costs = matrix(c(1, 0, 5, 0), nrow = 2, dimnames =
list("Predicted Credit" = c("good", "bad"),
Truth = c("good", "bad")))
costs
Truth
Predicted Credit good bad
good 1 5
bad 0 0
The chapter title reflects that up until now we have only considered two tasks, regression (specifically deterministic), and classification (specifically singlelabel). So far, this book has focused on detailed explanation of the mlr3
universe of packages, which is abstracted in such a way that allows users to choose the level of complexity that suits each project. For example, you could limit your usage of these packages to just mlr3
to train a very small subset of regression and classification learners on a set of data and then use your model to make predictions for new unseen data. You could extend this to many regression and classification learners with mlr3learners
and mlr3extralearners
. By making use of mlr3tuning
and mlr3pipelines
you could optimize your model further including with pre and postprocessing of data and algorithms. However, the real power of the mlr3
universe, is in its ability to take all of these features, and extend them to many machine learning tasks.
In Chapter 2 we introduced deterministic regression and deterministic & probabilistic singlelabel classification (Table 8.1). But our infrastructure also works well for survival analysis, density estimation, clustering, spatiotemporal analysis, timeseries forecasting, deep learning architectures, image analysis, multilabel classification, probabilistic regression, and many more. Some of these tasks are implemented in extension packages as part of the mlr3
universe (see Figure 1.1), some are available by creating pipelines with mlr3pipelines
, some are in development, and some are waiting to be developed (maybe by some readers of this book). In this chapter, we will take you through just a subset of these new tasks, focusing on the ones that have a stable API. As we work through this chapter we will refer to the ‘building blocks’ of mlr3
, this refers to the base classes that must be extended to create new tasks, these are Prediction
, Learner
, Measure
, and Task
.
Table 8.1 summarizes available extension tasks, including the package(s) they are implemented in, the stability of the task implementation, and a brief description. Only tasks with stable APIs are discussed in this chapter, the table also includes tasks in development.
Task  Package  Status  Description 

Deterministic regression  mlr3 
Stable  Point prediction of a continuous variable. 
Probabilistic regression 
mlr3 and mlr3proba

Stable  Probability distribution prediction of a continuous variable. 
Deterministic singlelabel classification  mlr3 
Stable  Prediction of a single class an observation falls into. 
Probabilistic singlelabel classification  mlr3 
Stable  Prediction of the probability of an observation falling into one or more mutually exclusive categories. 
Costsensitive classification 
mlr3 and mlr3pipelines

Stable  Classification predictions with unequal costs associated with misclassifications. 
Survival analysis  mlr3proba 
Stable  Timetoevent predictions with possible ‘censoring’. 
Density estimation  mlr3proba 
Stable  Unsupervised estimation of probability density functions. 
Spatiotemporal analysis 
mlr3spatiotempcv and mlr3spatial

Stable  Supervised prediction of data with spatial (e.g., coordinates) and/or temporal outcomes. 
Cluster analysis  mlr3cluster 
Stable  Unsupervised estimation of homogeneous clusters of data points. 
Time series forecasting  mlr3temporal 
Developing  Supervised predictions of target over time (e.g., daily temperature). 
Functional data analysis  mlr3fda 
Developing  Supervised predictions from functional data. 
We begin by discussing a task that does not require any additional packages or infrastructure, only the tools we have already learnt about from earlier chapters. In ‘regular’ classification, the aim is to optimize a metric (often the misclassification rate) whilst assuming all misclassification errors are deemed equally severe. A more general setting is costsensitive classification, in which costs caused by different kinds of errors may not be equal. The objective of costsensitive classification is to minimize the expected costs. As we discuss this task we will work with mlr_tasks_german_credit
(Appendix C) as a running example.
Imagine in this task that an insurance company, InsureU, provides fixed loans of $5K over a one year period and customers are expected to pay back $6K at the end of this period. InsureU needs to be predict if a new customer will have good credit to decide if a loan should be given. This is a deterministic classification problem where InsureU is classifying if a customer will be in class ‘Good’ or ‘Bad’. Now we can write up the potential costs associated with each prediction and the eventual truth:
costs = matrix(c(1, 0, 5, 0), nrow = 2, dimnames =
list("Predicted Credit" = c("good", "bad"),
Truth = c("good", "bad")))
costs
Truth
Predicted Credit good bad
good 1 5
bad 0 0
If InsureU thinks a customer has bad credit then there is no profit or loss, the loan is not provided. If a customer has good credit and returns the loan then InsureU makes a $1K profit, but if they default then InsureU loses $5K. Note that costsensitive classification is a minimization problem where we assume lower costs mean higher profits/positive outcomes, hence above we wrote the profit and loss as 1
and +5
respectively.
We will now see how to implement a more nuanced approach to classification errors with MeasureClassifCosts
. This measure takes one argument, which is a matrix with row and column names corresponding to the class labels in the task of interest. Let’s put our insurance example into practice, notice that we have already named the cost matrix as required for the measure:
library(mlr3verse)
task = tsk("german_credit")
cost_measure = msr("classif.costs", costs = costs)
cost_measure
<MeasureClassifCosts:classif.costs>: Costsensitive Classification
* Packages: mlr3
* Range: [Inf, Inf]
* Minimize: TRUE
* Average: macro
* Parameters: normalize=TRUE
* Properties: 
* Predict type: response
learners = lrns(
paste0("classif.", c("log_reg", "featureless", "ranger")))
bmr = benchmark(benchmark_grid(task, learners, rsmp("cv", folds = 3)))
bmr$aggregate(cost_measure)[, c(4, 7)]
learner_id classif.costs
1: classif.log_reg 0.1790683
2: classif.featureless 0.8001654
3: classif.ranger 0.2491294
In this experiment we find that the logistic regression learner happens to perform best as it minimizes the expected costs (and maximizes expected profits) and the featureless learner performs the worst. However, we could improve this prediction by considering thresholding.
As we have discussed in Chapter 2, thresholding is a method to determine at what probability an observation will fall into one outcome class or another. Currently in our running example, the models above will predict a customer has good credit (in the class ‘Good’) if the probability of good credit is greater than 0.5. However, this may not be a sensible approach as the cost of a false positive and false negative is not equal. In fact, a false positive results in a cost of +5 whereas a false negative only results in a cost of 0, hence we would prefer a model with a higher false negative rates and lower false positive rates. This is highlighted in the "threshold"
autoplot
:
prediction = lrn("classif.log_reg",
predict_type = "prob")$train(task)$predict(task)
autoplot(prediction, type = "threshold", measure = cost_measure)
As expected, the optimal threshold is greater than 0.5, indicating that to maximize profits, the majority of observations should be predicted to have bad credit.
