# Chapter 7 - Combining Different Models for Ensemble Learning¶

Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s).

In [1]:
%load_ext watermark
%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scipy,sklearn

Sebastian Raschka
last updated: 2016-09-29

CPython 3.5.2
IPython 5.1.0

numpy 1.11.1
pandas 0.18.1
matplotlib 1.5.1
scipy 0.18.1
sklearn 0.18


The use of watermark is optional. You can install this IPython extension via "pip install watermark". For more information, please see: https://github.com/rasbt/watermark.

### Overview¶

In [2]:
from IPython.display import Image
%matplotlib inline

In [3]:
# Added version check for recent scikit-learn 0.18 checks
from distutils.version import LooseVersion as Version
from sklearn import __version__ as sklearn_version


# Learning with ensembles¶

In [4]:
Image(filename='./images/07_01.png', width=500)

Out[4]:
In [5]:
Image(filename='./images/07_02.png', width=500)

Out[5]:
In [6]:
from scipy.misc import comb
import math

def ensemble_error(n_classifier, error):
k_start = math.ceil(n_classifier / 2.0)
probs = [comb(n_classifier, k) * error**k * (1-error)**(n_classifier - k)
for k in range(k_start, n_classifier + 1)]
return sum(probs)


Note

For historical reasons, Python 2.7's math.ceil returns a float instead of an integer like in Python 3.x. Although Although this book was written for Python >3.4, let's make it compatible to Python 2.7 by casting it to an it explicitely:

In [7]:
from scipy.misc import comb
import math

def ensemble_error(n_classifier, error):
k_start = int(math.ceil(n_classifier / 2.0))
probs = [comb(n_classifier, k) * error**k * (1-error)**(n_classifier - k)
for k in range(k_start, n_classifier + 1)]
return sum(probs)

In [8]:
ensemble_error(n_classifier=11, error=0.25)

Out[8]:
0.034327507019042969
In [9]:
import numpy as np

error_range = np.arange(0.0, 1.01, 0.01)
ens_errors = [ensemble_error(n_classifier=11, error=error)
for error in error_range]

In [10]:
import matplotlib.pyplot as plt

plt.plot(error_range,
ens_errors,
label='Ensemble error',
linewidth=2)

plt.plot(error_range,
error_range,
linestyle='--',
label='Base error',
linewidth=2)

plt.xlabel('Base error')
plt.ylabel('Base/Ensemble error')
plt.legend(loc='upper left')
plt.grid()
plt.tight_layout()
# plt.savefig('./figures/ensemble_err.png', dpi=300)
plt.show()


# Implementing a simple majority vote classifier¶

In [11]:
import numpy as np

np.argmax(np.bincount([0, 0, 1],
weights=[0.2, 0.2, 0.6]))

Out[11]:
1
In [12]:
ex = np.array([[0.9, 0.1],
[0.8, 0.2],
[0.4, 0.6]])

p = np.average(ex,
axis=0,
weights=[0.2, 0.2, 0.6])
p

Out[12]:
array([ 0.58,  0.42])
In [13]:
np.argmax(p)

Out[13]:
0
In [14]:
from sklearn.base import BaseEstimator
from sklearn.base import ClassifierMixin
from sklearn.preprocessing import LabelEncoder
from sklearn.externals import six
from sklearn.base import clone
from sklearn.pipeline import _name_estimators
import numpy as np
import operator

class MajorityVoteClassifier(BaseEstimator,
ClassifierMixin):
""" A majority vote ensemble classifier

Parameters
----------
classifiers : array-like, shape = [n_classifiers]
Different classifiers for the ensemble

vote : str, {'classlabel', 'probability'} (default='label')
If 'classlabel' the prediction is based on the argmax of
class labels. Else if 'probability', the argmax of
the sum of probabilities is used to predict the class label
(recommended for calibrated classifiers).

weights : array-like, shape = [n_classifiers], optional (default=None)
If a list of int or float values are provided, the classifiers
are weighted by importance; Uses uniform weights if weights=None.

"""
def __init__(self, classifiers, vote='classlabel', weights=None):

self.classifiers = classifiers
self.named_classifiers = {key: value for key, value
in _name_estimators(classifiers)}
self.vote = vote
self.weights = weights

def fit(self, X, y):
""" Fit classifiers.

Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Matrix of training samples.

y : array-like, shape = [n_samples]
Vector of target class labels.

