Default of Credit Card Clients¶
https://archive.ics.uci.edu/ml/datasets/default+of+credit+card+clients
Abstract¶
This research aimed at the case of customers’ default payments in Taiwan and compares the predictive accuracy of probability of default among six data mining methods.
Attributes:¶
24
Date Donated
2016-01-26
Associated Tasks:
Classification
Missing Values?
N/A
Number of Web Hits:
29657
Data Set Information:¶
This research aimed at the case of customers default payments in Taiwan and compares the predictive accuracy of probability of default among six data mining methods. From the perspective of risk management, the result of predictive accuracy of the estimated probability of default will be more valuable than the binary result of classification - credible or not credible clients. Because the real probability of default is unknown, this study presented the novel Sorting Smoothing Method to estimate the real probability of default. With the real probability of default as the response variable (Y), and the predictive probability of default as the independent variable (X), the simple linear regression result (Y = A + BX) shows that the forecasting model produced by artificial neural network has the highest coefficient of determination; its regression intercept (A) is close to zero, and regression coefficient (B) to one. Therefore, among the six data mining techniques, artificial neural network is the only one that can accurately estimate the real probability of default.
Attribute Information:¶
This research employed a binary variable, default payment (Yes = 1, No = 0), as the response variable. This study reviewed the literature and used the following 23 variables as explanatory variables:
X1: Amount of the given credit (NT dollar): it includes both the individual consumer credit and his/her family (supplementary) credit. X2: Gender (1 = male; 2 = female). X3: Education (1 = graduate school; 2 = university; 3 = high school; 4 = others). X4: Marital status (1 = married; 2 = single; 3 = others). X5: Age (year). X6 - X11: History of past payment. We tracked the past monthly payment records (from April to September, 2005) as follows: X6 = the repayment status in September, 2005; X7 = the repayment status in August, 2005; . . .;X11 = the repayment status in April, 2005. The measurement scale for the repayment status is: -1 = pay duly; 1 = payment delay for one month; 2 = payment delay for two months; . . .; 8 = payment delay for eight months; 9 = payment delay for nine months and above. X12-X17: Amount of bill statement (NT dollar). X12 = amount of bill statement in September, 2005; X13 = amount of bill statement in August, 2005; . . .; X17 = amount of bill statement in April, 2005. X18-X23: Amount of previous payment (NT dollar). X18 = amount paid in September, 2005; X19 = amount paid in August, 2005; . . .;X23 = amount paid in April, 2005.
In [1]:
import os
from sklearn.tree import DecisionTreeClassifier, export_graphviz
import pandas as pd
import numpy as np
from sklearn.cross_validation import train_test_split
from sklearn import cross_validation, metrics
from sklearn.ensemble import RandomForestClassifier
from sklearn.naive_bayes import BernoulliNB
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from time import time
from sklearn.pipeline import Pipeline
from sklearn.metrics import roc_auc_score , classification_report
from sklearn.grid_search import GridSearchCV
from sklearn.pipeline import Pipeline
from sklearn.metrics import precision_score, recall_score, accuracy_score, classification_report
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import LabelEncoder
In [2]:
# read .csv from provided dataset
xls_filename="default of credit card clients.xls"
# df=pd.read_csv(csv_filename,index_col=0)
df=pd.read_excel(xls_filename, skiprows=1)
In [3]:
df.head()
Out[3]:
In [4]:
df.columns
Out[4]:
In [5]:
features=list(df.columns[1:-1])
X=df[features]
y = df['default payment next month']
# split dataset to 60% training and 40% testing
X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.4, random_state=0)
In [6]:
print X_train.shape, y_train.shape
Feature importances with forests of trees¶
This examples shows the use of forests of trees to evaluate the importance of features on an artificial classification task. The red bars are the feature importances of the forest, along with their inter-trees variability.