To automate the process of optimizing the threshold, we can make use of mlr3tuning
(Chapter 4) and mlr3pipelines
(Chapter 6) by creating a graph with PipeOpTuneThreshold
. Continuing the same example:
gr = po("learner_cv", lrn("classif.log_reg", predict_type = "prob")) %>>%
po("tunethreshold", measure = cost_measure)
learners = list(as_learner(gr), lrn("classif.log_reg"))
bmr = benchmark(benchmark_grid(task, learners, rsmp("cv", folds = 3)))
bmr$aggregate(cost_measure)[, c(4, 7)]
learner_id classif.costs
1: classif.log_reg.tunethreshold 0.1060282
2: classif.log_reg 0.1481062
As expected, our tuned learner performs much better and may even make InsureU a profit not a loss.
Probabilistic regression is a simple extension to deterministic regression in which the goal is to predict a full distribution around a single ‘point prediction’. By example, instead of just predicting someone’s height, \(\mu\), we could also predict how confident we are about our prediction, usually estimated as a standard error, \(\sigma\). This ‘confidence’ could be expressed as a confidence interval, for example \(\mu \pm \sigma\), or by assuming a distribution, for example \(\mathcal{N}(\mu, \sigma)\).
Predicting a confidence interval is possible using only features in mlr3
. Several (but not all) implemented regression learners can make standard error predictions by setting predict_type = "se"
. For compatible learners this means the learner will predict both the ‘usual’ response
predict type, as well as the standard error of the prediction, se
. Manually combining these predict types leads to a confidence interval. An example is in Figure 8.1 where we assume a symmetric Normal 95% confidence interval.
t = tsk("mtcars")
split = partition(t)
l = lrn("regr.ranger", predict_type = "se")
l$train(t, split$train)
p = l$predict(t, split$test)
p
<PredictionRegr> for 11 observations:
row_ids truth response se
4 21.4 20.91669 1.7147686
8 24.4 23.27838 0.7933228
21 21.5 23.73936 1.0114484

31 15.0 15.63936 0.5377532
19 30.4 29.63470 1.3813498
26 27.3 30.38791 1.4538484
This representation is more informative than a standard ‘point prediction’ as it includes confidence about the predictions. For example, the top prediction in Figure 8.1 might seem like a ‘good’ prediction as the mean response is close to the truth. However, the error bars suggest that we actually have low confidence in the prediction. On the other hand, the fourth prediction from the top is slightly further from the truth, but we are much more confident about our predictions. Analogously to classification, we might think of the top prediction as “P(Y = 30) = 0.4” versus the fourth prediction as “P(Y = 23) = 0.7” (numbers not exact). This level of detail allows more nuanced metrics to be utilized to measure probabilistic predictions, which we will turn to in the next section.
In the example above we used the estimated standard error to calculate an approximate symmetric Normal confidence interval. Instead we could have plugged the predicted response
and se
into a probability distribution as an estimate of the distribution mean and standard deviation. By assuming a probability distribution, we can make our predictions even more detailed by not just considering the mean and standard error of the distribution, but also the probability density function, cumulative distribution function, and all other common properties and methods.
distr6
implements many probability distributions with R6
and provides a flexible interface that was originally designed to be used with mlr3proba
. Below we demonstrate construction of two distributions (Uniform and Normal) in distr6
and how to access their methods and properties, below we call the pdf
(probability density function) and cdf
(cumulative distribution function) methods and look at the most important properties with summary
. Full details of the distr6
interface can be found on the package website^{1}.
library(distr6)
response = 5
se = 2
# construct Uniform distribution
unif = dstr("Uniform",
lower = response  se * sqrt(3),
upper = response + se * sqrt(3))
# summary of distribution properties
summary(unif)
Uniform Probability Distribution.
Parameterised with:
Id Support Value Tags
1: lower ℝ 1.535898 required
2: upper ℝ 8.464102 required
Quick Statistics
Mean: 5
Variance: 4
Skewness: 0
Ex. Kurtosis: 1.2
Support: [1.53589838486225,8.46410161513775] Scientific Type: ℝ
Traits: continuous; univariate
Properties: symmetric; platykurtic; no skew
[,1] [,2] [,3] [,4] [,5] [,6]
cdf 0 0.0669873 0.2113249 0.3556624 0.5000000 0.6443376
pdf 0 0.1443376 0.1443376 0.1443376 0.1443376 0.1443376
In the above example we manually transformed the response
and se
‘predictions’ to be compatible with a Uniform distribution construction, but learning these transformations can be time consuming. mlr3proba
includes a pipeline pipeline_probregr()
that incorporates the key steps of distribution prediction for probabilistic regression, which are:
response
predictionsse
predictionsThis pipeline is a wrapper around PipeOpProbregr
, and is showcased in the code below where we specify three inputs: 1) a random forest as the main learner, which predicts response
; 2) a featureless learner to estimate the standard deviation, which simply predicts the future standard error as the sample standard deviation in the training set; and 3) we assume a Normal distribution for the predicted distribution. We visualize the quality of predictions in Figure 8.2.
library(mlr3verse)
library(mlr3proba)
library(ggplot2)
# create our pipeline
l = as_learner(ppl("probregr",
learner = lrn("regr.ranger"),
learner_se = lrn("regr.featureless"),
dist = "Normal")
)
# train and predict
task = tsk("mtcars")
split = partition(task)
l$train(task, split$train)
p = l$predict(task, split$test)
p
<PredictionRegr> for 11 observations:
row_ids truth response se distr
4 21.4 19.19134 5.683925 <VectorDistribution[11]>
9 22.8 22.49444 5.683925 <VectorDistribution[11]>
27 26.0 25.11810 5.683925 <VectorDistribution[11]>

29 15.8 17.75105 5.683925 <VectorDistribution[11]>
19 30.4 28.32432 5.683925 <VectorDistribution[11]>
20 33.9 28.61724 5.683925 <VectorDistribution[11]>
plot_probregr(p, 3, "point", "random") +
ggtitle(sprintf("Logloss = %s", round(p$score(msr("regr.logloss")), 2)))
The $distr
column in our PredictionRegr
contains objects inheriting from distr6::Distribution
, which allows querying of all standard probability distribution methods and properties, as we have seen in the code above. This example shows that although none of our predictions were perfect – the truth was not exactly in line with the peak of the predicted distributions – in each case the truth was at least within an area of reasonable confidence.
In future versions of mlr3proba
we will extend functionality further by adding models that can make probabilistic predictions (e.g., with Bayesian methods), more losses (e.g., Brier score), and a dedicated predict type for interval predictions. We now turn to the next task implemented in mlr3proba
, which follows closely from probabilistic regression.
