StackingCVClassifier

An ensemble-learning meta-classifier for stacking using cross-validation to prepare the inputs for the level-2 classifier to prevent overfitting.

from mlxtend.classifier import StackingCVClassifier

Overview

Stacking is an ensemble learning technique to combine multiple classification models via a meta-classifier. The StackingCVClassifier extends the standard stacking algorithm (implemented as StackingClassifier) using cross-validation to prepare the input data for the level-2 classifier.

In the standard stacking procedure, the first-level classifiers are fit to the same training set that is used prepare the inputs for the second-level classifier, which may lead to overfitting. The StackingCVClassifier, however, uses the concept of cross-validation: the dataset is split into k folds, and in k successive rounds, k-1 folds are used to fit the first level classifier; in each round, the first-level classifiers are then applied to the remaining 1 subset that was not used for model fitting in each iteration. The resulting predictions are then stacked and provided -- as input data -- to the second-level classifier. After the training of the StackingCVClassifier, the first-level classifiers are fit to the entire dataset as illustrated in the figure below.

More formally, the Stacking Cross-Validation algorithm can be summarized as follows (source: [1]):

References

• [1] Tang, J., S. Alelyani, and H. Liu. "Data Classification: Algorithms and Applications." Data Mining and Knowledge Discovery Series, CRC Press (2015): pp. 498-500.
• [2] Wolpert, David H. "Stacked generalization." Neural networks 5.2 (1992): 241-259.

Example 1 - Simple Stacking CV Classification

from sklearn import datasets

iris = datasets.load_iris()
X, y = iris.data[:, 1:3], iris.target

from sklearn import model_selection
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from mlxtend.classifier import StackingCVClassifier
import numpy as np

RANDOM_SEED = 42

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=RANDOM_SEED)
clf3 = GaussianNB()
lr = LogisticRegression()

# The StackingCVClassifier uses scikit-learn's check_cv
# internally, which doesn't support a random seed. Thus
# NumPy's random seed need to be specified explicitely for
# deterministic behavior
np.random.seed(RANDOM_SEED)
sclf = StackingCVClassifier(classifiers=[clf1, clf2, clf3], 
                            meta_classifier=lr)

print('3-fold cross validation:\n')

for clf, label in zip([clf1, clf2, clf3, sclf], 
                      ['KNN', 
                       'Random Forest', 
                       'Naive Bayes',
                       'StackingClassifier']):

    scores = model_selection.cross_val_score(clf, X, y, 
                                              cv=3, scoring='accuracy')
    print("Accuracy: %0.2f (+/- %0.2f) [%s]" 
          % (scores.mean(), scores.std(), label))

3-fold cross validation:

Accuracy: 0.91 (+/- 0.01) [KNN]
Accuracy: 0.90 (+/- 0.03) [Random Forest]
Accuracy: 0.92 (+/- 0.03) [Naive Bayes]
Accuracy: 0.93 (+/- 0.02) [StackingClassifier]

import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions
import matplotlib.gridspec as gridspec
import itertools

gs = gridspec.GridSpec(2, 2)

fig = plt.figure(figsize=(10,8))

for clf, lab, grd in zip([clf1, clf2, clf3, sclf], 
                         ['KNN', 
                          'Random Forest', 
                          'Naive Bayes',
                          'StackingCVClassifier'],
                          itertools.product([0, 1], repeat=2)):

    clf.fit(X, y)
    ax = plt.subplot(gs[grd[0], grd[1]])
    fig = plot_decision_regions(X=X, y=y, clf=clf)
    plt.title(lab)
plt.show()

Example 2 - Using Probabilities as Meta-Features

Alternatively, the class-probabilities of the first-level classifiers can be used to train the meta-classifier (2nd-level classifier) by setting use_probas=True. For example, in a 3-class setting with 2 level-1 classifiers, these classifiers may make the following "probability" predictions for 1 training sample:

• classifier 1: [0.2, 0.5, 0.3]
• classifier 2: [0.3, 0.4, 0.4]

This results in k features, where k = [n_classes * n_classifiers], by stacking these level-1 probabilities:

• [0.2, 0.5, 0.3, 0.3, 0.4, 0.4]

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()
lr = LogisticRegression()

# The StackingCVClassifier uses scikit-learn's check_cv
# internally, which doesn't support a random seed. Thus
# NumPy's random seed need to be specified explicitely for
# deterministic behavior
np.random.seed(RANDOM_SEED)
sclf = StackingCVClassifier(classifiers=[clf1, clf2, clf3],
                            use_probas=True,
                            meta_classifier=lr)

print('3-fold cross validation:\n')

for clf, label in zip([clf1, clf2, clf3, sclf], 
                      ['KNN', 
                       'Random Forest', 
                       'Naive Bayes',
                       'StackingClassifier']):

    scores = model_selection.cross_val_score(clf, X, y, 
                                              cv=3, scoring='accuracy')
    print("Accuracy: %0.2f (+/- %0.2f) [%s]" 
          % (scores.mean(), scores.std(), label))

3-fold cross validation:

Accuracy: 0.91 (+/- 0.01) [KNN]
Accuracy: 0.91 (+/- 0.06) [Random Forest]
Accuracy: 0.92 (+/- 0.03) [Naive Bayes]
Accuracy: 0.95 (+/- 0.04) [StackingClassifier]

Example 3 - Stacked CV Classification and GridSearch

To set up a parameter grid for scikit-learn's GridSearch, we simply provide the estimator's names in the parameter grid -- in the special case of the meta-regressor, we append the 'meta-' prefix.

from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import GridSearchCV
from mlxtend.classifier import StackingCVClassifier

# Initializing models

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=RANDOM_SEED)
clf3 = GaussianNB()
lr = LogisticRegression()

# The StackingCVClassifier uses scikit-learn's check_cv
# internally, which doesn't support a random seed. Thus
# NumPy's random seed need to be specified explicitely for
# deterministic behavior
np.random.seed(RANDOM_SEED)
sclf = StackingCVClassifier(classifiers=[clf1, clf2, clf3], 
                            meta_classifier=lr)

params = {'kneighborsclassifier__n_neighbors': [1, 5],
          'randomforestclassifier__n_estimators': [10, 50],
          'meta-logisticregression__C': [0.1, 10.0]}

grid = GridSearchCV(estimator=sclf, 
                    param_grid=params, 
                    cv=5,
                    refit=True)
grid.fit(X, y)

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]))

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

0.673 +/- 0.01 {'kneighborsclassifier__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.920 +/- 0.02 {'kneighborsclassifier__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.893 +/- 0.02 {'kneighborsclassifier__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
0.667 +/- 0.00 {'kneighborsclassifier__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
Best parameters: {'kneighborsclassifier__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
Accuracy: 0.95

In case we are planning to use a regression algorithm multiple times, all we need to do is to add an additional number suffix in the parameter grid as shown below:

from sklearn.model_selection import GridSearchCV

# Initializing models

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=RANDOM_SEED)
clf3 = GaussianNB()
lr = LogisticRegression()

# The StackingCVClassifier uses scikit-learn's check_cv
# internally, which doesn't support a random seed. Thus
# NumPy's random seed need to be specified explicitely for
# deterministic behavior
np.random.seed(RANDOM_SEED)
sclf = StackingCVClassifier(classifiers=[clf1, clf1, clf2, clf3], 
                            meta_classifier=lr)

params = {'kneighborsclassifier-1__n_neighbors': [1, 5],
          'kneighborsclassifier-2__n_neighbors': [1, 5],
          'randomforestclassifier__n_estimators': [10, 50],
          'meta-logisticregression__C': [0.1, 10.0]}

grid = GridSearchCV(estimator=sclf, 
                    param_grid=params, 
                    cv=5,
                    refit=True)
grid.fit(X, y)

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]))