In [7]:
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.ensemble import ExtraTreesClassifier
# Build a classification task using 3 informative features
# Build a forest and compute the feature importances
forest = ExtraTreesClassifier(n_estimators=250,
random_state=0)
forest.fit(X, y)
importances = forest.feature_importances_
std = np.std([tree.feature_importances_ for tree in forest.estimators_],
axis=0)
indices = np.argsort(importances)[::-1]
# Print the feature ranking
print("Feature ranking:")
for f in range(X.shape[1]):
print("%d. feature %d - %s (%f) " % (f + 1, indices[f], features[indices[f]], importances[indices[f]]))
# Plot the feature importances of the forest
plt.figure(num=None, figsize=(14, 10), dpi=80, facecolor='w', edgecolor='k')
plt.title("Feature importances")
plt.bar(range(X.shape[1]), importances[indices],
color="r", yerr=std[indices], align="center")
plt.xticks(range(X.shape[1]), indices)
plt.xlim([-1, X.shape[1]])
plt.show()
In [8]:
importances[indices[:5]]
Out[8]:
In [9]:
for f in range(5):
print("%d. feature %d - %s (%f)" % (f + 1, indices[f], features[indices[f]] ,importances[indices[f]]))
In [10]:
best_features = []
for i in indices[:5]:
best_features.append(features[i])
In [11]:
# Plot the top 5 feature importances of the forest
plt.figure(num=None, figsize=(8, 6), dpi=80, facecolor='w', edgecolor='k')
plt.title("Feature importances")
plt.bar(range(5), importances[indices][:5],
color="r", yerr=std[indices][:5], align="center")
plt.xticks(range(5), best_features)
plt.xlim([-1, 5])
plt.show()
Decision Tree accuracy and time elapsed caculation¶
In [12]:
t0=time()
print "DecisionTree"
#dt = DecisionTreeClassifier(min_samples_split=1,random_state=99)
dt = DecisionTreeClassifier(min_samples_split=20,max_depth=5,random_state=99)
clf_dt=dt.fit(X_train,y_train)
print "Acurracy: ", clf_dt.score(X_test,y_test)
t1=time()
print "time elapsed: ", t1-t0
cross validation for DT¶
In [13]:
tt0=time()
print "cross result========"
scores = cross_validation.cross_val_score(dt, X,y, cv=5)
print scores
print scores.mean()
tt1=time()
print "time elapsed: ", tt1-tt0
print "\n"
Tuning our hyperparameters using GridSearch¶
In [14]:
from sklearn.metrics import classification_report
pipeline = Pipeline([
('clf', DecisionTreeClassifier(criterion='entropy'))
])
parameters = {
'clf__max_depth': (5, 25 , 50),
'clf__min_samples_split': (1, 5, 10),
'clf__min_samples_leaf': (1, 2, 3)
}
grid_search = GridSearchCV(pipeline, parameters, n_jobs=-1, verbose=1, scoring='f1')
grid_search.fit(X_train, y_train)
print 'Best score: %0.3f' % grid_search.best_score_
print 'Best parameters set:'
best_parameters = grid_search.best_estimator_.get_params()
for param_name in sorted(parameters.keys()):
print '\t%s: %r' % (param_name, best_parameters[param_name])
predictions = grid_search.predict(X_test)
print classification_report(y_test, predictions)
Random Forest accuracy and time elapsed caculation¶
In [15]:
t2=time()
print "RandomForest"
rf = RandomForestClassifier(n_estimators=100,n_jobs=-1)
clf_rf = rf.fit(X_train,y_train)
print "Acurracy: ", clf_rf.score(X_test,y_test)
t3=time()
print "time elapsed: ", t3-t2
cross validation for RF¶
In [16]:
tt2=time()
print "cross result========"
scores = cross_validation.cross_val_score(rf, X,y, cv=5)
print scores
print scores.mean()
tt3=time()
print "time elapsed: ", tt3-tt2
print "\n"
Receiver Operating Characteristic (ROC) curve¶
In [17]:
roc_auc_score(y_test,rf.predict(X_test))
Out[17]:
In [18]:
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve, auc
predictions = rf.predict_proba(X_test)
false_positive_rate, recall, thresholds = roc_curve(y_test, predictions[:, 1])
roc_auc = auc(false_positive_rate, recall)
plt.title('Receiver Operating Characteristic')
plt.plot(false_positive_rate, recall, 'b', label='AUC = %0.2f' % roc_auc)
plt.legend(loc='lower right')
plt.plot([0, 1], [0, 1], 'r--')
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0])
plt.ylabel('Recall')
plt.xlabel('Fall-out')
plt.show()
Tuning Models using GridSearch¶
In [19]:
pipeline2 = Pipeline([
('clf', RandomForestClassifier(criterion='entropy'))
])
parameters = {
'clf__n_estimators': (25, 50, 100),
'clf__max_depth': (5, 25 , 50),
'clf__min_samples_split': (1, 5, 10),
'clf__min_samples_leaf': (1, 2, 3)
}
grid_search = GridSearchCV(pipeline2, parameters, n_jobs=-1, verbose=1, scoring='accuracy', cv=3)
grid_search.fit(X_train, y_train)
print 'Best score: %0.3f' % grid_search.best_score_
print 'Best parameters set:'
best_parameters = grid_search.best_estimator_.get_params()
for param_name in sorted(parameters.keys()):
print '\t%s: %r' % (param_name, best_parameters[param_name])
predictions = grid_search.predict(X_test)
print 'Accuracy:', accuracy_score(y_test, predictions)
print classification_report(y_test, predictions)
OOB Errors for Random Forests¶
In [62]:
import matplotlib.pyplot as plt
from collections import OrderedDict
from sklearn.datasets import make_classification
from sklearn.ensemble import RandomForestClassifier, ExtraTreesClassifier
RANDOM_STATE = 123
# NOTE: Setting the `warm_start` construction parameter to `True` disables
# support for paralellised ensembles but is necessary for tracking the OOB
# error trajectory during training.
ensemble_clfs = [
("RandomForestClassifier, max_features='sqrt'",
RandomForestClassifier(warm_start=True, oob_score=True,
max_features="sqrt",
random_state=RANDOM_STATE)),
("RandomForestClassifier, max_features='log2'",
RandomForestClassifier(warm_start=True, max_features='log2',
oob_score=True,
random_state=RANDOM_STATE)),
("RandomForestClassifier, max_features=None",
RandomForestClassifier(warm_start=True, max_features=None,
oob_score=True,
random_state=RANDOM_STATE))
]
# Map a classifier name to a list of (<n_estimators>, <error rate>) pairs.
error_rate = OrderedDict((label, []) for label, _ in ensemble_clfs)
# Range of `n_estimators` values to explore.
min_estimators = 15
max_estimators = 175
for label, clf in ensemble_clfs:
for i in range(min_estimators, max_estimators + 1):
clf.set_params(n_estimators=i)
clf.fit(X, y)
# Record the OOB error for each `n_estimators=i` setting.
oob_error = 1 - clf.oob_score_
error_rate[label].append((i, oob_error))
# Generate the "OOB error rate" vs. "n_estimators" plot.
for label, clf_err in error_rate.items():
xs, ys = zip(*clf_err)
plt.plot(xs, ys, label=label)
plt.xlim(min_estimators, max_estimators)
plt.xlabel("n_estimators")
plt.ylabel("OOB error rate")
plt.legend(loc="upper right")
plt.show()
Naive Bayes accuracy and time elapsed caculation¶
In [22]:
t4=time()
print "NaiveBayes"
nb = BernoulliNB()
clf_nb=nb.fit(X_train,y_train)
print "Acurracy: ", clf_nb.score(X_test,y_test)
t5=time()
print "time elapsed: ", t5-t4
cross-validation for NB¶
In [23]:
tt4=time()
print "cross result========"
scores = cross_validation.cross_val_score(nb, X,y, cv=5)
print scores
print scores.mean()
tt5=time()
print "time elapsed: ", tt5-tt4
print "\n"
KNN accuracy and time elapsed caculation¶
In [24]:
t6=time()
print "KNN"
# knn = KNeighborsClassifier(n_neighbors=3)
knn = KNeighborsClassifier()
clf_knn=knn.fit(X_train, y_train)
print "Acurracy: ", clf_knn.score(X_test,y_test)
t7=time()
print "time elapsed: ", t7-t6
cross validation for KNN¶
In [25]:
tt6=time()
print "cross result========"
scores = cross_validation.cross_val_score(knn, X,y, cv=5)
print scores
print scores.mean()
tt7=time()
print "time elapsed: ", tt7-tt6
print "\n"
In [26]:
from sklearn.cross_validation import cross_val_score
from sklearn.pipeline import Pipeline
from sklearn import grid_search
knn = KNeighborsClassifier()
parameters = {'n_neighbors': (10, 15, 25)}
grid = grid_search.GridSearchCV(knn, parameters, n_jobs=-1, verbose=1, scoring='accuracy')
grid.fit(X_train, y_train)
print 'Best score: %0.3f' % grid.best_score_
print 'Best parameters set:'
best_parameters = grid.best_estimator_.get_params()
for param_name in sorted(parameters.keys()):
print '\t%s: %r' % (param_name, best_parameters[param_name])
predictions = grid.predict(X_test)
print classification_report(y_test, predictions)
Ensemble Learning¶
In [27]:
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)))
# 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
Combining different algorithms for classification with majority vote¶
In [28]:
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=5,
min_samples_leaf=5,
min_samples_split=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))
You may be wondering why we trained the logistic regression and k-nearest neighbors classifier as part of a pipeline. The reason behind it is that, both the logistic regression and k-nearest neighbors algorithms (using the Euclidean distance metric) are not scale-invariant in contrast with decision trees.