Survival analysis is a field of statistics concerned with trying to predict/estimate the time until an event takes place. This predictive problem is unique as survival models are trained and tested on data that may include ‘censoring’, which occurs when the event of interest does not take place. Survival analysis can be hard to explain in the abstract, so as a working example consider a marathon runner in a race. Here the ‘survival problem’ is trying to predict the time when the marathon runner finishes the race. However, if the event of interest does not take place, i.e., marathon runner gives up and does not finish the race, then they are said to be censored. Instead of throwing away information about censoring events, survival analysis datasets include a status variable that provides information about the ‘status’ of an observation. So in our example we might write the runner’s outcome as \((4, 1)\) if they finish the race at 4 hours, otherwise if they give up at 2 hours we would write \((2, 0)\).
The key to modelling in survival analysis is that we assume there exists a hypothetical time the marathon runner would have finished if they had not been censored, it is then the job of a survival learner to estimate what the true survival time would have been for a similar runner, assuming they are not censored (see Figure 8.3). Mathematically, this is represented by the hypothetical event time, \(Y\), the hypothetical censoring time, \(C\), the observed outcome time, \(T = min(Y, C)\), the event indicator \(\Delta = (T = Y)\), and as usual some features, \(X\). Learners are trained on \((T, \Delta)\) but, critically, make predictions of \(Y\) from previously unseen features. This means that unlike classification and regression, learners are trained on two variables, \((T, \Delta)\), which, in R, is often captured in a survival::Surv
object. An example of this is in the code below, where we randomly generate 6 survival times and 6 event indicators, an outcome with a +
indicates the outcome is censoring, otherwise it is the event of interest.
[1] 0.7110534+ 0.5259401 0.3869013+ 0.7185668 0.8801807+ 0.1211602
Readers familiar with survival analysis will recognize that the description above applies specifically to ‘right censoring’. Currently, this is the only form of censoring available in the mlr3
universe, hence restricting our discussion to that setting. For a good introduction to survival analysis see Collett (2014) or for machine learning in survival analysis specifically see R. Sonabend and Bender (2023).
For the remainder of this section we will look at how mlr3proba
(R. Sonabend et al. 2021) extends the building blocks of mlr3
for survival analysis. We will begin by looking at objects used to construct machine learning tasks for survival analysis, then we will turn to the learners we have implemented to solve these tasks, before looking at measures for evaluating survival analysis predictions, and then finally we will consider how to transform prediction types.
As we saw in the introduction to this section, survival algorithms require two targets for training, this means the new TaskSurv
object expects two targets. The simplest way to create a survival task is to use as_task_surv
, as in the following code chunk. Note how as_task_surv
coerces the target columns into a survival::Surv
object.
library("mlr3verse")
library("mlr3proba")
library("survival")
task = as_task_surv(survival::rats, time = "time",
event = "status", type = "right", id = "rats")
task$head()
time status litter rx sex
1: 101 0 1 1 f
2: 49 1 1 0 f
3: 104 0 1 0 f
4: 91 0 2 1 m
5: 104 0 2 0 m
6: 102 0 2 0 m
In the above example we used the survival::rats
dataset, which looks at predicting if a drug treatment was successful in preventing 150 rats from developing tumors. Note that the dataset (by its own admission) is not perfect and should generally be treated as ‘dummy’ data, which is good for examples but not realworld analysis.
As well as creating your own tasks, you can load any of the tasks shipped with mlr3proba
:
key label task_type nrow ncol properties lgl int
1: actg ACTG 320 surv 1151 13 0 3
2: gbcs German Breast Cancer surv 686 10 0 4
3: grace GRACE 1000 surv 1000 8 0 2
4: lung Lung Cancer surv 228 10 0 7
5: rats Rats surv 300 5 0 2
6: unemployment Unemployment Duration surv 3343 6 0 1
7: whas Worcester Heart Attack surv 481 11 0 4
5 variables not shown: [dbl, chr, fct, ord, pxc]
The interface for LearnerSurv
and PredictionSurv
objects is identical to the regression and classification settings discussed in Chapter 2. Similarly to these settings, survival learners are constructed with "lrn"
; available learners are listed in Appendix D.
The primary difference in constructing a survival learner (and the resulting predictions) is the number of possible predict_type
options that can be passed to lrn
.
Similarly to deterministic regression (Section 2.1), a survival model can make a single point prediction, and similarly to probabilistic regression (Section 8.2), a survival model could also make a prediction of a probability distribution. mlr3proba
has a different predict interface to mlr3
as all possible types of prediction (‘predict types’) are returned for all survival models. The reason for this decision is that all these predict types can be transformed to one another and it is therefore computationally simpler to return all at once instead of rerunning models to change predict type. In survival analysis, the following predictions can be made:
response
 Predicted survival time.distr
 Predicted survival distribution, either discrete or continuous.lp
 Linear predictor calculated as the fitted coefficients multiplied by the test data.crank
 Continuous risk ranking.We will go through each of these prediction types in more detail and with examples to make them less abstract. We will use the following setup for most of the examples. In this chunk we are partitioning the survival::rats
and training a Cox Proportional Hazards model (mlr_learners_surv.coxph
) on the training set and making predictions for the predict set. For this model, all predict types except response
can be computed.
t = tsk("rats")
split = partition(t)
p = lrn("surv.coxph")$train(t, split$train)$predict(t, split$test)
p
<PredictionSurv> for 99 observations:
row_ids time status crank lp distr
4 91 FALSE 2.4935516 2.4935516 <list[1]>
5 104 FALSE 2.8118294 2.8118294 <list[1]>
6 102 FALSE 2.8118294 2.8118294 <list[1]>

253 92 TRUE 0.4733165 0.4733165 <list[1]>
255 102 TRUE 0.1550388 0.1550388 <list[1]>
277 89 TRUE 0.5081450 0.5081450 <list[1]>
predict_type = "response"
Counterintuitively for many, the response
prediction of predicted survival times is actually the least common predict type in survival analysis. The likely reason for this is due to the presence of censoring. We rarely observe the true survival time for many observations and therefore it is unlikely any survival model can confidently make predictions for survival times. This is illustrated in the code below.