Returns
-------
self : object

"""
if self.vote not in ('probability', 'classlabel'):
raise ValueError("vote must be 'probability' or 'classlabel'"
"; got (vote=%r)"
% self.vote)

if self.weights and len(self.weights) != len(self.classifiers):
raise ValueError('Number of classifiers and weights must be equal'
'; got %d weights, %d classifiers'
% (len(self.weights), len(self.classifiers)))

# is important for np.argmax call in self.predict
self.lablenc_ = LabelEncoder()
self.lablenc_.fit(y)
self.classes_ = self.lablenc_.classes_
self.classifiers_ = []
for clf in self.classifiers:
fitted_clf = clone(clf).fit(X, self.lablenc_.transform(y))
self.classifiers_.append(fitted_clf)
return self

def predict(self, X):
""" Predict class labels for X.

Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Matrix of training samples.

Returns
----------
maj_vote : array-like, shape = [n_samples]
Predicted class labels.

"""
if self.vote == 'probability':
maj_vote = np.argmax(self.predict_proba(X), axis=1)
else:  # 'classlabel' vote

#  Collect results from clf.predict calls
predictions = np.asarray([clf.predict(X)
for clf in self.classifiers_]).T

maj_vote = np.apply_along_axis(
lambda x:
np.argmax(np.bincount(x,
weights=self.weights)),
axis=1,
arr=predictions)
maj_vote = self.lablenc_.inverse_transform(maj_vote)
return maj_vote

def predict_proba(self, X):
""" Predict class probabilities for X.

Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Training vectors, where n_samples is the number of samples and
n_features is the number of features.

Returns
----------
avg_proba : array-like, shape = [n_samples, n_classes]
Weighted average probability for each class per sample.

"""
probas = np.asarray([clf.predict_proba(X)
for clf in self.classifiers_])
avg_proba = np.average(probas, axis=0, weights=self.weights)
return avg_proba

def get_params(self, deep=True):
""" Get classifier parameter names for GridSearch"""
if not deep:
return super(MajorityVoteClassifier, self).get_params(deep=False)
else:
out = self.named_classifiers.copy()
for name, step in six.iteritems(self.named_classifiers):
for key, value in six.iteritems(step.get_params(deep=True)):
out['%s__%s' % (name, key)] = value
return out


## Combining different algorithms for classification with majority vote¶

In [15]:
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import LabelEncoder
if Version(sklearn_version) < '0.18':
from sklearn.cross_validation import train_test_split
else:
from sklearn.model_selection import train_test_split

X, y = iris.data[50:, [1, 2]], iris.target[50:]
le = LabelEncoder()
y = le.fit_transform(y)

X_train, X_test, y_train, y_test =\
train_test_split(X, y,
test_size=0.5,
random_state=1)

In [16]:
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.pipeline import Pipeline
if Version(sklearn_version) < '0.18':
from sklearn.cross_validation import cross_val_score
else:
from sklearn.model_selection import cross_val_score

clf1 = LogisticRegression(penalty='l2',
C=0.001,
random_state=0)

clf2 = DecisionTreeClassifier(max_depth=1,
criterion='entropy',
random_state=0)

clf3 = KNeighborsClassifier(n_neighbors=1,
p=2,
metric='minkowski')

pipe1 = Pipeline([['sc', StandardScaler()],
['clf', clf1]])
pipe3 = Pipeline([['sc', StandardScaler()],
['clf', clf3]])

clf_labels = ['Logistic Regression', 'Decision Tree', 'KNN']

print('10-fold cross validation:\n')
for clf, label in zip([pipe1, clf2, pipe3], clf_labels):
scores = cross_val_score(estimator=clf,
X=X_train,
y=y_train,
cv=10,
scoring='roc_auc')
print("ROC AUC: %0.2f (+/- %0.2f) [%s]"
% (scores.mean(), scores.std(), label))

10-fold cross validation:

ROC AUC: 0.92 (+/- 0.20) [Logistic Regression]
ROC AUC: 0.92 (+/- 0.15) [Decision Tree]
ROC AUC: 0.93 (+/- 0.10) [KNN]

In [17]:
# Majority Rule (hard) Voting

mv_clf = MajorityVoteClassifier(classifiers=[pipe1, clf2, pipe3])

clf_labels += ['Majority Voting']
all_clf = [pipe1, clf2, pipe3, mv_clf]

for clf, label in zip(all_clf, clf_labels):
scores = cross_val_score(estimator=clf,
X=X_train,
y=y_train,
cv=10,
scoring='roc_auc')
print("ROC AUC: %0.2f (+/- %0.2f) [%s]"
% (scores.mean(), scores.std(), label))