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

0.673 +/- 0.01 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.920 +/- 0.02 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.893 +/- 0.02 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.947 +/- 0.02 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.940 +/- 0.02 {'kneighborsclassifier-1__n_neighbors': 1, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.953 +/- 0.02 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.927 +/- 0.03 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 10}
0.667 +/- 0.00 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 0.1, 'randomforestclassifier__n_estimators': 50}
0.940 +/- 0.03 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
0.940 +/- 0.03 {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 5, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 50}
Best parameters: {'kneighborsclassifier-1__n_neighbors': 5, 'kneighborsclassifier-2__n_neighbors': 1, 'meta-logisticregression__C': 10.0, 'randomforestclassifier__n_estimators': 10}
Accuracy: 0.95

Note

The StackingCVClassifier also enables grid search over the classifiers argument. However, due to the current implementation of GridSearchCV in scikit-learn, it is not possible to search over both, differenct classifiers and classifier parameters at the same time. For instance, while the following parameter dictionary works

params = {'randomforestclassifier__n_estimators': [1, 100],
'classifiers': [(clf1, clf1, clf1), (clf2, clf3)]}

it will use the instance settings of clf1, clf2, and clf3 and not overwrite it with the 'n_estimators' settings from 'randomforestclassifier__n_estimators': [1, 100].

Example 4 - Stacking of Classifiers that Operate on Different Feature Subsets

The different level-1 classifiers can be fit to different subsets of features in the training dataset. The following example illustrates how this can be done on a technical level using scikit-learn pipelines and the ColumnSelector:

from sklearn.datasets import load_iris
from mlxtend.classifier import StackingCVClassifier
from mlxtend.feature_selection import ColumnSelector
from sklearn.pipeline import make_pipeline
from sklearn.linear_model import LogisticRegression

iris = load_iris()
X = iris.data
y = iris.target

pipe1 = make_pipeline(ColumnSelector(cols=(0, 2)),
                      LogisticRegression())
pipe2 = make_pipeline(ColumnSelector(cols=(1, 2, 3)),
                      LogisticRegression())

sclf = StackingCVClassifier(classifiers=[pipe1, pipe2], 
                            meta_classifier=LogisticRegression())

sclf.fit(X, y)

StackingCVClassifier(classifiers=[Pipeline(steps=[('columnselector', ColumnSelector(cols=(0, 2))), ('logisticregression', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
          penalty='l2', random_state=None, solve...='l2', random_state=None, solver='liblinear', tol=0.0001,
          verbose=0, warm_start=False))])],
           cv=2,
           meta_classifier=LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
          verbose=0, warm_start=False),
           shuffle=True, stratify=True, use_features_in_secondary=False,
           use_probas=False, verbose=0)

API

StackingCVClassifier(classifiers, meta_classifier, use_probas=False, cv=2, use_features_in_secondary=False, stratify=True, shuffle=True, verbose=0, store_train_meta_features=False, use_clones=True)

A 'Stacking Cross-Validation' classifier for scikit-learn estimators.

New in mlxtend v0.4.3

Notes

The StackingCVClassifier uses scikit-learn's check_cv internally, which doesn't support a random seed. Thus NumPy's random seed need to be specified explicitely for deterministic behavior, for instance, by setting np.random.seed(RANDOM_SEED) prior to fitting the StackingCVClassifier

Parameters

• classifiers : array-like, shape = [n_classifiers]

  A list of classifiers. Invoking the fit method on the StackingCVClassifer will fit clones of these original classifiers that will be stored in the class attribute self.clfs_.

• meta_classifier : object

  The meta-classifier to be fitted on the ensemble of classifiers

• use_probas : bool (default: False)

  If True, trains meta-classifier based on predicted probabilities instead of class labels.

• cv : int, cross-validation generator or an iterable, optional (default: 2)

  Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 2-fold cross validation, - integer, to specify the number of folds in a (Stratified)KFold, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits. For integer/None inputs, it will use either a KFold or StratifiedKFold cross validation depending the value of stratify argument.

• use_features_in_secondary : bool (default: False)

  If True, the meta-classifier will be trained both on the predictions of the original classifiers and the original dataset. If False, the meta-classifier will be trained only on the predictions of the original classifiers.

• stratify : bool (default: True)

  If True, and the cv argument is integer it will follow a stratified K-Fold cross validation technique. If the cv argument is a specific cross validation technique, this argument is omitted.