In the example below we train and predict from a survival support vector machine (mlr_learners_surv.svm
), note we use type = "regression"
to select the algorithm that optimizes survival time predictions. We then compare the predictions from the model to the true data.
library(mlr3extralearners)
pred = lrn("surv.svm", type = "regression", gamma.mu = 1e3)$
train(t, split$train)$predict(t, split$test)
data.frame(pred = pred$response[1:3], truth = pred$truth[1:3])
pred truth
1 89.34273 91+
2 89.34125 104+
3 89.34125 102+
As can be seen from the output, our predictions are all less than the true observed time, which means we know our model definitely underestimated the truth. However, because each of the true values are censored times, we have absolutely no way of knowing if these predictions are slightly bad or absolutely terrible, i.e., the true survival times could be \(105, 92, 92\) or they could be \(300, 1000, 200\). Hence, with no realistic way to evaluate these models, survival time predictions are rarely useful.
predict_type = "distr"
So unlike regression in which deterministic/point predictions are most common, in survival analysis distribution predictions are much more common. You will therefore find that the majority of survival models in mlr3proba
will make distribution predictions by default. As with probabilistic regression, we implement these predictions using the distr6
interface, which allows visualization and evaluation of survival curves (defined as 1  cumulative distribution function). In the example below we train a Cox PH model on the rats
dataset and then plot the survival function of the first three predictions and evaluation this function for all three predictions at \(t = \{40,70,120\}\).
predict_type = "lp"
lp
, often written as \(\eta\) in academic writing, is computationally the simplest prediction and has a natural analogue in regression modelling. Readers familiar with linear regression will know that when fitting a simple linear regression model, \(Y = X\beta\), we are actually estimating the values for \(\beta\), and the estimated linear predictor (lp) is then \(X\hat{\beta}\), where \(\hat{\beta}\) are our estimated coefficients. In simple survival models, the linear predictor is the same quantity (but estimated in a slightly more complicated way). The learner implementations in mlr3proba
are primarily machinelearning focused and few of these models have a simple linear form, which means that lp
cannot be computed for most of these.
predict_type = "crank"
The final prediction type, crank
, is the most common in survival analysis and perhaps also the most confusing. Academic texts will often refer to ‘risk’ predictions in survival analysis (hence why survival models are often known as ‘risk prediction models’), without defining what ‘risk’ means. Often risk is defined as \(exp(\eta)\) as this is a common quantity found in simple linear survival models. However, sometimes risk is defined as \(exp(\eta)\), and sometimes it can be an arbitrary quantity that does not have a meaningful interpretation. To prevent this confusion in mlr3proba
, we define the predict type crank
, which stands for continuous ranking. This is best explained by example.
Continuing from the previous example we output the first three crank
predictions. The output tells us that the second rat is at the higher risk of death (larger values represent higher risk) and the third rat is at the lowest risk of death. The distance between predictions also tells us that the difference in risk between the first and second rat is smaller than the difference between the second and third. The key points in this interpretation are: 1) lower values represent lower risk; 2) the difference between values has meaning but should not be overinterpreted; and 3) the actual values are meaningless. The last point is the most important, comparing these values between samples (or papers or experiments) is not meaningful.
The crank
prediction type is informative and common in practice because it allows identifying observations at lower/higher risk to each other, which is useful for resource allocation and prioritization (e.g., which patient should be given an expensive treatment), and clinical trials (e.g., are people in a treatment arm at lower risk of disease X than people in the control arm.).
Survival models in mlr3proba
are evaluated with MeasureSurv
objects, which are constructed in the usual way with "msr"
; measures currently implemented are listed in see Appendix D.
In general survival measures can be grouped into the following:
crank
and/or lp
predictions.crank
and/or distr
predictions.distr
predictions. key predict_type
1: surv.brier distr
2: surv.calib_alpha distr
3: surv.calib_beta lp
4: surv.chambless_auc lp
5: surv.cindex crank
6: surv.dcalib distr
There is a lot of debate in the literature around the ‘best’ survival measures to use to evaluate models, as a general rule we recommend RCLL (mlr_measures_surv.rcll
) to evaluate the quality of distr
predictions, concordance index (mlr_measures_surv.cindex
) to evaluate a model’s discrimination, and DCalibration (mlr_measures_surv.dcalib
) to evaluate a model’s calibration.
Throughout mlr3proba
documentation we refer to “native” and “composed” predictions. We define a ‘native’ prediction as the prediction made by a model without any postprocessing, whereas a ‘composed’ prediction is one that is returned after postprocessing.
In mlr3proba
we make use of composition internally to return a "crank"
prediction for every learner. This is to ensure that we can meaningfully benchmark all models according to at least one criterion. The package uses the following rules to create "crank"
predictions:
crank = risk
(we may multiply this by \(1\) to ensure the ‘low value low risk’ interpretation).response
prediction then we set crank = response
.lp
prediction then we set crank = lp
(or crank = lp
if needed).distr
prediction then we set crank
as the sum of the cumulative hazard function (see R. Sonabend, Bender, and Vollmer (2022) for full discussion as to why we picked this method).At the start of this section we mentioned that it is possible to transform prediction types between each other. In mlr3proba
this is possible with ‘compositor’ pipelines (Chapter 6). There are a number of pipelines implemented in the package but two in particular focus on predict type transformation:
pipeline_crankcompositor()
 Transforms a "distr"
prediction to "crank"
; andpipeline_distrcompositor()
 Transforms a "lp"
prediction to "distr"
.In practice, the second pipeline is more common as we internally use a version of the first pipeline whenever we return predictions from survival models. You may want to use the first pipeline to overwrite the default method of transforming distributions to rankings. For now we will just look at the second pipeline.
In the example below we load the rats
dataset, remove factor columns, and then partition the data into training and testing. We construct the distrcompositor
pipeline around a survival GLMnet learner (mlr_learners_surv.glmnet
) which by default can only make predictions for "lp"
and "crank"
. In the pipeline we specify that we will estimate the baseline distribution with a KaplanMeier estimator (estimator = "kaplan"
) and that we want to assume a proportional hazards form for our estimated distribution. We then train and predict in the usual way and in our output we can now see a distr
prediction.
library(mlr3verse)
library(mlr3extralearners)
task = tsk("rats")
task$select(c("litter", "rx"))
split = partition(task)
learner = lrn("surv.glmnet")
# no distr output
learner$train(task, split$train)$predict(task, split$test)
<PredictionSurv> for 99 observations:
row_ids time status crank.1 lp.1
1 101 FALSE 0.52464562 0.52464562
4 91 FALSE 0.53174836 0.53174836
6 102 FALSE 0.01420547 0.01420547

231 78 TRUE 0.54691061 0.54691061
235 80 TRUE 1.07865896 1.07865896
249 66 TRUE 0.58952702 0.58952702
pipe = as_learner(ppl(
"distrcompositor",
learner = learner,
estimator = "kaplan",
form = "ph"
))
# now with distr
pipe$train(task, split$train)$predict(task, split$test)
<PredictionSurv> for 99 observations:
row_ids time status crank.1 lp.1 distr
1 101 FALSE 0.52464562 0.52464562 <list[1]>
4 91 FALSE 0.53174836 0.53174836 <list[1]>
6 102 FALSE 0.01420547 0.01420547 <list[1]>

231 78 TRUE 0.54691061 0.54691061 <list[1]>
235 80 TRUE 1.07865896 1.07865896 <list[1]>
249 66 TRUE 0.58952702 0.58952702 <list[1]>
Mathematically, we have done the following:
For more details about prediction types and compositions we recommend Kalbfleisch and Prentice (2011).
