In a benchmark experiment different learning methods are applied to one or several data sets with the aim to compare and rank the algorithms with respect to one or more performance measures.

In mlr a benchmark experiment can be conducted by calling function benchmark() on a base::list() of makeLearner()s and a base::list() of Task()s. benchmark() basically executes resample() for each combination of makeLearner() and Task(). You can specify an individual resampling strategy for each Task() and select one or multiple performance measures to be calculated.

# Conducting benchmark experiments

We start with a small example. Two learners, MASS::lda() and a rpart::rpart(), are applied to one classification problem (sonar.task()). As resampling strategy we choose "Holdout". The performance is thus calculated on a single randomly sampled test data set.

In the example below we create a resample description (makeResampleDesc()), which is automatically instantiated by benchmark(). The instantiation is done only once per Task(), i.e., the same training and test sets are used for all learners. It is also possible to directly pass a makeResampleInstance().

If you would like to use a fixed test data set instead of a randomly selected one, you can create a suitable makeResampleInstance() through function makeFixedHoldoutInstance().

For convenience, if you don’t want to pass any additional arguments to makeLearner(), you don’t need to generate the makeLearner()s explicitly, but it’s sufficient to provide the learner name. In the above example we could also have written:

In the printed summary table every row corresponds to one pair of Task() and makeLearner(). The entries show the mean misclassification error, the default performance measure for classification, on the test data set.

The result bmr is an object of class BenchmarkResult(). Basically, it contains a base::list() of lists of ResampleResult() objects, first ordered by Task() and then by makeLearner().

## Making experiments reproducible

Typically, we would want our experiment results to be reproducible. mlr obeys the set.seed function, so make sure to use set.seed at the beginning of your script if you would like your results to be reproducible.

Note that if you are using parallel computing, you may need to adjust how you call set.seed depending on your usecase. One possibility is to use set.seed(123, "L'Ecuyer") in order to ensure the results are reproducible for each child process. See the examples in parallel::mclapply() for more information on reproducibility and parallel computing.

# Accessing benchmark results

mlr provides several accessor functions, named getBMR<WhatToExtract>, that permit to retrieve information for further analyses. This includes for example the performances or predictions of the learning algorithms under consideration.

## Learner performances

Let’s have a look at the benchmark result above. getBMRPerformances() returns individual performances in resampling runs, while getBMRAggrPerformances() gives the aggregated values.

Since we used holdout as resampling strategy, individual and aggregated performance values coincide.

By default, nearly all “getter” functions return a nested base::list(), with the first level indicating the task and the second level indicating the learner. If only a single learner or, as in our case a single task is considered, setting drop = TRUE simplifies the result to a flat base::list().

Often it is more convenient to work with base::data.frame()s. You can easily convert the result structure by setting as.df = TRUE.

## Predictions

Per default, the BenchmarkResult() contains the learner predictions. If you do not want to keep them, e.g., to conserve memory, set keep.pred = FALSE when calling benchmark().

You can access the predictions using function getBMRPredictions(). Per default, you get a nested base::list() of ResamplePrediction()objects. As above, you can use the drop or as.df options to simplify the result.

getBMRPredictions(bmr)

getBMRPredictions(bmr)

## $Sonar-example ##$Sonar-example$classif.lda ## Resampled Prediction for: ## Resample description: holdout with 0.67 split rate. ## Predict: test ## Stratification: FALSE ## predict.type: prob ## threshold: M=0.50,R=0.50 ## time (mean): 0.00 ## id truth prob.M prob.R response iter set ## 1 194 M 0.001914379 9.980856e-01 R 1 test ## 2 18 R 0.474564117 5.254359e-01 R 1 test ## 3 196 M 0.996712551 3.287449e-03 M 1 test ## 4 10 R 0.001307244 9.986928e-01 R 1 test ## 5 134 M 0.999999755 2.445735e-07 M 1 test ## 6 34 R 0.999761364 2.386361e-04 M 1 test ## ... (#rows: 70, #cols: 7) ## ##$Sonar-example\$classif.rpart
## Resampled Prediction for:
## Resample description: holdout with 0.67 split rate.
## Predict: test
## Stratification: FALSE
## predict.type: response
## threshold:
## time (mean): 0.00
##    id truth response iter  set
## 1 194     M        M    1 test
## 2  18     R        R    1 test
## 3 196     M        M    1 test
## 4  10     R        R    1 test
## 5 134     M        M    1 test
## 6  34     R        M    1 test
## ... (#rows: 70, #cols: 5)

##         task.id  learner.id  id truth      prob.M       prob.R response
## 1 Sonar-example classif.lda 194     M 0.001914379 9.980856e-01        R
## 2 Sonar-example classif.lda  18     R 0.474564117 5.254359e-01        R
## 3 Sonar-example classif.lda 196     M 0.996712551 3.287449e-03        M
## 4 Sonar-example classif.lda  10     R 0.001307244 9.986928e-01        R
## 5 Sonar-example classif.lda 134     M 0.999999755 2.445735e-07        M
## 6 Sonar-example classif.lda  34     R 0.999761364 2.386361e-04        M
##   iter  set
## 1    1 test
## 2    1 test
## 3    1 test
## 4    1 test
## 5    1 test
## 6    1 test

It is also easily possible to access results for certain learners or tasks via their IDs. For this purpose many “getter” functions have a learner.ids and a task.ids argument.