• shuffle : bool (default: True)

  If True, and the cv argument is integer, the training data will be shuffled at fitting stage prior to cross-validation. If the cv argument is a specific cross validation technique, this argument is omitted.

• verbose : int, optional (default=0)

  Controls the verbosity of the building process. - verbose=0 (default): Prints nothing - verbose=1: Prints the number & name of the regressor being fitted and which fold is currently being used for fitting - verbose=2: Prints info about the parameters of the regressor being fitted - verbose>2: Changes verbose param of the underlying regressor to self.verbose - 2

• store_train_meta_features : bool (default: False)

  If True, the meta-features computed from the training data used for fitting the meta-classifier stored in the self.train_meta_features_ array, which can be accessed after calling fit.

• use_clones : bool (default: True)

  Clones the classifiers for stacking classification if True (default) or else uses the original ones, which will be refitted on the dataset upon calling the fit method. Hence, if use_clones=True, the original input classifiers will remain unmodified upon using the StackingCVClassifier's fit method. Setting use_clones=False is recommended if you are working with estimators that are supporting the scikit-learn fit/predict API interface but are not compatible to scikit-learn's clone function.

Attributes

• clfs_ : list, shape=[n_classifiers]

  Fitted classifiers (clones of the original classifiers)

• meta_clf_ : estimator

  Fitted meta-classifier (clone of the original meta-estimator)

• train_meta_features : numpy array, shape = [n_samples, n_classifiers]

  meta-features for training data, where n_samples is the number of samples in training data and n_classifiers is the number of classfiers.

Examples

For usage examples, please see http://rasbt.github.io/mlxtend/user_guide/classifier/StackingCVClassifier/

Methods

---

fit(X, y, groups=None, sample_weight=None)

Fit ensemble classifers and the meta-classifier.

Parameters

• X : numpy array, shape = [n_samples, n_features]

  Training vectors, where n_samples is the number of samples and n_features is the number of features.

• y : numpy array, shape = [n_samples]

  Target values.

• groups : numpy array/None, shape = [n_samples]

  The group that each sample belongs to. This is used by specific folding strategies such as GroupKFold()

• sample_weight : array-like, shape = [n_samples], optional

  Sample weights passed as sample_weights to each regressor in the regressors list as well as the meta_regressor. Raises error if some regressor does not support sample_weight in the fit() method.

Returns

• self : object

---

fit_transform(X, y=None, fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters

• X : numpy array of shape [n_samples, n_features]

  Training set.

• y : numpy array of shape [n_samples]

  Target values.

Returns

• X_new : numpy array of shape [n_samples, n_features_new]

  Transformed array.

---

get_params(deep=True)

Return estimator parameter names for GridSearch support.

---

predict(X)

Predict target values for X.

Parameters

• X : numpy array, shape = [n_samples, n_features]

  Training vectors, where n_samples is the number of samples and n_features is the number of features.

Returns

• labels : array-like, shape = [n_samples]

  Predicted class labels.

---

predict_meta_features(X)

Get meta-features of test-data.

Parameters

• X : numpy array, shape = [n_samples, n_features]

  Test vectors, where n_samples is the number of samples and n_features is the number of features.

Returns

• meta-features : numpy array, shape = [n_samples, n_classifiers]

  Returns the meta-features for test data.

---

predict_proba(X)

Predict class probabilities for X.

Parameters

• X : numpy array, shape = [n_samples, n_features]

  Training vectors, where n_samples is the number of samples and n_features is the number of features.

Returns

• proba : array-like, shape = [n_samples, n_classes]

  Probability for each class per sample.

---

score(X, y, sample_weight=None)

Returns the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters

• X : array-like, shape = (n_samples, n_features)

  Test samples.

• y : array-like, shape = (n_samples) or (n_samples, n_outputs)

  True labels for X.

• sample_weight : array-like, shape = [n_samples], optional

  Sample weights.

Returns

• score : float

  Mean accuracy of self.predict(X) wrt. y.

---

set_params(params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it's possible to update each component of a nested object.

Returns

self