Finally, we will put all the above into practice in a small benchmark experiment. We first load the grace
dataset and subset to the first 500 rows. We then select the RCLL, DCalibration, and Cindex to evaluate predictions, setup the same pipeline we used in the previous experiment, and load a Cox PH and KaplanMeier estimator. We run our experiment with 3fold crossvalidation and aggregate the results.
library(mlr3verse)
library(mlr3extralearners)
task = tsk("grace")$filter(1:500)
msr_txt = paste0("surv.", c("cindex", "dcalib", "rcll"))
measures = msrs(msr_txt)
pipe = as_learner(ppl(
"distrcompositor",
learner = lrn("surv.glmnet"),
estimator = "kaplan",
form = "ph"
))
pipe$id = "Coxnet"
learners = c(lrns(c("surv.coxph", "surv.kaplan")), pipe)
bmr = benchmark(benchmark_grid(task, learners, rsmp("cv", folds = 3)))
bmr$aggregate(measures)[, c("learner_id", ..msr_txt)]
learner_id surv.cindex surv.dcalib surv.rcll
1: surv.coxph 0.8237529 3.788224 3.114973
2: surv.kaplan 0.5000000 4.165848 3.263463
3: Coxnet 0.8258842 9.480867 3.131287
In this small experiment, Coxnet and Cox PH have the best discrimination, Cox PH has the best calibration, and Coxnet and Cox PH have similar overall predictive accuracy.
Density estimation is the learning task to estimate the unknown distribution from which a univariate dataset is generated, or put more simply to estimate the probability density (or mass) function for a variable. Density estimation is implemented in mlr3proba
, similarly to the previous two tasks that can also predict probability distributions (hence the name “mlr3probabilistic”). Unconditional density estimation, i.e., estimation of a target without any covariates, is viewed as an unsupervised task, which means the ‘truth’ is never known. For a good overview to density estimation see Silverman (1986).
The package mlr3proba
extends mlr3
with the following objects for density estimation:
TaskDens
to define density tasksLearnerDens
as the base class for density estimatorsPredictionDens
for density predictionsMeasureDens
as specialized class for density performance measuresWe will consider each in turn.
As density estimation is an unsupervised task, there is no target for prediction. In the code below we construct a density task using as_task_dens
which takes one argument, a data.frame
type object with exactly one column (which we will use to estimate the underlying distribution).
<TaskDens:data.frame(x = rnorm(1000))> (1000 x 1)
* Target: 
* Properties: 
* Features (1):
 dbl (1): x
As with other tasks, we have included a couple tasks that come shipped with mlr3proba
:
Density learners can make one of three possible prediction types.
distr
 probability distributionpdf
 probability density functioncdf
 cumulative distribution functionAll learners will return a distr
and pdf
prediction but only some can make cdf
predictions. Similarly to survival analysis and probabilistic regression, the distr
predict type is implemented using distr6
.
learn = lrn("dens.hist")
p = learn$train(task, 1:900)$predict(task, 901:1000)
x = seq.int(2, 2, 0.01)
ggplot(data.frame(x = x, y = p$distr$pdf(x)), aes(x = x, y = y)) +
geom_line() + theme_minimal()
The pdf
and cdf
predict types are simply wrappers around distr$pdf
and distr$cdf
respectively, which is best demonstrated by example:
<PredictionDens> for 3 observations:
row_ids pdf cdf distr
11 0.6 0.5036701 <Distribution[39]>
12 0.6 0.7035210 <Distribution[39]>
13 0.4 0.9134401 <Distribution[39]>
[,1] [,2]
[1,] 0.5036701 0.5036701
[2,] 0.7035210 0.7035210
[3,] 0.9134401 0.9134401
The reason for returning pdf
and cdf
in this way is to enable measures that can be used to evaluate the quality of our estimations, which we will return to in the next section.
Currently the only measure implemented in mlr3proba
for density estimation is logloss, which is defined in the same way as in classification and probabilistic regression, \(L(y) = log(\hat{f}_Y(y))\), where \(\hat{f}_Y\) is our estimated probability density function. Putting this together with the above we are now ready to train a density learner, estimate a distribution, and evaluate our estimation:
Some readers may spot parallels between density estimation and probabilistic regression (Section 8.2). In fact, density estimation is just a special case of probabilistic regression, occurring when we make an unconditional prediction. For example, given average rainfall across the USA, estimating the distribution of rainfall would be unsupervised density estimation. If we now wanted to estimate the distribution of rainfall next year given rainfall this year, then we would be back to supervised probabilistic regression. This is illustrated in the code below.
We load the precip
dataset and train, predict, and score a Normal kernel density estimation density learner (mlr_learners_dens.kde
). We then create a new dataset based on precip
but with an added variable for rainfall next year. Now we can specify a target for prediction based on another covariate, thus making this a supervised learning task. We then use the probregr
pipeline (Section 8.2) and train, predict, and score a random forest learner (`r ref(“mlr_learners_regr.ranger”)). Note the key difference in these outputs is that whilst both make distribution predictions, the former (density) estimates a single probability distribution for the variable of interest, whereas the latter (regression) predicts a distribution for each observation.
task = tsk("precip")
split = partition(task)
learn = lrn("dens.kde", kernel = "Norm")
p = learn$train(task, split$train)$predict(task, split$test)
p
<PredictionDens> for 23 observations:
row_ids pdf distr
3 0.008201882 <Distribution[39]>
4 0.017647600 <Distribution[39]>
6 0.012930403 <Distribution[39]>

57 0.022636656 <Distribution[39]>
60 0.018232811 <Distribution[39]>
69 0.012844688 <Distribution[39]>
dens.logloss
3.868815
df = task$data()
df$next_year = (df$precip * 1.5) + rnorm(length(df$precip))
task = as_task_regr(df, target = "next_year")
pipe = as_learner(ppl("probregr", lrn("regr.ranger"), dist = "Normal"))
p = pipe$train(task, split$train)$predict(task, split$test)
p
<PredictionRegr> for 23 observations:
row_ids truth response se distr
3 9.855528 13.32877 1.9314220 <VectorDistribution[23]>
4 73.348915 71.81530 1.5944345 <VectorDistribution[23]>
6 24.690852 25.88878 1.0082043 <VectorDistribution[23]>

57 69.050214 68.72069 0.8467608 <VectorDistribution[23]>
60 70.349208 71.81530 1.5944345 <VectorDistribution[23]>
69 22.141849 23.37564 1.0210862 <VectorDistribution[23]>
regr.logloss
2.408236
Finally, we conduct a small benchmark study on the mlr_tasks_faithful
task using some of the integrated density learners:
library(mlr3extralearners)
task = tsk("faithful")
learners = lrns(c("dens.hist", "dens.pen", "dens.kde"))
measure = msr("dens.logloss")
bmr = benchmark(benchmark_grid(task, learners, rsmp("cv", folds = 3)))
bmr$aggregate(measure)
autoplot(bmr, measure = measure)
The results of this experiment show that the sophisticated Penalized Density Estimator does not outperform the baseline histogram, but that the Kernel Density Estimator has at least consistently better (i.e. lower logloss) results.
Cluster analysis is another unsupervised task implemented in mlr3
. The objective of cluster analysis is to group data into clusters, where each cluster contains similar observations. The similarity is based on specified metrics that are task and applicationdependent. Unlike classification where we try to predict a class for each observation, in cluster analysis there is no ‘true’ label or class to predict.
The package mlr3cluster
extends mlr3
with the following objects for cluster analysis:
TaskClust
to define clustering tasksLearnerClust
as base class for clustering learnersPredictionClust
as specialized class for Prediction
objectsMeasureClust
as specialized class for performance measuresWe will consider each in turn.
Similarly to density estimation (Section 8.4), there is no target for prediction and so no truth
field in TaskClust
. Let’s look at the cluster::ruspini
dataset often used for cluster analysis examples.
The dataset has 75 rows and two columns and was first introduced in Ruspini (1970) to illustrate different clustering techniques. As we will see from the plots below, the observations form four natural clusters.
In the code below we construct a cluster task using as_task_clust
which only takes one argument, a data.frame
type object.
<TaskClust:ruspini> (75 x 2)
* Target: 
* Properties: 
* Features (2):
 int (2): x, y
Technically, we did not need to create a new task for ruspini dataset since it is already included in the package. Currently we have two clustering tasks shipped with mlr3cluster
:
As with density estimation, we refer to training
and predicting
for clustering to be consistent with the mlr3
interface, but strictly speaking this should be clustering
and assigning
(the latter we will return to shortly). Two predict_types
are available for clustering learners:
partition
– estimate of which cluster an observation falls intoprob
– probability of an observation belonging to each clusterHence, similarly to classification, prediction types of clustering learners are either deterministic (partition
) or probabilistic (prob
).
Below we construct a CMeans clustering learner with prob
prediction type and 3 clusters, train it on the cluster::ruspini
dataset and then return the cluster assignments ($assignments
) for each observation.
<LearnerClustCMeans:clust.cmeans>: Fuzzy CMeans Clustering Learner
* Model: 
* Parameters: centers=3
* Packages: mlr3, mlr3cluster, e1071
* Predict Types: partition, [prob]
* Feature Types: logical, integer, numeric
* Properties: complete, fuzzy, partitional
[1] 3 3 3 3 3 3
As clustering is unsupervised, it often does not make sense to use predict
for new data however this is still possible using the mlr3
interface:
<PredictionClust> for 2 observations:
row_ids partition prob.1 prob.2 prob.3
31 1 0.9663368 0.01814576 0.01551747
32 1 0.9782005 0.01177975 0.01001979
# using same data for estimation (common use case)
prediction = learner$train(task)$predict(task)
autoplot(prediction, task)
Whilst two prediction types are possible, there are some learners where ‘prediction’ can never make sense, for example in hierarchical clustering. In hierarchical clustering, the goal is to build a hierarchy of nested clusters by either splitting large clusters into smaller ones or merging smaller clusters into bigger ones. The final result is a tree or dendrogram which can change if a new data point is added. For consistency, mlr3cluster
offers predict
method for hierarchical clusters but with a warning:
Warning: Learner 'clust.hclust' doesn't predict on new data and predictions may
not make sense on new data
<PredictionClust> for 75 observations:
row_ids partition
1 1
2 1
3 1

73 1
74 1
75 1
In this case, the predict
method simply cuts the dendrogram into the number of clusters specified by k
parameter of the learner.
As previously discussed, unsupervised tasks do not have ground truth data to compare to in model evaluation. However, we can still measure the quality of cluster assignments by quantifying how closely objects within the same cluster are related (cluster cohesion) as well as how distinct different clusters are from each other (cluster separation). There are a few builtin evaluation metrics available to assess the quality of clustering, see Appendix D.
Two common measures are the within sum of squares (WSS) measure, mlr_measures_clust.wss
, and the silhouette coefficient, mlr_measures_clust.silhouette
. WSS calculates the sum of squared differences between observations and centroids, which is a quantification of cluster cohesion (smaller values indicate clusters more compact). The silhouette coefficient quantifies how well each point belongs to its assigned cluster versus neighboring clusters, where scores closer to 1
indicate well clustered and scores closer to 1
indicate poorly clustered. Note that the silhouette measure in mlr3cluster
returns the mean silhouette score across all observations and when there is only a single cluster, the measure simply outputs 0.
Putting this together with the above we can now score our cluster estimation (note we must pass the task
to msr
):
clust.wss clust.silhouette
5.106348e+04 6.327047e01
The very high WSS and middling mean silhouette coefficient indicate that our clusters could do with a bit more work. Often reducing an unsupervised task to a quantitative measure may not be useful (given no ground truth) and instead visualization may be a more effective tool for assessing the quality of the clusters.
It is easy to rely on clustering measures to assess the quality of clustering. However, this should be done with some care, by example consider cluster analysis on the following dataset.
spirals = mlbench::mlbench.spirals(n = 300, sd = 0.01)
task = as_task_clust(as.data.frame(spirals$x))
autoplot(task)
Now fitting our clustering learner.
learners = list(
lrn("clust.kmeans"),
lrn("clust.dbscan", eps = 0.1)
)
measures = list(msr("clust.silhouette"))
bmr = benchmark(benchmark_grid(task, learners, rsmp("insample")))
bmr$aggregate(measures)[, c(4, 7)]
learner_id clust.silhouette
1: clust.kmeans 0.37258038
2: clust.dbscan 0.02915828
We can see that Kmeans clustering gives us a higher average silhouette score and might assume that Kmeans learner with 2 centroids is a a better choice than DBSCAN method. However, now take a look at the cluster assignment plots.
prediction_kmeans = bmr$resample_results$resample_result[[1]]$prediction()
prediction_dbscan = bmr$resample_results$resample_result[[2]]$prediction()
autoplot(prediction_kmeans, task)
The two learners arrived at different results – the Kmeans algorithm assigned points that are part of the same line into two different clusters whereas DBSCAN assigned each line to its own cluster. Which one of these approaches is correct? The answer is it depends on your specific task and the goal of cluster analysis. If we had only relied on the silhouette score, then the details of how exactly the clustering was done would have been masked and we would not be able to decide which method was appropriate for the task.
As with other tasks, we use mlr3viz
to visualize performance of cluster learners. The two most important plots are principal components analysis (PCA) and silhouette plots.
PCA is a commonly used dimension reduction method in ML to reduce the number of variables in a dataset or to visualize the most important ‘components’, which are linear transformations of the dataset features. Components are considered more important if they have higher variance (and therefore more predictive power). In the context of clustering, by plotting observations against the first two components, and then coloring them by cluster, we could visualize our high dimensional dataset and we would expect to see observations in distinct groups.
Since our running example only has two features, PCA does not make sense to visualize the data. So we will use a task based on the USArrests
dataset instead. By plotting the result of PCA, we see that our model has separated observations into two clusters along the first two principal components.
task = mlr_tasks$get("usarrests")
learner = lrn("clust.kmeans")
prediction = learner$train(task)$predict(task)
autoplot(prediction, task, type = "pca")
Silhouette plots visually assess the quality of the estimated clusters by visualizing if observations in a cluster are wellplaced both individually and as a group. The plots include a dotted line which visualizes the average silhouette coefficient across all data points and each data point’s silhouette value is represented by a bar colored by cluster. In our particular case, the average silhouette index is 0.59. If the average silhouette value for a given cluster is below the average silhouette coefficient line then this implies that the cluster is not well defined.
Continuing with our new example, we find that a lot of observations are actually below the average line and close to zero, and therefore the quality of our cluster assignments is not very good, meaning that many observations are likely assigned to the wrong cluster.
Finally, we conduct a small benchmark study using the ruspini
data and with a few integrated cluster learners:
task = tsk("ruspini")
learners = list(
lrn("clust.featureless"),
lrn("clust.kmeans", centers = 4L),
lrn("clust.cmeans", centers = 3L)
)
measures = list(msr("clust.wss"), msr("clust.silhouette"))
bmr = benchmark(benchmark_grid(task, learners, rsmp("insample")))
bmr$aggregate(measures)[, c(4, 7, 8)]
learner_id clust.wss clust.silhouette
1: clust.featureless 244373.87 0.0000000
2: clust.kmeans 49512.16 0.5056154
3: clust.cmeans 51063.48 0.6327047
The experiment shows that using the Kmeans algorithm with four centers has the best cluster cohesion (lowest within sum of squares) and the best average silhouette score.
The final task we will discuss in this book is spatial analysis. Spatial analysis can be a subset of any other machine learning task (e.g., regression or classification) and is defined by the presence of spatial information in a dataset, usually stored as coordinates that are often named “x” and “y” or “lat” and “lon” (for ‘latitude’ and ‘longitude’ respectively.)
Spatial analysis is its own task as spatial data must be handled carefully due to the complexity of ‘autocorrelation’. Where correlation is defined as a statistical association between two variables, autocorrelation is a statistical association within one variable. In machine learning terms, in a dataset with features and observations, correlation occurs when two or more features are statistically associated in some way, whereas autocorrelation occurs when two or more observations are statistically associated across one feature. Autocorrelation therefore violates one of the fundamental assumptions of ML that all observations in a dataset are independent, which results in lower confidence about the quality of a trained ML model and we therefore cannot trust any performance estimates (Hastie, Friedman, and Tibshirani 2001).
Autocorrelation is present in spatial data as there is implicit information encoded in coordinates, such as whether two observations (e.g., cities, countries, continents) are close together or far apart. By example, say we are predicting the number of cases of a disease two months after outbreak in Germany. Outbreaks radiate outwards from an epicenter and therefore countries closer to Germany will have higher numbers of cases and countries further away will have lower numbers (Fig Figure 8.4, bottom), thus there is autocorrelation in the ‘country’.
Unlike other tasks we have looked at in this chapter, there is no underlying difference to the implemented learners or measures, instead we provide new resampling methods in mlr3spatiotempcv
to account for any overconfidence in predictions that might occur from autocorrelation. To make use of these resamplings we have also implemented special tasks in mlr3spatial
to hold spatial data.
Throughout this section we will use the mlr3spatiotempcv::ecuador
dataset and task as a working example.
TaskClassifST
and TaskRegrST
To make use of spatial resampling methods, we have implemented two extensions of TaskClassif
and TaskRegr
to accommodate spatial data, TaskClassifST
and TaskRegrST
respectively. Below we only show classification examples but regression follows trivially.
library(mlr3spatial)
library(mlr3spatiotempcv)
# create task from `data.frame`
task = as_task_classif_st(ecuador, id = "ecuador_task",
target = "slides", positive = "TRUE",
coordinate_names = c("x", "y"), crs = 32717)
# or create task from 'sf' object
data_sf = sf::st_as_sf(ecuador, coords = c("x", "y"), crs = 32717)
task = as_task_classif_st(data_sf, target = "slides", positive = "TRUE")
task
<TaskClassifST:data_sf> (751 x 11)
* Target: slides
* Properties: twoclass
* Features (10):
 dbl (10): carea, cslope, dem, distdeforest, distroad,
distslidespast, hcurv, log.carea, slope, vcurv
* Coordinates:
X Y
1: 712882.5 9560002
2: 715232.5 9559582
3: 715392.5 9560172
4: 715042.5 9559312
5: 715382.5 9560142

747: 714472.5 9558482
748: 713142.5 9560992
749: 713322.5 9560562
750: 715392.5 9557932
751: 713802.5 9560862
Once a task is created, you can train and predict as normal.
<PredictionClassif> for 751 observations:
row_ids truth response
1 TRUE TRUE
2 TRUE TRUE
3 TRUE TRUE

749 FALSE FALSE
750 FALSE FALSE
751 FALSE TRUE
However as discussed above, it is best to use the specialized resampling methods in order to have trustworthy estimates of model performance.
Before we look at the spatial resampling methods implemented in mlr3spatiotempcv
we will first show what can go wrong if standard resampling methods are used. Below we benchmark a decision tree on the mlr_tasks_ecuador
task using two different repeated crossvalidation resampling methods, the first (“NSpCV”) is a standard resampling method from mlr3
, the second (“SpCV”) is from mlr3spatiotempcv
and is optimized for spatial data. The example highlights how “NSpCV” makes it appear as if the decision tree is performing better than it is with significantly higher estimated performance, however this is an overconfident prediction due to the autocorrelation in the data.
learner = lrn("classif.rpart", predict_type = "prob")
rsmp_nsp = rsmp("repeated_cv", folds = 3, repeats = 2, id = "NSpCV")
rsmp_sp = rsmp("repeated_spcv_coords", folds = 3, repeats = 2, id = "SpCV")
design = benchmark_grid(task, learner, c(rsmp_nsp, rsmp_sp))
bmr = benchmark(design)
bmr$aggregate(msr("classif.acc"))[, c(5, 7)]
resampling_id classif.acc
1: NSpCV 0.6864064
2: SpCV 0.5842370
In the above example, the nonspatial resampling method means that the train and test data are very similar due to spatial autocorrelation, and so this is almost as bad as evaluating a model on the training data (see Chapter 2). In contrast, the spatial method has accommodated for autocorrelation and the test data is therefore less correlated (though still some association will remain) with the training data. Visually this can be seen using builtin autoplot
methods. In Figure 8.5 we visualize how the task is partitioned according to the spatial resampling method (Figure 8.5 top) and nonspatial resampling method (Figure 8.5 bottom). There is a clear separation between coordinates using the ‘correct’ spatial resampling method whereas the train and test splits overlap significantly (and are therefore highly correlated) using the nonspatial method.
library(patchwork)
autoplot(rsmp_sp, task, fold_id = c(1:3), size = 0.7) /
autoplot(rsmp_nsp, task, fold_id = c(1:3), size = 0.7) &
scale_y_continuous(breaks = seq(3.97, 4, 0.01)) &
scale_x_continuous(breaks = seq(79.06, 79.08, 0.02))
Now we have seen why spatial resampling methods matter we can take a look at what is implemented in mlr3spatiotempcv
. At the time of writing we have implemented 19 different resampling methods for spatial and spatiotemporal analysis. These are categorized into:
The choice of method may depend on specific characteristics of the dataset and there is no easy rule to pick one method over another, full details of different methods can be found in Schratz et al. (2021) – the paper deliberately avoids recommending one method over another as the ‘optimal’ choice is highly dependent on the predictive task, autocorrelation in the data, and the spatial structure of the sampling design. The documentation for each of the implemented methods includes details of each method as well as references to original publications.
Until now we have looked at resampling to accommodate spatiotemporal features, but what if you want to make spatiotemporal predictions? In this case the goal is to make classification or regression predictions for spatial coordinates at a pixel level, usually by creating and labelling raster images.
To enable these predictions we have created a new function, predict_spatial
, to allow spatial predictions using any of the following spatial data classes:
stars
(from package stars
)SpatRaster
(from package terra
)RasterLayer
(from package raster
)RasterStack
(from package raster
)To use a raster image for prediction, it must be wrapped in TaskUnsupervised
. In the example below we load the leipzig_points
file for training and coerce this to a spatiotemporal task with as_task_classif_st
, and we load the leipzig_raster
raster image and coerce this to an unsupervised task. Both files are shipped with, and can be downloaded from, mlr3spatial
.
library(sf)
# load sample points
leipzig_vector = sf::read_sf(system.file("extdata",
"leipzig_points.gpkg", package = "mlr3spatial"),
stringsAsFactors = TRUE)
# create training data
tsk_leipzig = as_task_classif_st(leipzig_vector, target = "land_cover")
# load raster image
leipzig_raster = terra::rast(system.file("extdata", "leipzig_raster.tif",
package = "mlr3spatial"))
# create testing data
tsk_predict = as_task_unsupervised(leipzig_raster)
Now we can continue as normal to train and predict with a classification learner, in this case a random forest.
lrn = lrn("classif.ranger")$train(tsk_leipzig)
pred = predict_spatial(tsk_predict, lrn, format = "terra")
pred
class : SpatRaster
dimensions : 206, 154, 1 (nrow, ncol, nlyr)
resolution : 10, 10 (x, y)
extent : 731810, 733350, 5692030, 5694090 (xmin, xmax, ymin, ymax)
coord. ref. : WGS 84 / UTM zone 32N (EPSG:32632)
source : file265478673975.tif
categories : categories
name : land_cover
min value : forest
max value : water
In this example we specified creation of a terra
object, which can be visualized with inbuilt plotting methods.
In this chapter, we explored going beyond deterministic regression and classification to see how functions in the mlr3
can be used to implement other machine learning tasks. Costsensitive classification extends the ‘normal’ classification setting by assuming errors associated with false negatives and false positives are unequal. Running costsensitive classification experiments is possible just using features in mlr3
. Probabilistic regression extend deterministic regression by making predictions over a full probability distribution and not just a single point. You can train and predict probabilistic regression models with mlr3
or more effectively in pipelines with mlr3proba
. Survival analysis, also available in mlr3proba
, is a special form of probabilistic regression when the outcome is censored, which means it may never be observed within a given time frame. The final task in mlr3proba
is density estimation, the unsupervised task concerned with estimating univariate probability distributions. Using mlr3cluster
, you can perform cluster analysis on observations, which involves grouping observations together according to similarities in their variables. Finally, with mlr3spatial
and mlr3spatiotempcv
, it is possible to perform spatial analysis to make predictions using coordinates as features and to make spatial predictions. The mlr3
interface is highly extensible, which means future machine learning tasks can (and will) be added to our universe and we will add these to this chapter of the book in future editions.
We will run set.seed(11)
before each of our solutions so you can reproduce our results.
Run a benchmark experiment on the german_credit
task with algorithms: featureless
, log_reg
, ranger
. Tune the featureless
model using tunetreshold
and learner_cv
. Use 2fold 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. Are your results surprising?
Use the probregr
pipeline to create a probabilistic regression model using: xgboost for the response
prediction, featureless learner for the se
prediction, and assuming an Cauchy distribution. Train and predict on task = tsk("mtcars"); split = partition(task)
. Evaluate your model with the logloss measure.
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.
Estimate the density of the tsk("precip")
data using logspline
(from mlr3extralearners
). Run this experiment using task = tsk("precip"); split = partition(task)
. Evaluate your model with the logloss measure.
Run a benchmark clustering experiment on the wine
dataset without a label column. Compare the performance of 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?
Run a (spatially) unbiased classification benchmark experiment on the ecuador
task with a featureless learner and xgboost, evaluate with the binary Brier score.