# 📃 Solution for Exercise M5.01¶

In the previous notebook, we showed how a tree with a depth of 1 level was working. The aim of this exercise is to repeat part of the previous experiment for a depth with 2 levels to show how the process of partitioning is repeated over time.

Before to start, we will:

• split the dataset into training and testing dataset;

• define the function to show the classification decision function.

```import pandas as pd

culmen_columns = ["Culmen Length (mm)", "Culmen Depth (mm)"]
target_column = "Species"
```

Note

If you want a deeper overview regarding this dataset, you can refer to the Appendix - Datasets description section at the end of this MOOC.

```from sklearn.model_selection import train_test_split

data, target = penguins[culmen_columns], penguins[target_column]
data_train, data_test, target_train, target_test = train_test_split(
data, target, random_state=0
)
range_features = {
feature_name: (data[feature_name].min() - 1, data[feature_name].max() + 1)
for feature_name in data.columns
}
```
```import numpy as np
import matplotlib.pyplot as plt

def plot_decision_function(fitted_classifier, range_features, ax=None):
"""Plot the boundary of the decision function of a classifier."""
from sklearn.preprocessing import LabelEncoder

feature_names = list(range_features.keys())
# create a grid to evaluate all possible samples
plot_step = 0.02
xx, yy = np.meshgrid(
np.arange(*range_features[feature_names], plot_step),
np.arange(*range_features[feature_names], plot_step),
)

# compute the associated prediction
Z = fitted_classifier.predict(np.c_[xx.ravel(), yy.ravel()])
Z = LabelEncoder().fit_transform(Z)
Z = Z.reshape(xx.shape)

# make the plot of the boundary and the data samples
if ax is None:
_, ax = plt.subplots()
ax.contourf(xx, yy, Z, alpha=0.4, cmap="RdBu")

return ax
```

Create a decision tree classifier with a maximum depth of 2 levels and fit the training data. Once this classifier trained, plot the data and the decision boundary to see the benefit of increasing the depth.

```# solution
from sklearn.tree import DecisionTreeClassifier

tree = DecisionTreeClassifier(max_depth=2)
tree.fit(data_train, target_train)
```
```DecisionTreeClassifier(max_depth=2)
```
```import seaborn as sns

palette = ["tab:red", "tab:blue", "black"]
ax = sns.scatterplot(data=penguins, x=culmen_columns, y=culmen_columns,
hue=target_column, palette=palette)
plot_decision_function(tree, range_features, ax=ax)
plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')
_ = plt.title("Decision boundary using a decision tree")
``` Did we make use of the feature “Culmen Length”? Plot the tree using the function `sklearn.tree.plot_tree` to find out!

```# solution
from sklearn.tree import plot_tree

_, ax = plt.subplots(figsize=(16, 12))
_ = plot_tree(tree, feature_names=culmen_columns,
class_names=tree.classes_, impurity=False, ax=ax)
``` The resulting tree has 7 nodes: 3 of them are “split nodes” and 4 are “leaf nodes” (or simply “leaves”), organized in 2 levels. We see that the second tree level used the “Culmen Length” to make two new decisions. Qualitatively, we saw that such a simple tree was enough to classify the penguins’ species.

Compute the accuracy of the decision tree on the testing data.

```# solution
test_score = tree.fit(data_train, target_train).score(data_test, target_test)
print(f"Accuracy of the DecisionTreeClassifier: {test_score:.2f}")
```
```Accuracy of the DecisionTreeClassifier: 0.97
```

At this stage, we have the intuition that a decision tree is built by successively partitioning the feature space, considering one feature at a time.

We predict an Adelie penguin if the feature value is below the threshold, which is not surprising since this partition was almost pure. If the feature value is above the threshold, we predict the Gentoo penguin, the class that is most probable.