
nr              task_id learner_id resampling_id iters warnings
1            Moneyball     ranger            cv     3        0
2            Moneyball      rpart            cv     3        0
3                quake     ranger            cv     3        0
4                quake      rpart            cv     3        0
5              sensory     ranger            cv     3        0
---
16               boston      rpart            cv     3        0
17 house_prices_nominal     ranger            cv     3        0
18 house_prices_nominal      rpart            cv     3        0
19  MIP-2016-regression     ranger            cv     3        0
20  MIP-2016-regression      rpart            cv     3        0
errors
0
0
0
0
0
---
0
0
0
0
0``````
1. Conduct a global Friedman test and interpret the results using `regr.mse`. Why do we not need to use the post-hoc test?

As a first step, we load `mlr3benchmark` and create a benchmark aggregate using `msr("regr.mse")`.

``````library(mlr3benchmark)
bma = as_benchmark_aggr(bmr, measures = msr("regr.mse"))
bma``````
``````<BenchmarkAggr> of 20 rows with 10 tasks, 2 learners and 1 measure
1:            Moneyball     ranger 6.167e+02
2:            Moneyball      rpart 1.357e+03
3:                quake     ranger 3.827e-02
4:                quake      rpart 3.567e-02
5:              sensory     ranger 5.072e-01
---
16:               boston      rpart 2.293e+01
17: house_prices_nominal     ranger 9.020e+08
18: house_prices_nominal      rpart 1.949e+09
19:  MIP-2016-regression     ranger 7.505e+08
20:  MIP-2016-regression      rpart 6.277e+08``````

We can now use the `\$friedman_test()` method to apply the test to the experiment results. We do not need a post-hoc test, because we are only comparing two algorithms.

``bma\$friedman_test()``
``````
Friedman rank sum test

data:  mse and learner_id and task_id
Friedman chi-squared = 1.6, df = 1, p-value = 0.2``````

This experimental design was not able to detect a significant difference on the 5% level so we cannot reject our null hypothesis that the regression tree performs equally well as the random forest.

1. Inspect the ranks of the results.

We inspect the ranks using the `\$rank_data()` method of the `BenchmarkAggr`, where we specify `minimize` to `TRUE`, because a lower mean square error is better.

``bma\$rank_data(minimize = TRUE)``
``````       Moneyball quake sensory socmob space_ga tecator us_crime boston
ranger         1     2       1      1        1       2        1      1
rpart          2     1       2      2        2       1        2      2
house_prices_nominal MIP-2016-regression
ranger                    1                   2
rpart                     2                   1``````

The random forest is better on 7 of the 10 tasks.

## A.12 Solutions to Chapter 12

1. Prepare a `mlr3` regression task for `fifa` data. Select only variables describing the age and skills of footballers. Train any predictive model for this task, e.g. `lrn("regr.ranger")`.
``````library(DALEX)
library(ggplot2)
data("fifa", package = "DALEX")
old_theme = set_theme_dalex("ema")

library(mlr3)
library(mlr3learners)
set.seed(1)

fifa20 = fifa[,5:42]

learner = lrn("regr.ranger")
learner\$model``````
``````Ranger result

Call:

Type:                             Regression
Number of trees:                  500
Sample size:                      5000
Number of independent variables:  37
Mtry:                             6
Target node size:                 5
Variable importance mode:         none
Splitrule:                        variance
OOB prediction error (MSE):       1.023e+13
R squared (OOB):                  0.8699 ``````
1. Use the permutation importance method to calculate variable importance ranking. Which variable is the most important? Is it surprising?