If you don’t like the default IDs, you can set the IDs of learners and tasks via the id option of makeLearner() and makeTask(). Moreover, you can conveniently change the ID of a makeLearner() via function setLearnerid().

## IDs

The IDs of all makeLearner()s, Task()s and Measure’s (makeMeasure()) in a benchmark experiment can be retrieved as follows:

## Fitted models

Per default the BenchmarkResult() also contains the fitted models for all learners on all tasks. If you do not want to keep them set models = FALSE when calling benchmark(). The fitted models can be retrieved by function getBMRModels(). It returns a (possibly nested) base::list() of WrappedModel (makeWrappedModel()) objects.

# Merging benchmark results

Sometimes after completing a benchmark experiment it turns out that you want to extend it by another makeLearner() or another Task(). In this case you can perform an additional benchmark experiment and then use function mergeBenchmarkResults() to combine the results to a single BenchmarkResult() object that can be accessed and analyzed as usual.

For example in the benchmark experiment above we applied MASS::lda() and rpart::rpart() to the sonar.task(). We now perform a second experiment using a randomForest::randomForest() and quadratic discriminant analysis MASS::qda() and merge the results.

Note that in the above examples in each case a resample description (makeResampleDesc()) was passed to the benchmark() function. For this reason MASS::lda() and rpart::rpart() were most likely evaluated on a different training/test set pair than randomForest::randomForest() and MASS::qda().

Differing training/test set pairs across learners pose an additional source of variation in the results, which can make it harder to detect actual performance differences between learners. Therefore, if you suspect that you will have to extend your benchmark experiment by another makeLearner() later on it’s probably easiest to work with makeResampleInstance()s from the start. These can be stored and used for any additional experiments.

Alternatively, if you used a resample description in the first benchmark experiment you could also extract the makeResampleInstance()s from the BenchmarkResult() bmr and pass these to all further benchmark() calls.

# Benchmark analysis and visualization

mlr offers several ways to analyze the results of a benchmark experiment. This includes visualization, ranking of learning algorithms and hypothesis tests to assess performance differences between learners.

In order to demonstrate the functionality we conduct a slightly larger benchmark experiment with three learning algorithms that are applied to five classification tasks.

## Example: Comparing lda, rpart and random Forest

We consider MASS::lda(), classification trees rpart::rpart(), and random forests randomForest::randomForest(). Since the default learner IDs are a little long, we choose shorter names in the R code below.

We use five classification tasks. Three are already provided by mlr, two more data sets are taken from package mlbench::mlbench() and converted to Task()s by function convertMLBenchObjToTask().

For all tasks 10-fold cross-validation is chosen as resampling strategy. This is achieved by passing a single resample description (makeResampleDesc()) to benchmark(), which is then instantiated automatically once for each Task(). This way, the same instance is used for all learners applied to a single task.

It is also possible to choose a different resampling strategy for each Task() by passing a base::list() of the same length as the number of tasks that can contain both resample descriptions (makeResampleDesc()) and resample instances (makeResampleInstance()).

We use the mean misclassification error mmce as primary performance measure, but also calculate the balanced error rate ber and the training time timetrain.

# Create a list of learners
lrns = list(
makeLearner("classif.lda", id = "lda"),
makeLearner("classif.rpart", id = "rpart"),
makeLearner("classif.randomForest", id = "randomForest")
)

rdesc = makeResampleDesc("CV", iters = 10)
meas = list(mmce, ber, timetrain)
bmr = benchmark(lrns, tasks, rdesc, meas, show.info = FALSE)

