결정 트리: 이론과 구현

결정 트리란 무엇인가

지니 불순도

import numpy as np

def gini(labels):
    classes, counts = np.unique(labels, return_counts=True)
    probs = counts / counts.sum()
    return 1 - np.sum(probs ** 2)

print(gini([0, 0, 1, 1]))   # 0.5 (max mix)
print(gini([0, 0, 0, 0]))   # 0.0 (pure)

정보 이득과 entropy

import numpy as np

def entropy(labels):
    _, counts = np.unique(labels, return_counts=True)
    p = counts / counts.sum()
    return -np.sum(p * np.log2(p))

print(entropy([0, 0, 1, 1]))   # 1.0
print(entropy([0, 0, 0, 1]))   # ~0.81

DecisionTreeClassifier 학습

from sklearn.datasets import load_iris
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split

X, y = load_iris(return_X_y=True)
Xtr, Xte, ytr, yte = train_test_split(X, y, random_state=0)

clf = DecisionTreeClassifier(criterion="gini", random_state=0)
clf.fit(Xtr, ytr)
print("Accuracy:", clf.score(Xte, yte))

과적합과 max_depth

from sklearn.tree import DecisionTreeClassifier

shallow = DecisionTreeClassifier(max_depth=3, random_state=0)
deep = DecisionTreeClassifier(max_depth=None, random_state=0)
# shallow generalizes better on unseen data;
# deep often overfits the training set

기타 사전 가지치기 매개변수

from sklearn.tree import DecisionTreeClassifier

clf = DecisionTreeClassifier(
    max_depth=5,
    min_samples_split=10,
    min_samples_leaf=5,
    random_state=0,
)

plot_tree로 시각화하기

import matplotlib.pyplot as plt
from sklearn.tree import plot_tree
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import load_iris

X, y = load_iris(return_X_y=True)
clf = DecisionTreeClassifier(max_depth=3).fit(X, y)

plt.figure(figsize=(12, 6))
plot_tree(clf, filled=True, feature_names=load_iris().feature_names)
plt.show()

특성 중요도

from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import load_iris

data = load_iris()
clf = DecisionTreeClassifier(max_depth=3).fit(data.data, data.target)

for name, imp in zip(data.feature_names, clf.feature_importances_):
    print(f"{name}: {imp:.3f}")

비용-복잡도 가지치기 (ccp_alpha)

from sklearn.tree import DecisionTreeClassifier

base = DecisionTreeClassifier(random_state=0)
path = base.cost_complexity_pruning_path(Xtr, ytr)
alphas = path.ccp_alphas

pruned = DecisionTreeClassifier(ccp_alpha=0.01, random_state=0)
pruned.fit(Xtr, ytr)

최적의 Alpha 선택

from sklearn.tree import DecisionTreeClassifier

scores = []
for a in alphas:
    t = DecisionTreeClassifier(ccp_alpha=a, random_state=0)
    t.fit(Xtr, ytr)
    scores.append((a, t.score(Xte, yte)))

best = max(scores, key=lambda s: s[1])
print("Best alpha:", best[0])

장점과 단점

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