Stacking

Last updated 2020-02-12 Read time 3 min

Summary

Stacking trains multiple base models, then feeds their out-of-fold predictions into a meta-model.
The meta-model learns how to combine complementary strengths of different learners.
Proper out-of-fold construction is essential to prevent leakage and to keep validation performance trustworthy.

Intuition #

Instead of picking one best model, stacking learns a second-level model that decides when each base model should be trusted. It works well when base learners make different kinds of errors.

Detailed Explanation #

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import matplotlib.pyplot as plt

from sklearn.datasets import make_classification
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import StackingClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_auc_score
from sklearn.tree import export_graphviz
from subprocess import call

Create data for experiment #

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# Create data with 20 features
n_features = 20
X, y = make_classification(
    n_samples=2500,
    n_features=n_features,
    n_informative=10,
    n_classes=2,
    n_redundant=0,
    n_clusters_per_class=4,
    random_state=777,
)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.33, random_state=777
)

Plot the data with respect to multiple features #

Confirm that it does not appear to be classifiable by simple rules.

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plt.figure(figsize=(10, 10))
plt.subplot(2, 2, 1)
plt.scatter(X[:, 2], X[:, 7], c=y)
plt.xlabel("x2")
plt.ylabel("x7")
plt.subplot(2, 2, 2)
plt.scatter(X[:, 4], X[:, 9], c=y)
plt.xlabel("x4")
plt.ylabel("x9")
plt.subplot(2, 2, 3)
plt.scatter(X[:, 5], X[:, 1], c=y)
plt.xlabel("x5")
plt.ylabel("x1")
plt.subplot(2, 2, 4)
plt.scatter(X[:, 1], X[:, 3], c=y)
plt.xlabel("x1")
plt.ylabel("x3")
plt.show()

Confirm that it does not appear to be classifiable by simple… figure

Stacking vs. Random Forest #

Classification with Random Forest #

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model = RandomForestClassifier(n_estimators=50, max_depth=5, random_state=777)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
rf_score = roc_auc_score(y_test, y_pred)
print(f"ROC-AUC = {rf_score}")

ROC-AUC = 0.855797033310609

When stacking with multiple trees #

We can confirm that stacking with only DecisionTreeClassifier does not improve accuracy much.

sklearn.ensemble.StackingClassifier

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# Models used in base learner
estimators = [
    ("dt1", DecisionTreeClassifier(max_depth=3, random_state=777)),
    ("dt2", DecisionTreeClassifier(max_depth=4, random_state=777)),
    ("dt3", DecisionTreeClassifier(max_depth=5, random_state=777)),
    ("dt4", DecisionTreeClassifier(max_depth=6, random_state=777)),
]
# Number of models included in base learner
n_estimators = len(estimators)
# aggregation model
final_estimator = DecisionTreeClassifier(max_depth=3, random_state=777)
# train base-learner and aggregation model
clf = StackingClassifier(estimators=estimators, final_estimator=final_estimator)
clf.fit(X_train, y_train)
# evaluate
y_pred = clf.predict(X_test)
clf_score = roc_auc_score(y_test, y_pred)

print("ROC-AUC")
print(f"Decision Tree Stacking＝{clf_score}, Random Forest＝{rf_score}")

ROC-AUC
Decision Tree Stacking＝0.7359716965608031, Random Forest＝0.855797033310609

Visualize trees used for stacking #

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export_graphviz(
    clf.final_estimator_,
    out_file="tree_final_estimator.dot",
    class_names=["A", "B"],
    feature_names=[e[0] for e in estimators],
    proportion=True,
    filled=True,
)

call(
    [
        "dot",
        "-Tpng",
        "tree_final_estimator.dot",
        "-o",
        f"tree_final_estimator.png",
        "-Gdpi=200",
    ]
)
display(Image(filename="tree_final_estimator.png"))

Visualize trees used for stacking figure

Look at the feature importance of the trees used in the stacking. #

We see that although stacked, in the end only the fourth tree is used almost exclusively in the forecast.

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plt.figure(figsize=(6, 3))
plot_index = [i for i in range(n_estimators)]
plt.bar(plot_index, clf.final_estimator_.feature_importances_)
plt.xticks(plot_index, [e[0] for e in estimators])
plt.xlabel("model name")
plt.ylabel("feature-importance")
plt.show()

We see that although stacked, in the end only the fourth tre… figure

Check the performance of each tree in the base learner #

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scores = []
for clf_estim in clf.estimators_:
    print("====")
    y_pred = clf_estim.predict(X_test)
    scr = roc_auc_score(y_test, y_pred)
    scores.append(scr)
    print(clf_estim)
    print(scr)

n_estimators = len(estimators)
plot_index = [i for i in range(n_estimators)]

plt.figure(figsize=(8, 4))
plt.bar(plot_index, scores)
plt.xticks(plot_index, [e[0] for e in estimators])
plt.xlabel("model name")
plt.ylabel("roc-auc")
plt.show()

====
DecisionTreeClassifier(max_depth=3, random_state=777)
0.7660117774277722
====
DecisionTreeClassifier(max_depth=4, random_state=777)
0.7744128916993818
====
DecisionTreeClassifier(max_depth=5, random_state=777)
0.8000158677919086
====
DecisionTreeClassifier(max_depth=6, random_state=777)
0.8084639977432473

8084639977432473 figure