ROC AUC: 0.92 (+/- 0.20) [Logistic Regression]
ROC AUC: 0.92 (+/- 0.15) [Decision Tree]
ROC AUC: 0.93 (+/- 0.10) [KNN]
ROC AUC: 0.97 (+/- 0.10) [Majority Voting]


# Evaluating and tuning the ensemble classifier¶

In [18]:
from sklearn.metrics import roc_curve
from sklearn.metrics import auc

colors = ['black', 'orange', 'blue', 'green']
linestyles = [':', '--', '-.', '-']
for clf, label, clr, ls \
in zip(all_clf,
clf_labels, colors, linestyles):

# assuming the label of the positive class is 1
y_pred = clf.fit(X_train,
y_train).predict_proba(X_test)[:, 1]
fpr, tpr, thresholds = roc_curve(y_true=y_test,
y_score=y_pred)
roc_auc = auc(x=fpr, y=tpr)
plt.plot(fpr, tpr,
color=clr,
linestyle=ls,
label='%s (auc = %0.2f)' % (label, roc_auc))

plt.legend(loc='lower right')
plt.plot([0, 1], [0, 1],
linestyle='--',
color='gray',
linewidth=2)

plt.xlim([-0.1, 1.1])
plt.ylim([-0.1, 1.1])
plt.grid()
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')

# plt.tight_layout()
# plt.savefig('./figures/roc.png', dpi=300)
plt.show()

In [19]:
sc = StandardScaler()
X_train_std = sc.fit_transform(X_train)

In [20]:
from itertools import product

all_clf = [pipe1, clf2, pipe3, mv_clf]

x_min = X_train_std[:, 0].min() - 1
x_max = X_train_std[:, 0].max() + 1
y_min = X_train_std[:, 1].min() - 1
y_max = X_train_std[:, 1].max() + 1

xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1),
np.arange(y_min, y_max, 0.1))

f, axarr = plt.subplots(nrows=2, ncols=2,
sharex='col',
sharey='row',
figsize=(7, 5))

for idx, clf, tt in zip(product([0, 1], [0, 1]),
all_clf, clf_labels):
clf.fit(X_train_std, y_train)

Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

axarr[idx[0], idx[1]].contourf(xx, yy, Z, alpha=0.3)

axarr[idx[0], idx[1]].scatter(X_train_std[y_train==0, 0],
X_train_std[y_train==0, 1],
c='blue',
marker='^',
s=50)

axarr[idx[0], idx[1]].scatter(X_train_std[y_train==1, 0],
X_train_std[y_train==1, 1],
c='red',
marker='o',
s=50)

axarr[idx[0], idx[1]].set_title(tt)

plt.text(-3.5, -4.5,
s='Sepal width [standardized]',
ha='center', va='center', fontsize=12)
plt.text(-10.5, 4.5,
s='Petal length [standardized]',
ha='center', va='center',
fontsize=12, rotation=90)

plt.tight_layout()
# plt.savefig('./figures/voting_panel', bbox_inches='tight', dpi=300)
plt.show()

In [21]:
mv_clf.get_params()

