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# Post pruning decision trees with cost complexity pruning¶

The `DecisionTreeClassifier`

provides parameters such as
`min_samples_leaf`

and `max_depth`

to prevent a tree from overfiting. Cost
complexity pruning provides another option to control the size of a tree. In
`DecisionTreeClassifier`

, this pruning technique is parameterized by the
cost complexity parameter, `ccp_alpha`

. Greater values of `ccp_alpha`

increase the number of nodes pruned. Here we only show the effect of
`ccp_alpha`

on regularizing the trees and how to choose a `ccp_alpha`

based on validation scores.

See also Minimal Cost-Complexity Pruning for details on pruning.

```
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.tree import DecisionTreeClassifier
```

## Total impurity of leaves vs effective alphas of pruned tree¶

Minimal cost complexity pruning recursively finds the node with the “weakest
link”. The weakest link is characterized by an effective alpha, where the
nodes with the smallest effective alpha are pruned first. To get an idea of
what values of `ccp_alpha`

could be appropriate, scikit-learn provides
`DecisionTreeClassifier.cost_complexity_pruning_path`

that returns the
effective alphas and the corresponding total leaf impurities at each step of
the pruning process. As alpha increases, more of the tree is pruned, which
increases the total impurity of its leaves.

```
X, y = load_breast_cancer(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
clf = DecisionTreeClassifier(random_state=0)
path = clf.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas, impurities = path.ccp_alphas, path.impurities
```

In the following plot, the maximum effective alpha value is removed, because it is the trivial tree with only one node.

```
fig, ax = plt.subplots()
ax.plot(ccp_alphas[:-1], impurities[:-1], marker="o", drawstyle="steps-post")
ax.set_xlabel("effective alpha")
ax.set_ylabel("total impurity of leaves")
ax.set_title("Total Impurity vs effective alpha for training set")
```

Out:

```
Text(0.5, 1.0, 'Total Impurity vs effective alpha for training set')
```

Next, we train a decision tree using the effective alphas. The last value
in `ccp_alphas`

is the alpha value that prunes the whole tree,
leaving the tree, `clfs[-1]`

, with one node.

```
clfs = []
for ccp_alpha in ccp_alphas:
clf = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf.fit(X_train, y_train)
clfs.append(clf)
print(
"Number of nodes in the last tree is: {} with ccp_alpha: {}".format(
clfs[-1].tree_.node_count, ccp_alphas[-1]
)
)
```

Out:

```
Number of nodes in the last tree is: 1 with ccp_alpha: 0.3272984419327777
```

For the remainder of this example, we remove the last element in
`clfs`

and `ccp_alphas`

, because it is the trivial tree with only one
node. Here we show that the number of nodes and tree depth decreases as alpha
increases.

```
clfs = clfs[:-1]
ccp_alphas = ccp_alphas[:-1]
node_counts = [clf.tree_.node_count for clf in clfs]
depth = [clf.tree_.max_depth for clf in clfs]
fig, ax = plt.subplots(2, 1)
ax[0].plot(ccp_alphas, node_counts, marker="o", drawstyle="steps-post")
ax[0].set_xlabel("alpha")
ax[0].set_ylabel("number of nodes")
ax[0].set_title("Number of nodes vs alpha")
ax[1].plot(ccp_alphas, depth, marker="o", drawstyle="steps-post")
ax[1].set_xlabel("alpha")
ax[1].set_ylabel("depth of tree")
ax[1].set_title("Depth vs alpha")
fig.tight_layout()
```

## Accuracy vs alpha for training and testing sets¶

When `ccp_alpha`

is set to zero and keeping the other default parameters
of `DecisionTreeClassifier`

, the tree overfits, leading to
a 100% training accuracy and 88% testing accuracy. As alpha increases, more
of the tree is pruned, thus creating a decision tree that generalizes better.
In this example, setting `ccp_alpha=0.015`

maximizes the testing accuracy.

```
train_scores = [clf.score(X_train, y_train) for clf in clfs]
test_scores = [clf.score(X_test, y_test) for clf in clfs]
fig, ax = plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas, train_scores, marker="o", label="train", drawstyle="steps-post")
ax.plot(ccp_alphas, test_scores, marker="o", label="test", drawstyle="steps-post")
ax.legend()
plt.show()
```

**Total running time of the script:** ( 0 minutes 0.309 seconds)