With `iml`

``````library(iml)
model = Predictor\$new(learner,
data = fifa20,
y = fifa\$value_eur)

effect = FeatureImp\$new(model,
loss = "rmse")
effect\$plot()`````` With `DALEX`

``````library(DALEX)
ranger_exp = DALEX::explain(learner,
data = fifa20,
y = fifa\$value_eur,
label = "Fifa 2020",
verbose = FALSE)

ranger_effect = model_parts(ranger_exp, B = 5)
``````             variable mean_dropout_loss     label
1        _full_model_           1402526 Fifa 2020
2           value_eur           1402526 Fifa 2020
3           weight_kg           1471865 Fifa 2020
4 goalkeeping_kicking           1472795 Fifa 2020
5           height_cm           1474859 Fifa 2020
6    movement_balance           1475618 Fifa 2020``````
``plot(ranger_effect)`` 1. Use the Partial Dependence profile to draw the global behavior of the model for this variable. Is it aligned with your expectations?

With `iml`

``````num_features = c("movement_reactions", "skill_ball_control", "age")

effect = FeatureEffects\$new(model)
plot(effect, features = num_features)`````` With `DALEX`

``````num_features = c("movement_reactions", "skill_ball_control", "age")

ranger_profiles = model_profile(ranger_exp, variables = num_features)
plot(ranger_profiles)`````` 4 Choose one of the football players. You can choose some well-known striker (e.g. Robert Lewandowski) or a well-known goalkeeper (e.g. Manuel Neuer). The following tasks are worth repeating for several different choices.

``player_1 = fifa["R. Lewandowski", 5:42]``
1. For the selected footballer, calculate and plot the Shapley values. Which variable is locally the most important and has the strongest influence on the valuation of the footballer?

With `iml`

``````shapley = Shapley\$new(model, x.interest = player_1)
plot(shapley)`````` With `DALEX`

``````ranger_shap = predict_parts(ranger_exp,
new_observation = player_1,
type = "shap", B = 1)
plot(ranger_shap, show_boxplots = FALSE)`````` 1. For the selected footballer, calculate the Ceteris Paribus / Individual Conditional Expectation profiles to draw the local behavior of the model for this variable. Is it different from the global behavior?

With `DALEX`

``````num_features = c("movement_reactions", "skill_ball_control", "age")

ranger_ceteris = predict_profile(ranger_exp, player_1)
plot(ranger_ceteris, variables = num_features) +
ggtitle("Ceteris paribus for R. Lewandowski", " ")`````` ## A.13 Solutions to Chapter 14

1. Load the `adult_train` task and try to build a first model. Train a simple model and evaluate it on the `adult_test` task that is also available with `mlr3fairness`.

For now we simply load the data and look at the data.

``````library(mlr3)
library(mlr3fairness)
set.seed(8)

``````<TaskClassif:adult_train> (30718 x 13)
* Target: target
* Properties: twoclass
* Features (12):
- fct (7): education, marital_status, occupation, race,
relationship, sex, workclass
- int (5): age, capital_gain, capital_loss, education_num,
hours_per_week
* Protected attribute: sex``````

We can now train a simple model, e.g., a decision tree and evaluate for accuracy.

``````learner = lrn("classif.rpart")
prediction\$score()``````
``````classif.ce
0.161 ``````
1. Assume our goal is to achieve parity in false omission rates. Construct a fairness metric that encodes this and againg evaluate your model. Construct a fairness metric that encodes this and evaluate your model. In order to get a deeper understanding, look at the `groupwise_metrics` function to obtain performance in each group.

The metric is available via the key `"fairness.fomr"`. Note, that evaluating our prediction now requires that we also provide the task.

``````msr_1 = msr("fairness.fomr")
``````fairness.fomr
0.03533 ``````

The `groupwise_metrics` function creates a metric for each group specified in the `pta` column role:

``tsk_adult_test\$col_roles\$pta``
`` "sex"``
``msr_2 = groupwise_metrics(base_measure = msr("classif.fomr"), task = tsk_adult_test)``

We can then use this metric to evaluate our model again. This gives us the false omission rates for male and female individuals separately.

``prediction\$score(msr_2, tsk_adult_test)``
``````  subgroup.fomr_Male subgroup.fomr_Female
0.2442               0.2089 ``````
1. Improve your model by employing pipelines that use pre- or post-processing methods for fairness. Evaluate your model along the two metrics and visualize the results. Compare the different models using an appropriate visualization.

First we can again construct the learners above.