Out[21]:
{'decisiontreeclassifier': DecisionTreeClassifier(class_weight=None, criterion='entropy', max_depth=1,
max_features=None, max_leaf_nodes=None,
min_impurity_split=1e-07, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=0, splitter='best'),
'decisiontreeclassifier__class_weight': None,
'decisiontreeclassifier__criterion': 'entropy',
'decisiontreeclassifier__max_depth': 1,
'decisiontreeclassifier__max_features': None,
'decisiontreeclassifier__max_leaf_nodes': None,
'decisiontreeclassifier__min_impurity_split': 1e-07,
'decisiontreeclassifier__min_samples_leaf': 1,
'decisiontreeclassifier__min_samples_split': 2,
'decisiontreeclassifier__min_weight_fraction_leaf': 0.0,
'decisiontreeclassifier__presort': False,
'decisiontreeclassifier__random_state': 0,
'decisiontreeclassifier__splitter': 'best',
'pipeline-1': Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', LogisticRegression(C=0.001, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False)]]),
'pipeline-1__clf': LogisticRegression(C=0.001, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False),
'pipeline-1__clf__C': 0.001,
'pipeline-1__clf__class_weight': None,
'pipeline-1__clf__dual': False,
'pipeline-1__clf__fit_intercept': True,
'pipeline-1__clf__intercept_scaling': 1,
'pipeline-1__clf__max_iter': 100,
'pipeline-1__clf__multi_class': 'ovr',
'pipeline-1__clf__n_jobs': 1,
'pipeline-1__clf__penalty': 'l2',
'pipeline-1__clf__random_state': 0,
'pipeline-1__clf__solver': 'liblinear',
'pipeline-1__clf__tol': 0.0001,
'pipeline-1__clf__verbose': 0,
'pipeline-1__clf__warm_start': False,
'pipeline-1__sc': StandardScaler(copy=True, with_mean=True, with_std=True),
'pipeline-1__sc__copy': True,
'pipeline-1__sc__with_mean': True,
'pipeline-1__sc__with_std': True,
'pipeline-1__steps': [['sc',
StandardScaler(copy=True, with_mean=True, with_std=True)],
['clf',
LogisticRegression(C=0.001, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False)]],
'pipeline-2': Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform')]]),
'pipeline-2__clf': KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform'),
'pipeline-2__clf__algorithm': 'auto',
'pipeline-2__clf__leaf_size': 30,
'pipeline-2__clf__metric': 'minkowski',
'pipeline-2__clf__metric_params': None,
'pipeline-2__clf__n_jobs': 1,
'pipeline-2__clf__n_neighbors': 1,
'pipeline-2__clf__p': 2,
'pipeline-2__clf__weights': 'uniform',
'pipeline-2__sc': StandardScaler(copy=True, with_mean=True, with_std=True),
'pipeline-2__sc__copy': True,
'pipeline-2__sc__with_mean': True,
'pipeline-2__sc__with_std': True,
'pipeline-2__steps': [['sc',
StandardScaler(copy=True, with_mean=True, with_std=True)],
['clf',
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform')]]}
In [22]:
if Version(sklearn_version) < '0.18':
from sklearn.cross_validation import GridSearchCV
else:
from sklearn.model_selection import GridSearchCV

params = {'decisiontreeclassifier__max_depth': [1, 2],
'pipeline-1__clf__C': [0.001, 0.1, 100.0]}

grid = GridSearchCV(estimator=mv_clf,
param_grid=params,
cv=10,
scoring='roc_auc')
grid.fit(X_train, y_train)

if Version(sklearn_version) < '0.18':
for params, mean_score, scores in grid.grid_scores_:
print("%0.3f +/- %0.2f %r"
% (mean_score, scores.std() / 2.0, params))

else:
cv_keys = ('mean_test_score', 'std_test_score','params')

for r, _ in enumerate(grid.cv_results_['mean_test_score']):
print("%0.3f +/- %0.2f %r"
% (grid.cv_results_[cv_keys[0]][r],
grid.cv_results_[cv_keys[1]][r] / 2.0,
grid.cv_results_[cv_keys[2]][r]))

0.967 +/- 0.05 {'decisiontreeclassifier__max_depth': 1, 'pipeline-1__clf__C': 0.001}
0.967 +/- 0.05 {'decisiontreeclassifier__max_depth': 1, 'pipeline-1__clf__C': 0.1}
1.000 +/- 0.00 {'decisiontreeclassifier__max_depth': 1, 'pipeline-1__clf__C': 100.0}
0.967 +/- 0.05 {'decisiontreeclassifier__max_depth': 2, 'pipeline-1__clf__C': 0.001}
0.967 +/- 0.05 {'decisiontreeclassifier__max_depth': 2, 'pipeline-1__clf__C': 0.1}
1.000 +/- 0.00 {'decisiontreeclassifier__max_depth': 2, 'pipeline-1__clf__C': 100.0}

In [23]:
print('Best parameters: %s' % grid.best_params_)
print('Accuracy: %.2f' % grid.best_score_)

Best parameters: {'decisiontreeclassifier__max_depth': 1, 'pipeline-1__clf__C': 100.0}
Accuracy: 1.00


Note
By default, the default setting for refit in GridSearchCV is True (i.e., GridSeachCV(..., refit=True)), which means that we can use the fitted GridSearchCV estimator to make predictions via the predict method, for example:

grid = GridSearchCV(estimator=mv_clf,
param_grid=params,
cv=10,
scoring='roc_auc')
grid.fit(X_train, y_train)
y_pred = grid.predict(X_test)



In addition, the "best" estimator can directly be accessed via the best_estimator_ attribute.