Now let's move on to the more exciting part and combine the individual classifiers for majority rule voting in our MajorityVoteClassifier:
In [29]:
# Majority Rule (hard) Voting
mv_clf = MajorityVoteClassifier(
classifiers=[pipe1, clf2,pipe3])
clf_labels = ['Logistic Regression', 'Decision Tree', 'K Nearest Neighbours', '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))
Evaluating and tuning the ensemble classifier¶
In [30]:
%matplotlib inline
import matplotlib.pyplot as plt
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()
Plot class probabilities calculated by the VotingClassifier¶
In [33]:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import VotingClassifier
clf1 = LogisticRegression(random_state=123)
clf2 = RandomForestClassifier(random_state=123)
clf3 = GaussianNB()
eclf = VotingClassifier(estimators=[('lr', clf1), ('rf', clf2), ('gnb', clf3)],
voting='soft',
weights=[1, 1, 5])
# predict class probabilities for all classifiers
probas = [c.fit(X, y).predict_proba(X) for c in (clf1, clf2, clf3, eclf)]
# get class probabilities for the first sample in the dataset
class1_1 = [pr[0, 0] for pr in probas]
class2_1 = [pr[0, 1] for pr in probas]
# plotting
N = 4 # number of groups
ind = np.arange(N) # group positions
width = 0.35 # bar width
fig, ax = plt.subplots()
# bars for classifier 1-3
p1 = ax.bar(ind, np.hstack(([class1_1[:-1], [0]])), width, color='green')
p2 = ax.bar(ind + width, np.hstack(([class2_1[:-1], [0]])), width, color='lightgreen')
# bars for VotingClassifier
p3 = ax.bar(ind, [0, 0, 0, class1_1[-1]], width, color='blue')
p4 = ax.bar(ind + width, [0, 0, 0, class2_1[-1]], width, color='steelblue')
# plot annotations
plt.axvline(2.8, color='k', linestyle='dashed')
ax.set_xticks(ind + width)
ax.set_xticklabels(['LogisticRegression\nweight 1',
'GaussianNB\nweight 1',
'RandomForestClassifier\nweight 5',
'VotingClassifier\n(average probabilities)'],
rotation=40,
ha='right')
plt.ylim([0, 1])
plt.title('Class probabilities for sample 1 by different classifiers')
plt.legend([p1[0], p2[0]], ['class 1', 'class 2'], loc='upper left')
plt.show()
Bagging -- Building an ensemble of classifiers from bootstrap samples¶
Bagging is an ensemble learning technique that is closely related to the MajorityVoteClassifier,however, instead of using the same training set to fit the individual classifiers in the ensemble, we draw bootstrap samples (random samples with replacement) from the initial training set, which is why bagging is also known as bootstrap aggregating.
In [34]:
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 [35]:
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))
Leveraging weak learners via adaptive boosting¶
In [10]:
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 [11]:
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))
Two-class AdaBoost¶
In [63]:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.ensemble import AdaBoostClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import make_gaussian_quantiles
# Create and fit an AdaBoosted decision tree
bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=5),
algorithm="SAMME",
n_estimators=200)
bdt.fit(X, y)
plot_colors = "br"
plot_step = 0.02
class_names = "AB"
plt.figure(figsize=(10, 5))
# Plot the decision boundaries
plt.subplot(121)
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),
np.arange(y_min, y_max, plot_step))
Z = bdt.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
cs = plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)
plt.axis("tight")
# Plot the training points
for i, n, c in zip(range(2), class_names, plot_colors):
idx = np.where(y == i)
plt.scatter(X[idx, 0], X[idx, 1],
c=c, cmap=plt.cm.Paired,
label="Class %s" % n)
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.legend(loc='upper right')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Decision Boundary')
# Plot the two-class decision scores
twoclass_output = bdt.decision_function(X)
plot_range = (twoclass_output.min(), twoclass_output.max())
plt.subplot(122)
for i, n, c in zip(range(2), class_names, plot_colors):
plt.hist(twoclass_output[y == i],
bins=10,
range=plot_range,
facecolor=c,
label='Class %s' % n,
alpha=.5)
x1, x2, y1, y2 = plt.axis()
plt.axis((x1, x2, y1, y2 * 1.2))
plt.legend(loc='upper right')
plt.ylabel('Samples')
plt.xlabel('Score')
plt.title('Decision Scores')
plt.tight_layout()
plt.subplots_adjust(wspace=0.35)
plt.show()
Discrete versus Real AdaBoost¶
In [64]:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.tree import DecisionTreeClassifier
from sklearn.metrics import zero_one_loss
from sklearn.ensemble import AdaBoostClassifier
n_estimators = 400
# A learning rate of 1. may not be optimal for both SAMME and SAMME.R
learning_rate = 1.