## 1                 iris-example          lda     0.02000000    0.02222222
## 2                 iris-example        rpart     0.08000000    0.07555556
## 3                 iris-example randomForest     0.05333333    0.05250000
## 4             mlbench.ringnorm          lda     0.35000000    0.34605671
## 5             mlbench.ringnorm        rpart     0.17333333    0.17313632
## 6             mlbench.ringnorm randomForest     0.05666667    0.05724405
## 7             mlbench.waveform          lda     0.19000000    0.18257244
## 8             mlbench.waveform        rpart     0.28833333    0.28765247
## 9             mlbench.waveform randomForest     0.17500000    0.17418440
## 10 PimaIndiansDiabetes-example          lda     0.22778537    0.27148893
## 11 PimaIndiansDiabetes-example        rpart     0.25133288    0.28967870
## 12 PimaIndiansDiabetes-example randomForest     0.23427888    0.27464510
## 13               Sonar-example          lda     0.24619048    0.23986694
## 14               Sonar-example        rpart     0.30785714    0.31153361
## 15               Sonar-example randomForest     0.18738095    0.18359363
##    timetrain.test.mean
## 1               0.0039
## 2               0.0048
## 3               0.0330
## 4               0.0092
## 5               0.0116
## 6               0.3548
## 7               0.0084
## 8               0.0100
## 9               0.3675
## 10              0.0424
## 11              0.0066
## 12              0.4108
## 13              0.0147
## 14              0.0128
## 15              0.2335

From the aggregated performance values we can see that for the iris- and PimaIndiansDiabetes-example linear discriminant analysis (MASS::lda()) performs well while for all other tasks the randomForest::randomForest() seems superior. Training takes longer for the randomForest::randomForest() than for the other learners.

In order to draw any conclusions from the average performances at least their variability has to be taken into account or, preferably, the distribution of performance values across resampling iterations.

The individual performances on the 10 folds for every task, learner, and measure are retrieved below.

A closer look at the result reveals that the randomForest::randomForest() outperforms the classification tree (rpart::rpart()) in every instance, while linear discriminant analysis (MASS::lda()) performs better than rpart::rpart() most of the time. Additionally MASS::lda() sometimes even beats the randomForest::randomForest(). With increasing size of such benchmark() experiments, those tables become almost unreadable and hard to comprehend.

mlr features some plotting functions to visualize results of benchmark experiments that you might find useful. Moreover, mlr offers statistical hypothesis tests to assess performance differences between learners.

## Integrated plots

Plots are generated using ggplot2::ggplot2(). Further customization, such as renaming plot elements or changing colors, is easily possible.

### Visualizing performances

plotBMRBoxplots() creates box or violin plots which show the distribution of performance values across resampling iterations for one performance measure and for all learners and tasks (and thus visualize the output of getBMRPerformances()).

Below are both variants, box and violin plots. The first plot shows the mmce and the second plot the ber. Moreover, in the second plot we color the boxes according to the learner.ids.

plotBMRBoxplots(bmr, measure = mmce, order.lrn = getBMRLearnerIds(bmr))

Note that by default the measure names and the learner short.names are used as axis labels.

If you prefer the ids like, e.g., mmce and ber set pretty.names = FALSE (as done for the second plot). Of course you can also use the ggplot2::ggplot2() functionality like the ggplot2::labs() function to choose completely different labels.

One question which comes up quite often is how to change the panel headers (which default to the Task() IDs) and the learner names on the x-axis. For example looking at the above plots we would like to remove the “example” suffixes and the “mlbench” prefixes from the panel headers. Moreover, we want uppercase learner labels. Currently, the probably simplest solution is to change the factor levels of the plotted data as shown below.

### Visualizing aggregated performances

The aggregated performance values (resulting from getBMRAggrPerformances()) can be visualized by function plotBMRSummary(). This plot draws one line for each task on which the aggregated values of one performance measure for all learners are displayed. By default, the first measure in the base::list() of Measure’s (makeMeasure()) passed to benchmark() is used, in our example mmce. Moreover, a small vertical jitter is added to prevent overplotting.

### Calculating and visualizing ranks

Additional to the absolute performance, relative performance, i.e., ranking the learners is usually of interest and might provide valuable additional insight.

Function convertBMRToRankMatrix() calculates ranks based on aggregated learner performances of one measure. We choose the mean misclassification error. The rank structure can be visualized by plotBMRRanksAsBarChart().

Methods with best performance, i.e., with lowest mmce, are assigned the lowest rank. Linear discriminant analysis (MASS::lda()) is best for the iris and PimaIndiansDiabetes-examples while the randomForest::randomForest() shows best results on the remaining tasks.

plotBMRRanksAsBarChart() with option pos = "tile" shows a corresponding heat map. The ranks are displayed on the x-axis and the learners are color-coded.

plotBMRRanksAsBarChart(bmr, pos = "tile", order.lrn = getBMRLearnerIds(bmr))

A similar plot can also be obtained via plotBMRSummary(). With option trafo = "rank" the ranks are displayed instead of the aggregated performances.

plotBMRSummary(bmr, trafo = "rank", jitter = 0)

Alternatively, you can draw stacked bar charts (the default) or bar charts with juxtaposed bars (pos = "dodge") that are better suited to compare the frequencies of learners within and across ranks.

plotBMRRanksAsBarChart(bmr, order.lrn = getBMRLearnerIds(bmr))
plotBMRRanksAsBarChart(bmr, pos = "dodge", order.lrn = getBMRLearnerIds(bmr))

## Comparing learners using hypothesis tests

Many researchers feel the need to display an algorithm’s superiority by employing some sort of hypothesis testing. As non-parametric tests seem better suited for such benchmark results the tests provided in mlr are the Overall Friedman test and the Friedman-Nemenyi post hoc test.

