The visualization of decision boundaries helps to understand what the pros and cons of individual classification learners are. This posts demonstrates how to create such plots.
We load the mlr3 package.
We initialize the random number generator with a fixed seed for reproducibility, and decrease the verbosity of the logger to keep the output clearly represented.
set.seed(7832)
lgr::get_logger("mlr3")$set_threshold("warn")
Artificial Data Sets
The three artificial data sets are generated by task generators (implemented in mlr3):
XOR
Points are distributed on a 2-dimensional cube with corners \((\pm 1, \pm 1)\). Class is "red" if \(x\) and \(y\) have the same sign, and "black" otherwise.
Circle
Two circles with same center but different radii. Points in the smaller circle are "black", points only in the larger circle are "red".
Moons
Two interleaving half circles (“moons”).
Learners
We consider the following learners:
library("mlr3learners")
learners = list(
# k-nearest neighbours classifier
lrn("classif.kknn", id = "kkn", predict_type = "prob", k = 3),
# linear svm
lrn("classif.svm", id = "lin. svm", predict_type = "prob", kernel = "linear"),
# radial-basis function svm
lrn("classif.svm", id = "rbf svm", predict_type = "prob", kernel = "radial",
gamma = 2, cost = 1, type = "C-classification"),
# naive bayes
lrn("classif.naive_bayes", id = "naive bayes", predict_type = "prob"),
# single decision tree
lrn("classif.rpart", id = "tree", predict_type = "prob", cp = 0, maxdepth = 5),
# random forest
lrn("classif.ranger", id = "random forest", predict_type = "prob")
)
The hyperparameters are chosen in a way that the decision boundaries look “typical” for the respective classifier. Of course, with different hyperparameters, results may look very different.
Fitting the Models
To apply each learner on each task, we first build an exhaustive grid design of experiments with benchmark_grid() and then pass it to benchmark() to do the actual work. A simple holdout resampling is used here:
design = benchmark_grid(
tasks = tasks,
learners = learners,
resamplings = rsmp("holdout")
)
bmr = benchmark(design, store_models = TRUE)
A quick look into the performance values:
| task_id | learner_id | classif.acc |
|---|---|---|
| xor_200 | kkn | 0.9402985 |
| xor_200 | lin. svm | 0.5223881 |
| xor_200 | rbf svm | 0.9701493 |
| xor_200 | naive bayes | 0.4328358 |
| xor_200 | tree | 0.9402985 |
| xor_200 | random forest | 1.0000000 |
| moons_200 | kkn | 1.0000000 |
| moons_200 | lin. svm | 0.8805970 |
| moons_200 | rbf svm | 1.0000000 |
| moons_200 | naive bayes | 0.8955224 |
| moons_200 | tree | 0.8955224 |
| moons_200 | random forest | 0.9552239 |
| circle_200 | kkn | 0.8805970 |
| circle_200 | lin. svm | 0.4925373 |
| circle_200 | rbf svm | 0.8955224 |
| circle_200 | naive bayes | 0.7014925 |
| circle_200 | tree | 0.7462687 |
| circle_200 | random forest | 0.7761194 |
Plotting
To generate the plots, we iterate over the individual ResampleResult objects stored in the BenchmarkResult, and in each iteration we store the plot of the learner prediction generated by the mlr3viz package.
We now have a list of plots. Each one can be printed individually:
print(plots[[1]])
Note that only observations from the test data is plotted as points.
To get a nice annotated overview, we arranged all plots together in a single PDF file. The number in the upper right is the respective accuracy on the test set.
As you can see, the decision boundaries look very different. Some are linear, others are parallel to the axis, and yet others are highly non-linear. The boundaries are partly very smooth with a slow transition of probabilities, others are very abrupt. All these properties are important during model selection, and should be considered for your problem at hand.