%load_ext watermark
%watermark -v -p numpy,scipy,sklearn,pandas,matplotlib
CPython 3.7.3 IPython 7.5.0 numpy 1.16.3 scipy 1.2.1 sklearn 0.21.1 pandas 0.24.2 matplotlib 3.0.3
6장 – 결정 트리
이 노트북은 6장에 있는 모든 샘플 코드와 연습문제 해답을 가지고 있습니다.
파이썬 2와 3을 모두 지원합니다. 공통 모듈을 임포트하고 맷플롯립 그림이 노트북 안에 포함되도록 설정하고 생성한 그림을 저장하기 위한 함수를 준비합니다:
# 파이썬 2와 파이썬 3 지원
from __future__ import division, print_function, unicode_literals
# 공통
import numpy as np
import os
# 일관된 출력을 위해 유사난수 초기화
np.random.seed(42)
# 맷플롯립 설정
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
# 한글출력
matplotlib.rc('font', family='NanumBarunGothic')
matplotlib.rcParams['axes.unicode_minus'] = False
# 그림을 저장할 폴드
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "decision_trees"
def image_path(fig_id):
return os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID, fig_id)
def save_fig(fig_id, tight_layout=True):
if tight_layout:
plt.tight_layout()
plt.savefig(image_path(fig_id) + ".png", format='png', dpi=300)
from sklearn.datasets import load_iris
from sklearn.tree import DecisionTreeClassifier
iris = load_iris()
X = iris.data[:, 2:] # petal length and width
y = iris.target
tree_clf = DecisionTreeClassifier(max_depth=2, random_state=42)
tree_clf.fit(X, y)
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, presort=False, random_state=42, splitter='best')
from sklearn.tree import export_graphviz
export_graphviz(
tree_clf,
out_file=image_path("iris_tree.dot"),
feature_names=["꽃잎 길이 (cm)", "꽃잎 너비 (cm)"],
class_names=iris.target_names,
rounded=True,
filled=True
)
import graphviz
with open("images/decision_trees/iris_tree.dot") as f:
dot_graph = f.read()
dot = graphviz.Source(dot_graph)
dot.format = 'png'
dot.render(filename='iris_tree', directory='images/decision_trees', cleanup=True)
dot
from matplotlib.colors import ListedColormap
def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):
x1s = np.linspace(axes[0], axes[1], 100)
x2s = np.linspace(axes[2], axes[3], 100)
x1, x2 = np.meshgrid(x1s, x2s)
X_new = np.c_[x1.ravel(), x2.ravel()]
y_pred = clf.predict(X_new).reshape(x1.shape)
custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
if not iris:
custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
if plot_training:
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", label="Iris-Setosa")
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", label="Iris-Versicolor")
plt.plot(X[:, 0][y==2], X[:, 1][y==2], "g^", label="Iris-Virginica")
plt.axis(axes)
if iris:
plt.xlabel("꽃잎 길이", fontsize=14)
plt.ylabel("꽃잎 너비", fontsize=14)
else:
plt.xlabel(r"$x_1$", fontsize=18)
plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
if legend:
plt.legend(loc="lower right", fontsize=14)
plt.figure(figsize=(8, 4))
plot_decision_boundary(tree_clf, X, y)
plt.plot([2.45, 2.45], [0, 3], "k-", linewidth=2)
plt.plot([2.45, 7.5], [1.75, 1.75], "k--", linewidth=2)
plt.plot([4.95, 4.95], [0, 1.75], "k:", linewidth=2)
plt.plot([4.85, 4.85], [1.75, 3], "k:", linewidth=2)
plt.text(1.40, 1.0, "깊이=0", fontsize=15)
plt.text(3.2, 1.80, "깊이=1", fontsize=13)
plt.text(4.05, 0.5, "(깊이=2)", fontsize=11)
save_fig("decision_tree_decision_boundaries_plot")
plt.show()
tree_clf.predict_proba([[5, 1.5]])
array([[0. , 0.90740741, 0.09259259]])
tree_clf.predict([[5, 1.5]])
array([1])
X[(X[:, 1]==X[:, 1][y==1].max()) & (y==1)] # 가장 너비가 큰 Iris-Versicolor
array([[4.8, 1.8]])
not_widest_versicolor = (X[:, 1]!=1.8) | (y==2)
X_tweaked = X[not_widest_versicolor]
y_tweaked = y[not_widest_versicolor]
tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)
tree_clf_tweaked.fit(X_tweaked, y_tweaked)
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, presort=False, random_state=40, splitter='best')
plt.figure(figsize=(8, 4))
plot_decision_boundary(tree_clf_tweaked, X_tweaked, y_tweaked, legend=False)
plt.plot([0, 7.5], [0.8, 0.8], "k-", linewidth=2)
plt.plot([0, 7.5], [1.75, 1.75], "k--", linewidth=2)
plt.text(1.0, 0.9, "깊이=0", fontsize=15)
plt.text(1.0, 1.80, "깊이=1", fontsize=13)
save_fig("decision_tree_instability_plot")
plt.show()
from sklearn.datasets import make_moons
Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)
deep_tree_clf1 = DecisionTreeClassifier(random_state=42)
deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)
deep_tree_clf1.fit(Xm, ym)
deep_tree_clf2.fit(Xm, ym)
plt.figure(figsize=(11, 4))
plt.subplot(121)
plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
plt.title("규제 없음", fontsize=16)
plt.subplot(122)
plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
plt.title("min_samples_leaf = {}".format(deep_tree_clf2.min_samples_leaf), fontsize=14)
save_fig("min_samples_leaf_plot")
plt.show()
angle = np.pi / 180 * 20
rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])
Xr = X.dot(rotation_matrix)
tree_clf_r = DecisionTreeClassifier(random_state=42)
tree_clf_r.fit(Xr, y)
plt.figure(figsize=(8, 3))
plot_decision_boundary(tree_clf_r, Xr, y, axes=[0.5, 7.5, -1.0, 1], iris=False)
plt.show()
np.random.seed(6)
Xs = np.random.rand(100, 2) - 0.5
ys = (Xs[:, 0] > 0).astype(np.float32) * 2
angle = np.pi / 4
rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])
Xsr = Xs.dot(rotation_matrix)
tree_clf_s = DecisionTreeClassifier(random_state=42)
tree_clf_s.fit(Xs, ys)
tree_clf_sr = DecisionTreeClassifier(random_state=42)
tree_clf_sr.fit(Xsr, ys)
plt.figure(figsize=(11, 4))
plt.subplot(121)
plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
plt.subplot(122)
plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
save_fig("sensitivity_to_rotation_plot")
plt.show()
# 2차식으로 만든 데이터셋 + 잡음
np.random.seed(42)
m = 200
X = np.random.rand(m, 1)
y = 4 * (X - 0.5) ** 2
y = y + np.random.randn(m, 1) / 10
from sklearn.tree import DecisionTreeRegressor
tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)
tree_reg.fit(X, y)
DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, presort=False, random_state=42, splitter='best')
from sklearn.tree import DecisionTreeRegressor
tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)
tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)
tree_reg1.fit(X, y)
tree_reg2.fit(X, y)
def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel="$y$"):
x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)
y_pred = tree_reg.predict(x1)
plt.axis(axes)
plt.xlabel("$x_1$", fontsize=18)
if ylabel:
plt.ylabel(ylabel, fontsize=18, rotation=0)
plt.plot(X, y, "b.")
plt.plot(x1, y_pred, "r.-", linewidth=2, label=r"$\hat{y}$")
plt.figure(figsize=(11, 4))
plt.subplot(121)
plot_regression_predictions(tree_reg1, X, y)
for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
plt.plot([split, split], [-0.2, 1], style, linewidth=2)
plt.text(0.21, 0.65, "깊이=0", fontsize=15)
plt.text(0.01, 0.2, "깊이=1", fontsize=13)
plt.text(0.65, 0.8, "깊이=1", fontsize=13)
plt.legend(loc="upper center", fontsize=18)
plt.title("max_depth=2", fontsize=14)
plt.subplot(122)
plot_regression_predictions(tree_reg2, X, y, ylabel=None)
for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
plt.plot([split, split], [-0.2, 1], style, linewidth=2)
for split in (0.0458, 0.1298, 0.2873, 0.9040):
plt.plot([split, split], [-0.2, 1], "k:", linewidth=1)
plt.text(0.3, 0.5, "깊이=2", fontsize=13)
plt.title("max_depth=3", fontsize=14)
save_fig("tree_regression_plot")
plt.show()
export_graphviz(
tree_reg1,
out_file=image_path("regression_tree.dot"),
feature_names=["x1"],
rounded=True,
filled=True
)
import graphviz
with open("images/decision_trees/regression_tree.dot") as f:
dot_graph = f.read()
dot = graphviz.Source(dot_graph)
dot.format = 'png'
dot.render(filename='regression_tree', directory='images/decision_trees', cleanup=True)
dot
tree_reg1 = DecisionTreeRegressor(random_state=42)
tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)
tree_reg1.fit(X, y)
tree_reg2.fit(X, y)
x1 = np.linspace(0, 1, 500).reshape(-1, 1)
y_pred1 = tree_reg1.predict(x1)
y_pred2 = tree_reg2.predict(x1)
plt.figure(figsize=(11, 4))
plt.subplot(121)
plt.plot(X, y, "b.")
plt.plot(x1, y_pred1, "r.-", linewidth=2, label=r"$\hat{y}$")
plt.axis([0, 1, -0.2, 1.1])
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", fontsize=18, rotation=0)
plt.legend(loc="upper center", fontsize=18)
plt.title("규제 없음", fontsize=14)
plt.subplot(122)
plt.plot(X, y, "b.")
plt.plot(x1, y_pred2, "r.-", linewidth=2, label=r"$\hat{y}$")
plt.axis([0, 1, -0.2, 1.1])
plt.xlabel("$x_1$", fontsize=18)
plt.title("min_samples_leaf={}".format(tree_reg2.min_samples_leaf), fontsize=14)
save_fig("tree_regression_regularization_plot")
plt.show()
부록 A 참조.
문제: moons 데이터셋에 결정 트리를 훈련시키고 세밀하게 튜닝해보세요.
a. make_moons(n_samples=1000, noise=0.4)
를 사용해 데이터셋을 생성합니다.
random_state=42
를 지정하여 결과를 일정하게 만듭니다:
from sklearn.datasets import make_moons
X, y = make_moons(n_samples=10000, noise=0.4, random_state=42)
b. 이를 train_test_split()
을 사용해 훈련 세트와 테스트 세트로 나눕니다
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
c. DecisionTreeClassifier
의 최적의 매개변수를 찾기 위해 교차 검증과 함께 그리드 탐색을 수행합니다(GridSearchCV
를 사용하면 됩니다). 힌트: 여러 가지 max_leaf_nodes
값을 시도해보세요.
from sklearn.model_selection import GridSearchCV
params = {'max_leaf_nodes': list(range(2, 100)), 'min_samples_split': [2, 3, 4]}
grid_search_cv = GridSearchCV(DecisionTreeClassifier(random_state=42), params, cv=3, n_jobs=-1, verbose=1)
grid_search_cv.fit(X_train, y_train)
Fitting 3 folds for each of 294 candidates, totalling 882 fits
[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers. [Parallel(n_jobs=-1)]: Done 882 out of 882 | elapsed: 2.5s finished
GridSearchCV(cv=3, error_score='raise-deprecating', estimator=DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, presort=False, random_state=42, splitter='best'), iid='warn', n_jobs=-1, param_grid={'max_leaf_nodes': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, ...], 'min_samples_split': [2, 3, 4]}, pre_dispatch='2*n_jobs', refit=True, return_train_score=False, scoring=None, verbose=1)
grid_search_cv.best_estimator_
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None, max_features=None, max_leaf_nodes=17, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, presort=False, random_state=42, splitter='best')
d. 찾은 매개변수를 사용해 전체 훈련 세트에 대해 모델을 훈련시키고 테스트 세트에서 성능을 측정합니다. 대략 85~87%의 정확도가 나올 것입니다.
기본적으로 GridSearchCV
는 전체 훈련 세트로 찾은 최적의 모델을 다시 훈련시킵니다(refit=False
로 지정해서 바꿀 수 있습니다). 그래서 별도로 작업할 필요가 없습니다. 모델의 정확도를 바로 평가할 수 있습니다:
from sklearn.metrics import accuracy_score
y_pred = grid_search_cv.predict(X_test)
accuracy_score(y_test, y_pred)
0.8695
Exercise: 랜덤 포레스트를 만들어보세요.
a. 이전 연습문제에 이어서, 훈련 세트의 서브셋을 1,000개 생성합니다. 각각은 무작위로 선택된 100개의 샘플을 담고 있습니다. 힌트: 사이킷런의 ShuffleSplit
을 사용할 수 있습니다.
from sklearn.model_selection import ShuffleSplit
n_trees = 1000
n_instances = 100
mini_sets = []
rs = ShuffleSplit(n_splits=n_trees, test_size=len(X_train) - n_instances, random_state=42)
for mini_train_index, mini_test_index in rs.split(X_train):
X_mini_train = X_train[mini_train_index]
y_mini_train = y_train[mini_train_index]
mini_sets.append((X_mini_train, y_mini_train))
b. 앞에서 찾은 최적의 매개변수를 사용해 각 서브셋에 결정 트리를 훈련시킵니다. 테스트 세트로 이 1,000개의 결정 트리를 평가합니다. 더 작은 데이터셋에서 훈련되었기 때문에 이 결정 트리는 앞서 만든 결정 트리보다 성능이 떨어져 약8 0%의 정확도를 냅니다.
from sklearn.base import clone
forest = [clone(grid_search_cv.best_estimator_) for _ in range(n_trees)]
accuracy_scores = []
for tree, (X_mini_train, y_mini_train) in zip(forest, mini_sets):
tree.fit(X_mini_train, y_mini_train)
y_pred = tree.predict(X_test)
accuracy_scores.append(accuracy_score(y_test, y_pred))
np.mean(accuracy_scores)
0.8054499999999999
c. 이제 마술을 부릴 차례입니다. 각 테스트 세트 샘플에 대해 1,000개의 결정 트리 예측을 만들고 다수로 나온 예측만 취합니다(사이파이의 mode()
함수를 사용할 수 있습니다). 그러면 테스트 세트에 대한 _다수결 예측_이 만들어집니다.
Y_pred = np.empty([n_trees, len(X_test)], dtype=np.uint8)
for tree_index, tree in enumerate(forest):
Y_pred[tree_index] = tree.predict(X_test)
from scipy.stats import mode
y_pred_majority_votes, n_votes = mode(Y_pred, axis=0)
d. 테스트 세트에서 이 예측을 평가합니다. 앞서 만든 모델보다 조금 높은(약 0.5~1.5% 정도) 정확도를 얻게 될 것입니다. 축하합니다. 랜덤 포레스트 분류기를 훈련시켰습니다!
accuracy_score(y_test, y_pred_majority_votes.reshape([-1]))
0.872