While the ad hoc friedmanTestBMR() based on stats::friedman.test() is testing the hypothesis whether there is a significant difference between the employed learners, the post hoc friedmanPostHocTestBMR() tests for significant differences between all pairs of learners. Non parametric tests often do have less power then their parametric counterparts but less assumptions about underlying distributions have to be made. This often means many data sets are needed in order to be able to show significant differences at reasonable significance levels.

In our example, we want to compare the three learners on the selected data sets. First we might we want to test the hypothesis whether there is a difference between the learners.

In order to keep the computation time for this tutorial small, the makeLearner()s are only evaluated on five tasks. This also means that we operate on a relatively low significance level $$\alpha = 0.1$$. As we can reject the null hypothesis of the Friedman test at a reasonable significance level we might now want to test where these differences lie exactly.

At this level of significance, we can reject the null hypothesis that there exists no performance difference between the decision tree (rpart::rpart()) and the randomForest::randomForest().

## Critical differences diagram

In order to visualize differently performing learners, a critical differences diagramcan be plotted, using either the Nemenyi test (test = "nemenyi") or the Bonferroni-Dunn test (test = "bd").

The mean rank of learners is displayed on the x-axis.

• Choosing test = "nemenyi" compares all pairs of makeLearner()s to each other, thus the output are groups of not significantly different learners. The diagram connects all groups of learners where the mean ranks do not differ by more than the critical differences. Learners that are not connected by a bar are significantly different, and the learner(s) with the lower mean rank can be considered “better” at the chosen significance level.
• Choosing test = "bd" performs a pairwise comparison with a baseline. An interval which extends by the given critical difference in both directions is drawn around the makeLearner() chosen as baseline, though only comparisons with the baseline are possible. All learners within the interval are not significantly different, while the baseline can be considered better or worse than a given learner which is outside of the interval.

The critical difference $$\mathit{CD}$$ is calculated by $\mathit{CD} = q_\alpha \cdot \sqrt{\frac{k(k+1)}{6N}},$ where $$N$$ denotes the number of tasks, $$k$$ is the number of learners, and $$q_\alpha$$ comes from the studentized range statistic divided by $$\sqrt{2}$$. For details see Demsar (2006).

Function generateCritDifferencesData() does all necessary calculations while function plotCritDifferences() draws the plot. See the tutorial page about visualization for details on data generation and plotting functions.

# Nemenyi test
g = generateCritDifferencesData(bmr, p.value = 0.1, test = "nemenyi")
plotCritDifferences(g) + coord_cartesian(xlim = c(-1,5), ylim = c(0,2)) +
scale_colour_manual(values = c("lda" = "#F8766D", "rpart" = "#00BA38", "randomForest" = "#619CFF"))

# Bonferroni-Dunn test
g = generateCritDifferencesData(bmr, p.value = 0.1, test = "bd", baseline = "randomForest")
plotCritDifferences(g) + coord_cartesian(xlim = c(-1,5), ylim = c(0,2)) +
scale_colour_manual(values = c("lda" = "#F8766D", "rpart" = "#00BA38", "randomForest" = "#619CFF"))

## Custom plots

You can easily generate your own visualizations by customizing the ggplot2::ggplot() objects returned by the plots above, retrieve the data from the ggplot2::ggplot() objects and use them as basis for your own plots, or rely on the base::data.frame()s returned by getBMRPerformances() or getBMRAggrPerformances(). Here are some examples.

Instead of boxplots (as in plotBMRBoxplots()) we could create density plots to show the performance values resulting from individual resampling iterations.

In order to plot multiple performance measures in parallel, perf is reshaped to long format. Below we generate grouped boxplots showing the error rate and the training time timetrain.

It might also be useful to assess if learner performances in single resampling iterations, i.e., in one fold, are related. This might help to gain further insight, for example by having a closer look at train and test sets from iterations where one learner performs exceptionally well while another one is fairly bad. Moreover, this might be useful for the construction of ensembles of learning algorithms. Below, function GGally::ggpairs() from package GGally::GGally() is used to generate a scatterplot matrix of mean misclassification errors on the mlbench::Sonar() data set.