``````library(mlr3pipelines)
lrn_1 = po("reweighing_wts") %>>% lrn("classif.rpart")
lrn_2 = po("learner_cv", lrn("classif.rpart")) %>>%
po("EOd")``````

And run the benchmark again. Note, that we use three-fold CV this time for comparison.

``````learners = list(learner, lrn_1, lrn_2)
design = benchmark_grid(tsk_adult_train, learners, rsmp("cv", folds = 3L))
bmr = benchmark(design)
bmr\$aggregate(msrs(c("classif.acc", "fairness.fomr")))``````
``````   nr     task_id                   learner_id resampling_id iters
1:  1 adult_train                classif.rpart            cv     3
2:  2 adult_train reweighing_wts.classif.rpart            cv     3
3:  3 adult_train            classif.rpart.EOd            cv     3
2 variables not shown: [classif.acc, fairness.fomr]
Hidden columns: resample_result``````

We can now again visualize the result.

``````library(ggplot2)
scale_color_viridis_d("Learner") +
theme_minimal()`````` 1. Add `"race"` as a second sensitive attribute to your dataset. Add the information to your task and evaluate the initial model again. What changes? Again study the `groupwise_metrics`.

This can be achieved by adding “race” to the `"pta"` col_role.

``````tsk_adult_train\$set_col_roles("race", add_to = "pta")
``````<TaskClassif:adult_train> (30718 x 13)
* Target: target
* Properties: twoclass
* Features (12):
- fct (7): education, marital_status, occupation, race,
relationship, sex, workclass
- int (5): age, capital_gain, capital_loss, education_num,
hours_per_week
* Protected attribute: sex, race``````
``````tsk_adult_test\$set_col_roles("race", add_to = "pta")
``````fairness.fomr
0.8889 ``````

If we now evaluate for the intersection, we obtain a large deviation from `0`. Note, that the metric by default computes the maximum discrepancy between all metrics for the non-binary case.

If we now get the `groupwise_metrics`, we will get a metric for the intersection of each group.

``````msr_3 = groupwise_metrics(msr("classif.fomr"),  tsk_adult_train)
unname(sapply(msr_3, function(x) x\$id))``````
``````  "subgroup.fomr_Male, White"
 "subgroup.fomr_Male, Black"
 "subgroup.fomr_Female, Black"
 "subgroup.fomr_Female, White"
 "subgroup.fomr_Male, Asian-Pac-Islander"
 "subgroup.fomr_Male, Amer-Indian-Eskimo"
 "subgroup.fomr_Female, Other"
 "subgroup.fomr_Female, Asian-Pac-Islander"
 "subgroup.fomr_Female, Amer-Indian-Eskimo"
 "subgroup.fomr_Male, Other"               ``````
``prediction\$score(msr_3, tsk_adult_test)``
``````               subgroup.fomr_Male, White
0.2402
subgroup.fomr_Male, Black
0.2716
subgroup.fomr_Female, Black
0.2609
subgroup.fomr_Female, White
0.1919
subgroup.fomr_Male, Asian-Pac-Islander
0.3168
subgroup.fomr_Male, Amer-Indian-Eskimo
0.1667
subgroup.fomr_Female, Other
0.2500
subgroup.fomr_Female, Asian-Pac-Islander
0.3529
subgroup.fomr_Female, Amer-Indian-Eskimo
1.0000
subgroup.fomr_Male, Other
0.1111 ``````

And we can see, that the reason might be, that the false omission rate for female Amer-Indian-Eskimo is at `1.0`! We can investigate this further by looking at actual counts:

``table(tsk_adult_test\$data(cols = c("race", "sex", "target")))``
``````, , target = <=50K

sex
race                 Female Male
Amer-Indian-Eskimo     56   74
Asian-Pac-Islander    131  186
Black                 654  619
Other                  37   66
White                3544 6176

, , target = >50K

sex
race                 Female Male
Amer-Indian-Eskimo      3   16
Asian-Pac-Islander     26  106
Black                  41  133
Other                   5   19
White                 492 2931``````

One of the reasons might be that there are only 3 individuals in the “>50k” category! This is an often encountered problem, as error metrics have a large variance when samples are small. Note, that the pre- and post-processing methods in general do not all support multiple protected attributes.