Sebastian Raschka, 2015
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).
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%load_ext watermark
%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scipy,scikit-learn
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# to install watermark just uncomment the following line:
#%install_ext https://raw.githubusercontent.com/rasbt/watermark/master/watermark.py
In [1]:
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)
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ensemble_error(n_classifier=11, error=0.25)
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In [3]:
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 [4]:
import matplotlib.pyplot as plt
%matplotlib inline
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()
In [5]:
import numpy as np
np.argmax(np.bincount([0, 0, 1],
weights=[0.2, 0.2, 0.6]))
Out[5]:
In [6]:
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[6]:
In [7]:
np.argmax(p)
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In [8]:
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)"
% 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)))
# Use LabelEncoder to ensure class labels start with 0, which
# 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
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from sklearn import datasets
from sklearn.cross_validation import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import LabelEncoder
iris = datasets.load_iris()
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)
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from sklearn.cross_validation import cross_val_score
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.pipeline import Pipeline
import numpy as np
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))
In [24]:
# 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))
In [25]:
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()
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sc = StandardScaler()
X_train_std = sc.fit_transform(X_train)
In [28]:
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()
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mv_clf.get_params()
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In [38]:
from sklearn.grid_search 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)
for params, mean_score, scores in grid.grid_scores_:
print("%0.3f+/-%0.2f %r"
% (mean_score, scores.std() / 2, params))
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print('Best parameters: %s' % grid.best_params_)
print('Accuracy: %.2f' % grid.best_score_)
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import pandas as pd
df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data', header=None)
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 [75]:
from sklearn.preprocessing import LabelEncoder
from sklearn.cross_validation 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 [76]:
from sklearn.ensemble import BaggingClassifier
from sklearn.tree import DecisionTreeClassifier
tree = DecisionTreeClassifier(criterion='entropy',
max_depth=None)
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 [77]:
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))
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%matplotlib inline
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()
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from sklearn.ensemble import AdaBoostClassifier
tree = DecisionTreeClassifier(criterion='entropy',
max_depth=1)
ada = AdaBoostClassifier(base_estimator=tree,
n_estimators=500,
learning_rate=0.1,
random_state=0)
In [90]:
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))
ada = ada.fit(X_train, y_train)
y_train_pred = ada.predict(X_train)
y_test_pred = ada.predict(X_test)
ada_train = accuracy_score(y_train, y_train_pred)
ada_test = accuracy_score(y_test, y_test_pred)
print('AdaBoost train/test accuracies %.3f/%.3f'
% (ada_train, ada_test))
In [91]:
x_min, x_max = X_train[:, 0].min() - 1, X_train[:, 0].max() + 1
y_min, y_max = X_train[:, 1].min() - 1, 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(1, 2, sharex='col', sharey='row', figsize=(8, 3))
for idx, clf, tt in zip([0, 1],
[tree, ada],
['Decision Tree', 'AdaBoost']):
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/adaboost_region.png',
# dpi=300,
# bbox_inches='tight')
plt.show()