dt_stump = DecisionTreeClassifier(max_depth=1, min_samples_leaf=1)
dt_stump.fit(X_train, y_train)
dt_stump_err = 1.0 - dt_stump.score(X_test, y_test)
dt = DecisionTreeClassifier(max_depth=9, min_samples_leaf=1)
dt.fit(X_train, y_train)
dt_err = 1.0 - dt.score(X_test, y_test)
ada_discrete = AdaBoostClassifier(
base_estimator=dt_stump,
learning_rate=learning_rate,
n_estimators=n_estimators,
algorithm="SAMME")
ada_discrete.fit(X_train, y_train)
ada_real = AdaBoostClassifier(
base_estimator=dt_stump,
learning_rate=learning_rate,
n_estimators=n_estimators,
algorithm="SAMME.R")
ada_real.fit(X_train, y_train)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot([1, n_estimators], [dt_stump_err] * 2, 'k-',
label='Decision Stump Error')
ax.plot([1, n_estimators], [dt_err] * 2, 'k--',
label='Decision Tree Error')
ada_discrete_err = np.zeros((n_estimators,))
for i, y_pred in enumerate(ada_discrete.staged_predict(X_test)):
ada_discrete_err[i] = zero_one_loss(y_pred, y_test)
ada_discrete_err_train = np.zeros((n_estimators,))
for i, y_pred in enumerate(ada_discrete.staged_predict(X_train)):
ada_discrete_err_train[i] = zero_one_loss(y_pred, y_train)
ada_real_err = np.zeros((n_estimators,))
for i, y_pred in enumerate(ada_real.staged_predict(X_test)):
ada_real_err[i] = zero_one_loss(y_pred, y_test)
ada_real_err_train = np.zeros((n_estimators,))
for i, y_pred in enumerate(ada_real.staged_predict(X_train)):
ada_real_err_train[i] = zero_one_loss(y_pred, y_train)
ax.plot(np.arange(n_estimators) + 1, ada_discrete_err,
label='Discrete AdaBoost Test Error',
color='red')
ax.plot(np.arange(n_estimators) + 1, ada_discrete_err_train,
label='Discrete AdaBoost Train Error',
color='blue')
ax.plot(np.arange(n_estimators) + 1, ada_real_err,
label='Real AdaBoost Test Error',
color='orange')
ax.plot(np.arange(n_estimators) + 1, ada_real_err_train,
label='Real AdaBoost Train Error',
color='green')
ax.set_ylim((0.0, 0.5))
ax.set_xlabel('n_estimators')
ax.set_ylabel('error rate')
leg = ax.legend(loc='upper right', fancybox=True)
leg.get_frame().set_alpha(0.7)
plt.show()
Feature transformations with ensembles of trees¶
In [65]:
import numpy as np
np.random.seed(10)
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import (RandomTreesEmbedding, RandomForestClassifier,
GradientBoostingClassifier)
from sklearn.preprocessing import OneHotEncoder
from sklearn.cross_validation import train_test_split
from sklearn.metrics import roc_curve
from sklearn.pipeline import make_pipeline
n_estimator = 10
# It is important to train the ensemble of trees on a different subset
# of the training data than the linear regression model to avoid
# overfitting, in particular if the total number of leaves is
# similar to the number of training samples
X_train, X_train_lr, y_train, y_train_lr = train_test_split(X_train,
y_train,
test_size=0.5)
# Unsupervised transformation based on totally random trees
rt = RandomTreesEmbedding(max_depth=3, n_estimators=n_estimator,
random_state=0)
rt_lm = LogisticRegression()
pipeline = make_pipeline(rt, rt_lm)
pipeline.fit(X_train, y_train)
y_pred_rt = pipeline.predict_proba(X_test)[:, 1]
fpr_rt_lm, tpr_rt_lm, _ = roc_curve(y_test, y_pred_rt)
# Supervised transformation based on random forests
rf = RandomForestClassifier(max_depth=3, n_estimators=n_estimator)
rf_enc = OneHotEncoder()
rf_lm = LogisticRegression()
rf.fit(X_train, y_train)
rf_enc.fit(rf.apply(X_train))
rf_lm.fit(rf_enc.transform(rf.apply(X_train_lr)), y_train_lr)
y_pred_rf_lm = rf_lm.predict_proba(rf_enc.transform(rf.apply(X_test)))[:, 1]
fpr_rf_lm, tpr_rf_lm, _ = roc_curve(y_test, y_pred_rf_lm)
grd = GradientBoostingClassifier(n_estimators=n_estimator)
grd_enc = OneHotEncoder()
grd_lm = LogisticRegression()
grd.fit(X_train, y_train)
grd_enc.fit(grd.apply(X_train)[:, :, 0])
grd_lm.fit(grd_enc.transform(grd.apply(X_train_lr)[:, :, 0]), y_train_lr)
y_pred_grd_lm = grd_lm.predict_proba(
grd_enc.transform(grd.apply(X_test)[:, :, 0]))[:, 1]
fpr_grd_lm, tpr_grd_lm, _ = roc_curve(y_test, y_pred_grd_lm)
# The gradient boosted model by itself
y_pred_grd = grd.predict_proba(X_test)[:, 1]
fpr_grd, tpr_grd, _ = roc_curve(y_test, y_pred_grd)
# The random forest model by itself
y_pred_rf = rf.predict_proba(X_test)[:, 1]
fpr_rf, tpr_rf, _ = roc_curve(y_test, y_pred_rf)
plt.figure(1)
plt.plot([0, 1], [0, 1], 'k--')
plt.plot(fpr_rt_lm, tpr_rt_lm, label='RT + LR')
plt.plot(fpr_rf, tpr_rf, label='RF')
plt.plot(fpr_rf_lm, tpr_rf_lm, label='RF + LR')
plt.plot(fpr_grd, tpr_grd, label='GBT')
plt.plot(fpr_grd_lm, tpr_grd_lm, label='GBT + LR')
plt.xlabel('False positive rate')
plt.ylabel('True positive rate')
plt.title('ROC curve')
plt.legend(loc='best')
plt.show()
plt.figure(2)
plt.xlim(0, 0.2)
plt.ylim(0.8, 1)
plt.plot([0, 1], [0, 1], 'k--')
plt.plot(fpr_rt_lm, tpr_rt_lm, label='RT + LR')
plt.plot(fpr_rf, tpr_rf, label='RF')
plt.plot(fpr_rf_lm, tpr_rf_lm, label='RF + LR')
plt.plot(fpr_grd, tpr_grd, label='GBT')
plt.plot(fpr_grd_lm, tpr_grd_lm, label='GBT + LR')
plt.xlabel('False positive rate')
plt.ylabel('True positive rate')
plt.title('ROC curve (zoomed in at top left)')
plt.legend(loc='best')
plt.show()
PCA Decomposition¶
In [19]:
target_names = ['Shares > 1400' , 'Shares < 1400']
In [41]:
X.values
Out[41]:
In [42]:
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
pca = PCA(n_components=2)
reduced_X = pca.fit_transform(X)
In [48]:
for a in [red_x, red_y,blue_x,blue_y]:
print len(a)
In [49]:
red_x, red_y = [], []
blue_x, blue_y = [], []
for i in range(len(reduced_X)):
if y[i] == 0:
red_x.append(reduced_X[i][0])
red_y.append(reduced_X[i][1])
elif y[i] == 1:
blue_x.append(reduced_X[i][0])
blue_y.append(reduced_X[i][1])
plt.scatter(red_x, red_y, c='r', marker='x')
plt.scatter(blue_x, blue_y, c='b', marker='.')
plt.show()
In [33]:
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
"""
pca = PCA(n_components=2)
X_r = pca.fit(X.values).transform(X.values)
lda = LinearDiscriminantAnalysis(n_components=2)
X_r2 = lda.fit(X.values, y.values).transform(X.values)
"""
pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)
lda = LinearDiscriminantAnalysis(n_components=2)
X_r2 = lda.fit(X, y).transform(X)
# Percentage of variance explained for each components
print('explained variance ratio (first two components): %s'
% str(pca.explained_variance_ratio_))
plt.figure()
colors = ['blue','red']
for i in xrange(len(colors)):
px = X_r[:, 0][y == i]
py = X_r[:, 1][y == i]
plt.scatter(px, py, c=colors[i])
plt.legend(target_names)
plt.title('PCA')
plt.xlabel('First Principal Component')
plt.ylabel('Second Principal Component')
plt.figure()
colors = ['blue','red']
for i in xrange(len(colors)):
px = X_r2[:, 0][y == i]
py = X_pca[:, 1][y == i]
plt.scatter(px, py, c=colors[i])
plt.legend(target_names)
plt.title('LDA')
plt.xlabel('First Principal Component')
plt.ylabel('Second Principal Component')
plt.show()
"""
for c, i, target_name in zip("rb", [0, 1], target_names):
plt.scatter(X_r[y == i, 0], X_r[y == i, 1], c=c, label=target_name)
plt.legend()
plt.title('PCA')
plt.figure()
for c, i, target_name in zip("rb", [0, 1], target_names):
plt.scatter(X_r2[y == i, 0], X_r2[y == i, 1], c=c, label=target_name)
plt.legend()
plt.title('LDA')
plt.show()
"""
Out[33]:
In [25]:
plt.figure()
def plot_pca_scatter():
colors = ['blue','red']
for i in xrange(len(colors)):
px = X_pca[:, 0][y == i]
py = X_pca[:, 1][y == i]
plt.scatter(px, py, c=colors[i])
plt.legend(target_names)
plt.xlabel('First Principal Component')
plt.ylabel('Second Principal Component')
In [26]:
from sklearn.decomposition import PCA
estimator = PCA(n_components=2)
X_pca = estimator.fit_transform(X.values)
plot_pca_scatter() # Note that we only plot the first and second principal component
In [ ]:
plt.figure(figsize=(2. * n_col, 2.26 * n_row))
for i, comp in enumerate(images):
plt.subplot(n_row, n_col, i + 1)
plt.imshow(comp.reshape((8, 8)), interpolation='nearest')
plt.text(0, -1, str(i + 1) + '-component')
plt.xticks(())
plt.yticks(())
In [11]:
from sklearn.pipeline import Pipeline, FeatureUnion
from sklearn.grid_search import GridSearchCV
from sklearn.decomposition import PCA
from sklearn.feature_selection import SelectKBest
# This dataset is way to high-dimensional. Better do PCA:
pca = PCA(n_components=2)
# Maybe some original features where good, too?
selection = SelectKBest(k=1)
# Build estimator from PCA and Univariate selection:
combined_features = FeatureUnion([("pca", pca), ("univ_select", selection)])
# Use combined features to transform dataset:
X_features = combined_features.fit(X, y).transform(X)
dt = DecisionTreeClassifier(min_samples_split=1,max_depth=5,min_samples_leaf=5,random_state=99)
# Do grid search over k, n_components and max_depth:
pipeline = Pipeline([("features", combined_features), ("dt", dt)])
param_grid = dict(features__pca__n_components=[1, 2, 3],
features__univ_select__k=[1, 2],
dt__max_depth=[3, 5, 7])
grid_search = GridSearchCV(pipeline, param_grid=param_grid, verbose=10)
grid_search.fit(X, y)
print(grid_search.best_estimator_)
print(grid_search.best_score_)
Comparison of Calibration of Classifiers¶
In [27]:
import numpy as np
np.random.seed(0)
%matplotlib inline
import matplotlib.pyplot as plt
from sklearn.naive_bayes import GaussianNB
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.calibration import calibration_curve
# Create classifiers
lr = LogisticRegression()
gnb = GaussianNB()
knn = KNeighborsClassifier(n_neighbors=25)
rfc = RandomForestClassifier(n_estimators=100)
###############################################################################
# Plot calibration plots
plt.figure(figsize=(10, 10))
ax1 = plt.subplot2grid((3, 1), (0, 0), rowspan=2)
ax2 = plt.subplot2grid((3, 1), (2, 0))
ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated")
for clf, name in [(lr, 'Logistic'),
(gnb, 'Naive Bayes'),
(knn, 'K Neighbors Classifier'),
(rfc, 'Random Forest')]:
clf.fit(X_train, y_train)
if hasattr(clf, "predict_proba"):
prob_pos = clf.predict_proba(X_test)[:, 1]
else: # use decision function
prob_pos = clf.decision_function(X_test)
prob_pos = \
(prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min())
fraction_of_positives, mean_predicted_value = \
calibration_curve(y_test, prob_pos, n_bins=10)
ax1.plot(mean_predicted_value, fraction_of_positives, "s-",
label="%s" % (name, ))
ax2.hist(prob_pos, range=(0, 1), bins=10, label=name,
histtype="step", lw=2)
ax1.set_ylabel("Fraction of positives")
ax1.set_ylim([-0.05, 1.05])
ax1.legend(loc="lower right")
ax1.set_title('Calibration plots (reliability curve)')
ax2.set_xlabel("Mean predicted value")
ax2.set_ylabel("Count")
ax2.legend(loc="upper center", ncol=2)
plt.tight_layout()
plt.show()
Probability Calibration curves¶
In [28]:
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.naive_bayes import GaussianNB
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import (brier_score_loss, precision_score, recall_score,
f1_score)
from sklearn.calibration import CalibratedClassifierCV, calibration_curve
from sklearn.cross_validation import train_test_split
def plot_calibration_curve(est, name, fig_index):
"""Plot calibration curve for est w/o and with calibration. """
# Calibrated with isotonic calibration
isotonic = CalibratedClassifierCV(est, cv=2, method='isotonic')
# Calibrated with sigmoid calibration
sigmoid = CalibratedClassifierCV(est, cv=2, method='sigmoid')
# Logistic regression with no calibration as baseline
lr = LogisticRegression(C=1., solver='lbfgs')
fig = plt.figure(fig_index, figsize=(10, 10))
ax1 = plt.subplot2grid((3, 1), (0, 0), rowspan=2)
ax2 = plt.subplot2grid((3, 1), (2, 0))
ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated")
for clf, name in [(lr, 'Logistic'),
(est, name),
(isotonic, name + ' + Isotonic'),
(sigmoid, name + ' + Sigmoid')]:
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
if hasattr(clf, "predict_proba"):
prob_pos = clf.predict_proba(X_test)[:, 1]
else: # use decision function
prob_pos = clf.decision_function(X_test)
prob_pos = \
(prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min())
clf_score = brier_score_loss(y_test, prob_pos, pos_label=y.max())
print("%s:" % name)
print("\tBrier: %1.3f" % (clf_score))
print("\tPrecision: %1.3f" % precision_score(y_test, y_pred))
print("\tRecall: %1.3f" % recall_score(y_test, y_pred))
print("\tF1: %1.3f\n" % f1_score(y_test, y_pred))
fraction_of_positives, mean_predicted_value = \
calibration_curve(y_test, prob_pos, n_bins=10)
ax1.plot(mean_predicted_value, fraction_of_positives, "s-",
label="%s (%1.3f)" % (name, clf_score))
ax2.hist(prob_pos, range=(0, 1), bins=10, label=name,
histtype="step", lw=2)
ax1.set_ylabel("Fraction of positives")
ax1.set_ylim([-0.05, 1.05])
ax1.legend(loc="lower right")
ax1.set_title('Calibration plots (reliability curve)')
ax2.set_xlabel("Mean predicted value")
ax2.set_ylabel("Count")
ax2.legend(loc="upper center", ncol=2)
plt.tight_layout()
# Plot calibration cuve for Gaussian Naive Bayes
plot_calibration_curve(GaussianNB(), "Naive Bayes", 1)
# Plot calibration cuve for Linear SVC
plot_calibration_curve(DecisionTreeClassifier(), "Decision Tree", 2)
plt.show()
Plot classification probability¶
In [55]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import LogisticRegression
#PCA
pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)
n_features = X_r.shape[1]
C = 1.0
# Create different classifiers. The logistic regression cannot do
# multiclass out of the box.
classifiers = {'L1 logistic': LogisticRegression(C=C, penalty='l1'),
'L2 logistic': LogisticRegression(C=C, penalty='l2'),
'Decision Tree': DecisionTreeClassifier(max_depth=5,min_samples_leaf=5,min_samples_split=1,random_state=99),
'K Nearest Neighbors': KNeighborsClassifier(n_neighbors=3),
'Random Forest' : RandomForestClassifier(max_depth=25,min_samples_leaf=2,
min_samples_split=10,n_estimators=100,n_jobs=-1)
}
n_classifiers = len(classifiers)
plt.figure(figsize=(2 * 2, n_classifiers * 2))
plt.subplots_adjust(bottom=.2, top=.95)
xx = np.linspace(3, 9, 100)
yy = np.linspace(1, 5, 100).T
xx, yy = np.meshgrid(xx, yy)
Xfull = np.c_[xx.ravel(), yy.ravel()]
for index, (name, classifier) in enumerate(classifiers.items()):
classifier.fit(X_r, y)
y_pred = classifier.predict(X_r)
classif_rate = np.mean(y_pred.ravel() == y.ravel()) * 100
print("classif_rate for %s : %f " % (name, classif_rate))
# View probabilities=
probas = classifier.predict_proba(Xfull)
n_classes = np.unique(y_pred).size
for k in range(n_classes):
plt.subplot(n_classifiers, n_classes, index * n_classes + k + 1)
plt.title("Class %d" % k)
if k == 0:
plt.ylabel(name)
imshow_handle = plt.imshow(probas[:, k].reshape((100, 100)),
extent=(3, 9, 1, 5), origin='lower')
plt.xticks(())
plt.yticks(())
idx = (y_pred == k)
if idx.any():
plt.scatter(X_r[idx, 0], X_r[idx, 1], marker='o', c='k')
ax = plt.axes([0.15, 0.04, 0.7, 0.05])
plt.title("Probability")
plt.colorbar(imshow_handle, cax=ax, orientation='horizontal')
plt.show()
Recursive feature elimination with cross-validation¶
In [66]:
import matplotlib.pyplot as plt
from sklearn.cross_validation import StratifiedKFold
from sklearn.feature_selection import RFECV
from sklearn.datasets import make_classification
# Create the RFE object and compute a cross-validated score.
rf = RandomForestClassifier(max_depth=25,min_samples_leaf=2,min_samples_split=10,n_estimators=100,n_jobs=-1)
# The "accuracy" scoring is proportional to the number of correct classifications
rfecv = RFECV(estimator=rf, step=1, cv=StratifiedKFold(y, 2),
scoring='accuracy')
rfecv.fit(X, y)
print("Optimal number of features : %d" % rfecv.n_features_)
# Plot number of features VS. cross-validation scores
plt.figure()
plt.xlabel("Number of features selected")
plt.ylabel("Cross validation score (nb of correct classifications)")
plt.plot(range(1, len(rfecv.grid_scores_) + 1), rfecv.grid_scores_)
plt.show()