In [24]:
grid.best_estimator_.classifiers

Out[24]:
[Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', LogisticRegression(C=100.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False)]]),
DecisionTreeClassifier(class_weight=None, criterion='entropy', max_depth=1,
max_features=None, max_leaf_nodes=None,
min_impurity_split=1e-07, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=0, splitter='best'),
Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform')]])]
In [25]:
mv_clf = grid.best_estimator_

In [26]:
mv_clf.set_params(**grid.best_estimator_.get_params())

Out[26]:
MajorityVoteClassifier(classifiers=[Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', LogisticRegression(C=100.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solv...ski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform')]])],
vote='classlabel', weights=None)
In [27]:
mv_clf

Out[27]:
MajorityVoteClassifier(classifiers=[Pipeline(steps=[['sc', StandardScaler(copy=True, with_mean=True, with_std=True)], ['clf', LogisticRegression(C=100.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solv...ski',
metric_params=None, n_jobs=1, n_neighbors=1, p=2,
weights='uniform')]])],
vote='classlabel', weights=None)

# Bagging -- Building an ensemble of classifiers from bootstrap samples¶

In [28]:
Image(filename='./images/07_06.png', width=500)

Out[28]:
In [29]:
Image(filename='./images/07_07.png', width=400)

Out[29]:
In [30]:
import pandas as pd

'machine-learning-databases/wine/wine.data',

df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',
'Alcalinity of ash', 'Magnesium', 'Total phenols',
'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',
'Color intensity', 'Hue', 'OD280/OD315 of diluted wines',
'Proline']

# drop 1 class
df_wine = df_wine[df_wine['Class label'] != 1]

y = df_wine['Class label'].values
X = df_wine[['Alcohol', 'Hue']].values

In [31]:
from sklearn.preprocessing import LabelEncoder
if Version(sklearn_version) < '0.18':
from sklearn.cross_validation import train_test_split
else:
from sklearn.model_selection import train_test_split

le = LabelEncoder()
y = le.fit_transform(y)

X_train, X_test, y_train, y_test =\
train_test_split(X, y,
test_size=0.40,
random_state=1)

In [32]:
from sklearn.ensemble import BaggingClassifier
from sklearn.tree import DecisionTreeClassifier

tree = DecisionTreeClassifier(criterion='entropy',
max_depth=None,
random_state=1)

bag = BaggingClassifier(base_estimator=tree,
n_estimators=500,
max_samples=1.0,
max_features=1.0,
bootstrap=True,
bootstrap_features=False,
n_jobs=1,
random_state=1)

In [33]:
from sklearn.metrics import accuracy_score

tree = tree.fit(X_train, y_train)
y_train_pred = tree.predict(X_train)
y_test_pred = tree.predict(X_test)

tree_train = accuracy_score(y_train, y_train_pred)
tree_test = accuracy_score(y_test, y_test_pred)
print('Decision tree train/test accuracies %.3f/%.3f'
% (tree_train, tree_test))

bag = bag.fit(X_train, y_train)
y_train_pred = bag.predict(X_train)
y_test_pred = bag.predict(X_test)

bag_train = accuracy_score(y_train, y_train_pred)
bag_test = accuracy_score(y_test, y_test_pred)
print('Bagging train/test accuracies %.3f/%.3f'
% (bag_train, bag_test))

Decision tree train/test accuracies 1.000/0.833
Bagging train/test accuracies 1.000/0.896

In [34]:
import numpy as np
import matplotlib.pyplot as plt

x_min = X_train[:, 0].min() - 1
x_max = X_train[:, 0].max() + 1
y_min = X_train[:, 1].min() - 1
y_max = X_train[:, 1].max() + 1

xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1),
np.arange(y_min, y_max, 0.1))

f, axarr = plt.subplots(nrows=1, ncols=2,
sharex='col',
sharey='row',
figsize=(8, 3))

for idx, clf, tt in zip([0, 1],
[tree, bag],
['Decision Tree', 'Bagging']):
clf.fit(X_train, y_train)

Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

axarr[idx].contourf(xx, yy, Z, alpha=0.3)
axarr[idx].scatter(X_train[y_train == 0, 0],
X_train[y_train == 0, 1],
c='blue', marker='^')

axarr[idx].scatter(X_train[y_train == 1, 0],
X_train[y_train == 1, 1],
c='red', marker='o')

axarr[idx].set_title(tt)

axarr[0].set_ylabel('Alcohol', fontsize=12)
plt.text(10.2, -1.2,
s='Hue',
ha='center', va='center', fontsize=12)

plt.tight_layout()
# plt.savefig('./figures/bagging_region.png',
#            dpi=300,
#            bbox_inches='tight')
plt.show()


# Leveraging weak learners via adaptive boosting¶

In [35]:
Image(filename='./images/07_09.png', width=400)

Out[35]: