Chapter 7 – Ensemble Learning and Random Forests
This notebook contains all the sample code and solutions to the exercises in chapter 7.
 Run in Google Colab
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Warning: this is the code for the 1st edition of the book. Please visit https://github.com/ageron/handson-ml2 for the 2nd edition code, with up-to-date notebooks using the latest library versions.
Setup¶
First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:
In [1]:
# To support both python 2 and python 3
from __future__ import division, print_function, unicode_literals
# Common imports
import numpy as np
import os
# to make this notebook's output stable across runs
np.random.seed(42)
# To plot pretty figures
%matplotlib inline
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rc('axes', labelsize=14)
mpl.rc('xtick', labelsize=12)
mpl.rc('ytick', labelsize=12)
# Where to save the figures
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "ensembles"
IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID)
os.makedirs(IMAGES_PATH, exist_ok=True)
def save_fig(fig_id, tight_layout=True, fig_extension="png", resolution=300):
path = os.path.join(IMAGES_PATH, fig_id + "." + fig_extension)
print("Saving figure", fig_id)
if tight_layout:
plt.tight_layout()
plt.savefig(path, format=fig_extension, dpi=resolution)
Voting classifiers¶
In [2]:
heads_proba = 0.51
coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
In [3]:
plt.figure(figsize=(8,3.5))
plt.plot(cumulative_heads_ratio)
plt.plot([0, 10000], [0.51, 0.51], "k--", linewidth=2, label="51%")
plt.plot([0, 10000], [0.5, 0.5], "k-", label="50%")
plt.xlabel("Number of coin tosses")
plt.ylabel("Heads ratio")
plt.legend(loc="lower right")
plt.axis([0, 10000, 0.42, 0.58])
save_fig("law_of_large_numbers_plot")
plt.show()
Saving figure law_of_large_numbers_plot
In [4]:
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_moons
X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
Warning: In Scikit-Learn 0.20, some hyperparameters (solver, n_estimators, gamma, etc.) start issuing warnings about the fact that their default value will change in Scikit-Learn 0.22. To avoid these warnings and ensure that this notebooks keeps producing the same outputs as in the book, I set the hyperparameters to their old default value. In your own code, you can simply rely on the latest default values instead.
In [5]:
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import VotingClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
log_clf = LogisticRegression(solver="liblinear", random_state=42)
rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
svm_clf = SVC(gamma="auto", random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='hard')
In [6]:
voting_clf.fit(X_train, y_train)
Out[6]:
VotingClassifier(estimators=[('lr', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='warn',
n_jobs=None, penalty='l2', random_state=42, solver='liblinear',
tol=0.0001, verbose=0, warm_start=False)), ('rf', Rando...f',
max_iter=-1, probability=False, random_state=42, shrinking=True,
tol=0.001, verbose=False))],
flatten_transform=None, n_jobs=None, voting='hard', weights=None)
In [7]:
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
LogisticRegression 0.864 RandomForestClassifier 0.872 SVC 0.888 VotingClassifier 0.896
In [8]:
log_clf = LogisticRegression(solver="liblinear", random_state=42)
rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
svm_clf = SVC(gamma="auto", probability=True, random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='soft')
voting_clf.fit(X_train, y_train)
Out[8]:
VotingClassifier(estimators=[('lr', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='warn',
n_jobs=None, penalty='l2', random_state=42, solver='liblinear',
tol=0.0001, verbose=0, warm_start=False)), ('rf', Rando...bf',
max_iter=-1, probability=True, random_state=42, shrinking=True,
tol=0.001, verbose=False))],
flatten_transform=None, n_jobs=None, voting='soft', weights=None)
In [9]:
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
LogisticRegression 0.864 RandomForestClassifier 0.872 SVC 0.888 VotingClassifier 0.912
Bagging ensembles¶
In [10]:
from sklearn.ensemble import BaggingClassifier
from sklearn.tree import DecisionTreeClassifier
bag_clf = BaggingClassifier(
DecisionTreeClassifier(random_state=42), n_estimators=500,
max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
bag_clf.fit(X_train, y_train)
y_pred = bag_clf.predict(X_test)
In [11]:
from sklearn.metrics import accuracy_score
print(accuracy_score(y_test, y_pred))
0.904
In [12]:
tree_clf = DecisionTreeClassifier(random_state=42)
tree_clf.fit(X_train, y_train)
y_pred_tree = tree_clf.predict(X_test)
print(accuracy_score(y_test, y_pred_tree))
0.856
In [13]:
from matplotlib.colors import ListedColormap
def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
x1s = np.linspace(axes[0], axes[1], 100)
x2s = np.linspace(axes[2], axes[3], 100)
x1, x2 = np.meshgrid(x1s, x2s)
X_new = np.c_[x1.ravel(), x2.ravel()]
y_pred = clf.predict(X_new).reshape(x1.shape)
custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
if contour:
custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
plt.axis(axes)
plt.xlabel(r"$x_1$", fontsize=18)
plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
In [14]:
plt.figure(figsize=(11,4))
plt.subplot(121)
plot_decision_boundary(tree_clf, X, y)
plt.title("Decision Tree", fontsize=14)
plt.subplot(122)
plot_decision_boundary(bag_clf, X, y)
plt.title("Decision Trees with Bagging", fontsize=14)
save_fig("decision_tree_without_and_with_bagging_plot")
plt.show()
Saving figure decision_tree_without_and_with_bagging_plot
Random Forests¶
In [15]:
bag_clf = BaggingClassifier(
DecisionTreeClassifier(splitter="random", max_leaf_nodes=16, random_state=42),
n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)
In [16]:
bag_clf.fit(X_train, y_train)
y_pred = bag_clf.predict(X_test)
In [17]:
from sklearn.ensemble import RandomForestClassifier
rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)
rnd_clf.fit(X_train, y_train)
y_pred_rf = rnd_clf.predict(X_test)
In [18]:
np.sum(y_pred == y_pred_rf) / len(y_pred) # almost identical predictions
Out[18]:
0.976
In [19]:
from sklearn.datasets import load_iris
iris = load_iris()
rnd_clf = RandomForestClassifier(n_estimators=500, n_jobs=-1, random_state=42)
rnd_clf.fit(iris["data"], iris["target"])
for name, score in zip(iris["feature_names"], rnd_clf.feature_importances_):
print(name, score)
sepal length (cm) 0.11249225099876374 sepal width (cm) 0.023119288282510326 petal length (cm) 0.44103046436395765 petal width (cm) 0.4233579963547681
In [20]:
rnd_clf.feature_importances_
Out[20]:
array([0.11249225, 0.02311929, 0.44103046, 0.423358 ])
In [21]:
plt.figure(figsize=(6, 4))
for i in range(15):
tree_clf = DecisionTreeClassifier(max_leaf_nodes=16, random_state=42 + i)
indices_with_replacement = np.random.randint(0, len(X_train), len(X_train))
tree_clf.fit(X[indices_with_replacement], y[indices_with_replacement])
plot_decision_boundary(tree_clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.02, contour=False)
plt.show()
Out-of-Bag evaluation¶
In [22]:
bag_clf = BaggingClassifier(
DecisionTreeClassifier(random_state=42), n_estimators=500,
bootstrap=True, n_jobs=-1, oob_score=True, random_state=40)
bag_clf.fit(X_train, y_train)
bag_clf.oob_score_
Out[22]:
0.9013333333333333
In [23]:
bag_clf.oob_decision_function_
Out[23]:
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[0.98235294, 0.01764706],
[1. , 0. ],
[0. , 1. ],
[0.99465241, 0.00534759],
[0. , 1. ],
[0.06043956, 0.93956044],
[0.97619048, 0.02380952],
[1. , 0. ],
[0.03108808, 0.96891192],
[0.57291667, 0.42708333]])
In [24]:
from sklearn.metrics import accuracy_score
y_pred = bag_clf.predict(X_test)
accuracy_score(y_test, y_pred)
Out[24]:
0.912
Feature importance¶
In [25]:
try:
from sklearn.datasets import fetch_openml
mnist = fetch_openml('mnist_784', version=1, as_frame=False)
mnist.target = mnist.target.astype(np.int64)
except ImportError:
from sklearn.datasets import fetch_mldata
mnist = fetch_mldata('MNIST original')
In [26]:
rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
rnd_clf.fit(mnist["data"], mnist["target"])
Out[26]:
RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False)
In [27]:
def plot_digit(data):
image = data.reshape(28, 28)
plt.imshow(image, cmap = mpl.cm.hot,
interpolation="nearest")
plt.axis("off")
In [28]:
plot_digit(rnd_clf.feature_importances_)
cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])
cbar.ax.set_yticklabels(['Not important', 'Very important'])
save_fig("mnist_feature_importance_plot")
plt.show()
Saving figure mnist_feature_importance_plot
AdaBoost¶
In [29]:
from sklearn.ensemble import AdaBoostClassifier
ada_clf = AdaBoostClassifier(
DecisionTreeClassifier(max_depth=1), n_estimators=200,
algorithm="SAMME.R", learning_rate=0.5, random_state=42)
ada_clf.fit(X_train, y_train)
Out[29]:
AdaBoostClassifier(algorithm='SAMME.R',
base_estimator=DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=1,
max_features=None, max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, presort=False, random_state=None,
splitter='best'),
learning_rate=0.5, n_estimators=200, random_state=42)
In [30]:
plot_decision_boundary(ada_clf, X, y)
In [31]:
m = len(X_train)
plt.figure(figsize=(11, 4))
for subplot, learning_rate in ((121, 1), (122, 0.5)):
sample_weights = np.ones(m)
plt.subplot(subplot)
for i in range(5):
svm_clf = SVC(kernel="rbf", C=0.05, gamma="auto", random_state=42)
svm_clf.fit(X_train, y_train, sample_weight=sample_weights)
y_pred = svm_clf.predict(X_train)
sample_weights[y_pred != y_train] *= (1 + learning_rate)
plot_decision_boundary(svm_clf, X, y, alpha=0.2)
plt.title("learning_rate = {}".format(learning_rate), fontsize=16)
if subplot == 121:
plt.text(-0.7, -0.65, "1", fontsize=14)
plt.text(-0.6, -0.10, "2", fontsize=14)
plt.text(-0.5, 0.10, "3", fontsize=14)
plt.text(-0.4, 0.55, "4", fontsize=14)
plt.text(-0.3, 0.90, "5", fontsize=14)
save_fig("boosting_plot")
plt.show()
Saving figure boosting_plot
In [32]:
list(m for m in dir(ada_clf) if not m.startswith("_") and m.endswith("_"))
Out[32]:
['base_estimator_', 'classes_', 'estimator_errors_', 'estimator_weights_', 'estimators_', 'feature_importances_', 'n_classes_']
Gradient Boosting¶
In [33]:
np.random.seed(42)
X = np.random.rand(100, 1) - 0.5
y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)
In [34]:
from sklearn.tree import DecisionTreeRegressor
tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)
tree_reg1.fit(X, y)
Out[34]:
DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=42, splitter='best')
In [35]:
y2 = y - tree_reg1.predict(X)
tree_reg2 = DecisionTreeRegressor(max_depth=2, random_state=42)
tree_reg2.fit(X, y2)
Out[35]:
DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=42, splitter='best')
In [36]:
y3 = y2 - tree_reg2.predict(X)
tree_reg3 = DecisionTreeRegressor(max_depth=2, random_state=42)
tree_reg3.fit(X, y3)
Out[36]:
DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=42, splitter='best')
In [37]:
X_new = np.array([[0.8]])
In [38]:
y_pred = sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))
In [39]:
y_pred
Out[39]:
array([0.75026781])
In [40]:
def plot_predictions(regressors, X, y, axes, label=None, style="r-", data_style="b.", data_label=None):
x1 = np.linspace(axes[0], axes[1], 500)
y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)
plt.plot(X[:, 0], y, data_style, label=data_label)
plt.plot(x1, y_pred, style, linewidth=2, label=label)
if label or data_label:
plt.legend(loc="upper center", fontsize=16)
plt.axis(axes)
plt.figure(figsize=(11,11))
plt.subplot(321)
plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h_1(x_1)$", style="g-", data_label="Training set")
plt.ylabel("$y$", fontsize=16, rotation=0)
plt.title("Residuals and tree predictions", fontsize=16)
plt.subplot(322)
plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1)$", data_label="Training set")
plt.ylabel("$y$", fontsize=16, rotation=0)
plt.title("Ensemble predictions", fontsize=16)
plt.subplot(323)
plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_2(x_1)$", style="g-", data_style="k+", data_label="Residuals")
plt.ylabel("$y - h_1(x_1)$", fontsize=16)
plt.subplot(324)
plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1)$")
plt.ylabel("$y$", fontsize=16, rotation=0)
plt.subplot(325)
plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label="$h_3(x_1)$", style="g-", data_style="k+")
plt.ylabel("$y - h_1(x_1) - h_2(x_1)$", fontsize=16)
plt.xlabel("$x_1$", fontsize=16)
plt.subplot(326)
plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$")
plt.xlabel("$x_1$", fontsize=16)
plt.ylabel("$y$", fontsize=16, rotation=0)
save_fig("gradient_boosting_plot")
plt.show()
Saving figure gradient_boosting_plot
In [41]:
from sklearn.ensemble import GradientBoostingRegressor
gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0, random_state=42)
gbrt.fit(X, y)
Out[41]:
GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=1.0, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=3, n_iter_no_change=None, presort='auto',
random_state=42, subsample=1.0, tol=0.0001,
validation_fraction=0.1, verbose=0, warm_start=False)
In [42]:
gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)
gbrt_slow.fit(X, y)
Out[42]:
GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=200, n_iter_no_change=None, presort='auto',
random_state=42, subsample=1.0, tol=0.0001,
validation_fraction=0.1, verbose=0, warm_start=False)
In [43]:
plt.figure(figsize=(11,4))
plt.subplot(121)
plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label="Ensemble predictions")
plt.title("learning_rate={}, n_estimators={}".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)
plt.subplot(122)
plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])
plt.title("learning_rate={}, n_estimators={}".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)
save_fig("gbrt_learning_rate_plot")
plt.show()
Saving figure gbrt_learning_rate_plot
Gradient Boosting with Early stopping¶
In [44]:
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
X_train, X_val, y_train, y_val = train_test_split(X, y, random_state=49)
gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=120, random_state=42)
gbrt.fit(X_train, y_train)
errors = [mean_squared_error(y_val, y_pred)
for y_pred in gbrt.staged_predict(X_val)]
bst_n_estimators = np.argmin(errors) + 1
gbrt_best = GradientBoostingRegressor(max_depth=2,n_estimators=bst_n_estimators, random_state=42)
gbrt_best.fit(X_train, y_train)
Out[44]:
GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=55, n_iter_no_change=None, presort='auto',
random_state=42, subsample=1.0, tol=0.0001,
validation_fraction=0.1, verbose=0, warm_start=False)
In [45]:
min_error = np.min(errors)
In [46]:
plt.figure(figsize=(11, 4))
plt.subplot(121)
plt.plot(errors, "b.-")
plt.plot([bst_n_estimators, bst_n_estimators], [0, min_error], "k--")
plt.plot([0, 120], [min_error, min_error], "k--")
plt.plot(bst_n_estimators, min_error, "ko")
plt.text(bst_n_estimators, min_error*1.2, "Minimum", ha="center", fontsize=14)
plt.axis([0, 120, 0, 0.01])
plt.xlabel("Number of trees")
plt.title("Validation error", fontsize=14)
plt.subplot(122)
plot_predictions([gbrt_best], X, y, axes=[-0.5, 0.5, -0.1, 0.8])
plt.title("Best model (%d trees)" % bst_n_estimators, fontsize=14)
save_fig("early_stopping_gbrt_plot")
plt.show()
Saving figure early_stopping_gbrt_plot
In [47]:
gbrt = GradientBoostingRegressor(max_depth=2, warm_start=True, random_state=42)
min_val_error = float("inf")
error_going_up = 0
for n_estimators in range(1, 120):
gbrt.n_estimators = n_estimators
gbrt.fit(X_train, y_train)
y_pred = gbrt.predict(X_val)
val_error = mean_squared_error(y_val, y_pred)
if val_error < min_val_error:
min_val_error = val_error
error_going_up = 0
else:
error_going_up += 1
if error_going_up == 5:
break # early stopping
In [48]:
print(gbrt.n_estimators)
61
In [49]:
print("Minimum validation MSE:", min_val_error)
Minimum validation MSE: 0.002712853325235463
Using XGBoost¶
In [50]:
try:
import xgboost
except ImportError as ex:
print("Error: the xgboost library is not installed.")
xgboost = None
In [51]:
if xgboost is not None: # not shown in the book
xgb_reg = xgboost.XGBRegressor(random_state=42)
xgb_reg.fit(X_train, y_train)
y_pred = xgb_reg.predict(X_val)
val_error = mean_squared_error(y_val, y_pred)
print("Validation MSE:", val_error)
Validation MSE: 0.0028512559726563943
In [52]:
if xgboost is not None: # not shown in the book
xgb_reg.fit(X_train, y_train,
eval_set=[(X_val, y_val)], early_stopping_rounds=2)
y_pred = xgb_reg.predict(X_val)
val_error = mean_squared_error(y_val, y_pred)
print("Validation MSE:", val_error)
[0] validation_0-rmse:0.286719 Will train until validation_0-rmse hasn't improved in 2 rounds. [1] validation_0-rmse:0.258221 [2] validation_0-rmse:0.232634 [3] validation_0-rmse:0.210526 [4] validation_0-rmse:0.190232 [5] validation_0-rmse:0.172196 [6] validation_0-rmse:0.156394 [7] validation_0-rmse:0.142241 [8] validation_0-rmse:0.129789 [9] validation_0-rmse:0.118752 [10] validation_0-rmse:0.108388 [11] validation_0-rmse:0.100155 [12] validation_0-rmse:0.09208 [13] validation_0-rmse:0.084791 [14] validation_0-rmse:0.078699 [15] validation_0-rmse:0.073248 [16] validation_0-rmse:0.069391 [17] validation_0-rmse:0.066277 [18] validation_0-rmse:0.063458 [19] validation_0-rmse:0.060326 [20] validation_0-rmse:0.0578 [21] validation_0-rmse:0.055643 [22] validation_0-rmse:0.053943 [23] validation_0-rmse:0.053138 [24] validation_0-rmse:0.052415 [25] validation_0-rmse:0.051821 [26] validation_0-rmse:0.051226 [27] validation_0-rmse:0.051135 [28] validation_0-rmse:0.05091 [29] validation_0-rmse:0.050893 [30] validation_0-rmse:0.050725 [31] validation_0-rmse:0.050471 [32] validation_0-rmse:0.050285 [33] validation_0-rmse:0.050492 [34] validation_0-rmse:0.050348 Stopping. Best iteration: [32] validation_0-rmse:0.050285 Validation MSE: 0.002528626115371327
In [53]:
%timeit xgboost.XGBRegressor().fit(X_train, y_train) if xgboost is not None else None
5.22 ms ± 119 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [54]:
%timeit GradientBoostingRegressor().fit(X_train, y_train)
15.8 ms ± 421 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
Exercise solutions¶
1. to 7.¶
See Appendix A.
8. Voting Classifier¶
Exercise: Load the MNIST data and split it into a training set, a validation set, and a test set (e.g., use 50,000 instances for training, 10,000 for validation, and 10,000 for testing).
The MNIST dataset was loaded earlier.
In [55]:
from sklearn.model_selection import train_test_split
In [56]:
X_train_val, X_test, y_train_val, y_test = train_test_split(
mnist.data, mnist.target, test_size=10000, random_state=42)
X_train, X_val, y_train, y_val = train_test_split(
X_train_val, y_train_val, test_size=10000, random_state=42)
Exercise: Then train various classifiers, such as a Random Forest classifier, an Extra-Trees classifier, and an SVM.
In [57]:
from sklearn.ensemble import RandomForestClassifier, ExtraTreesClassifier
from sklearn.svm import LinearSVC
from sklearn.neural_network import MLPClassifier
In [58]:
random_forest_clf = RandomForestClassifier(n_estimators=10, random_state=42)
extra_trees_clf = ExtraTreesClassifier(n_estimators=10, random_state=42)
svm_clf = LinearSVC(random_state=42)
mlp_clf = MLPClassifier(random_state=42)
In [59]:
estimators = [random_forest_clf, extra_trees_clf, svm_clf, mlp_clf]
for estimator in estimators:
print("Training the", estimator)
estimator.fit(X_train, y_train)
Training the RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False)
Training the ExtraTreesClassifier(bootstrap=False, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False)
Training the LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
intercept_scaling=1, loss='squared_hinge', max_iter=1000,
multi_class='ovr', penalty='l2', random_state=42, tol=0.0001,
verbose=0)
/Users/ageron/.virtualenvs/ml/lib/python3.6/site-packages/sklearn/svm/base.py:922: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations. "the number of iterations.", ConvergenceWarning)
Training the MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,
beta_2=0.999, early_stopping=False, epsilon=1e-08,
hidden_layer_sizes=(100,), learning_rate='constant',
learning_rate_init=0.001, max_iter=200, momentum=0.9,
n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,
random_state=42, shuffle=True, solver='adam', tol=0.0001,
validation_fraction=0.1, verbose=False, warm_start=False)
In [60]:
[estimator.score(X_val, y_val) for estimator in estimators]
Out[60]:
[0.9469, 0.9492, 0.8641, 0.9629]
The linear SVM is far outperformed by the other classifiers. However, let's keep it for now since it may improve the voting classifier's performance.
Exercise: Next, try to combine them into an ensemble that outperforms them all on the validation set, using a soft or hard voting classifier.
In [61]:
from sklearn.ensemble import VotingClassifier
In [62]:
named_estimators = [
("random_forest_clf", random_forest_clf),
("extra_trees_clf", extra_trees_clf),
("svm_clf", svm_clf),
("mlp_clf", mlp_clf),
]
In [63]:
voting_clf = VotingClassifier(named_estimators)
In [64]:
voting_clf.fit(X_train, y_train)
/Users/ageron/.virtualenvs/ml/lib/python3.6/site-packages/sklearn/svm/base.py:922: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations. "the number of iterations.", ConvergenceWarning)
Out[64]:
VotingClassifier(estimators=[('random_forest_clf', RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
...=True, solver='adam', tol=0.0001,
validation_fraction=0.1, verbose=False, warm_start=False))],
flatten_transform=None, n_jobs=None, voting='hard', weights=None)
In [65]:
voting_clf.score(X_val, y_val)
Out[65]:
0.9616
In [66]:
[estimator.score(X_val, y_val) for estimator in voting_clf.estimators_]
Out[66]:
[0.9469, 0.9492, 0.8641, 0.9629]
Let's remove the SVM to see if performance improves. It is possible to remove an estimator by setting it to None using set_params() like this:
In [67]:
voting_clf.set_params(svm_clf=None)
Out[67]:
VotingClassifier(estimators=[('random_forest_clf', RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
...=True, solver='adam', tol=0.0001,
validation_fraction=0.1, verbose=False, warm_start=False))],
flatten_transform=None, n_jobs=None, voting='hard', weights=None)
This updated the list of estimators:
In [68]:
voting_clf.estimators
Out[68]:
[('random_forest_clf',
RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False)),
('extra_trees_clf',
ExtraTreesClassifier(bootstrap=False, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False)),
('svm_clf', None),
('mlp_clf',
MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,
beta_2=0.999, early_stopping=False, epsilon=1e-08,
hidden_layer_sizes=(100,), learning_rate='constant',
learning_rate_init=0.001, max_iter=200, momentum=0.9,
n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,
random_state=42, shuffle=True, solver='adam', tol=0.0001,
validation_fraction=0.1, verbose=False, warm_start=False))]
However, it did not update the list of trained estimators:
In [69]:
voting_clf.estimators_
Out[69]:
[RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False),
ExtraTreesClassifier(bootstrap=False, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,
oob_score=False, random_state=42, verbose=0, warm_start=False),
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
intercept_scaling=1, loss='squared_hinge', max_iter=1000,
multi_class='ovr', penalty='l2', random_state=42, tol=0.0001,
verbose=0),
MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,
beta_2=0.999, early_stopping=False, epsilon=1e-08,
hidden_layer_sizes=(100,), learning_rate='constant',
learning_rate_init=0.001, max_iter=200, momentum=0.9,
n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,
random_state=42, shuffle=True, solver='adam', tol=0.0001,
validation_fraction=0.1, verbose=False, warm_start=False)]
So we can either fit the VotingClassifier again, or just remove the SVM from the list of trained estimators:
In [70]:
del voting_clf.estimators_[2]
Now let's evaluate the VotingClassifier again:
In [71]:
voting_clf.score(X_val, y_val)
Out[71]:
0.9648
A bit better! The SVM was hurting performance. Now let's try using a soft voting classifier. We do not actually need to retrain the classifier, we can just set voting to "soft":
In [72]:
voting_clf.voting = "soft"
In [73]:
voting_clf.score(X_val, y_val)
Out[73]:
0.9703
That's a significant improvement, and it's much better than each of the individual classifiers.
Once you have found one, try it on the test set. How much better does it perform compared to the individual classifiers?
In [74]:
voting_clf.score(X_test, y_test)
Out[74]:
0.9689
In [75]:
[estimator.score(X_test, y_test) for estimator in voting_clf.estimators_]
Out[75]:
[0.9437, 0.9474, 0.9603]
The voting classifier reduced the error rate from about 4.0% for our best model (the MLPClassifier) to just 3.1%. That's about 22.5% less errors, not bad!
9. Stacking Ensemble¶
Exercise: Run the individual classifiers from the previous exercise to make predictions on the validation set, and create a new training set with the resulting predictions: each training instance is a vector containing the set of predictions from all your classifiers for an image, and the target is the image's class. Train a classifier on this new training set.
In [76]:
X_val_predictions = np.empty((len(X_val), len(estimators)), dtype=np.float32)
for index, estimator in enumerate(estimators):
X_val_predictions[:, index] = estimator.predict(X_val)
In [77]:
X_val_predictions
Out[77]:
array([[5., 5., 5., 5.],
[8., 8., 8., 8.],
[2., 2., 2., 2.],
...,
[7., 7., 7., 7.],
[6., 6., 6., 6.],
[7., 7., 7., 7.]], dtype=float32)
In [78]:
rnd_forest_blender = RandomForestClassifier(n_estimators=200, oob_score=True, random_state=42)
rnd_forest_blender.fit(X_val_predictions, y_val)
Out[78]:
RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
max_depth=None, max_features='auto', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, n_estimators=200, n_jobs=None,
oob_score=True, random_state=42, verbose=0, warm_start=False)
In [79]:
rnd_forest_blender.oob_score_
Out[79]:
0.9624
You could fine-tune this blender or try other types of blenders (e.g., an MLPClassifier), then select the best one using cross-validation, as always.
Exercise: Congratulations, you have just trained a blender, and together with the classifiers they form a stacking ensemble! Now let's evaluate the ensemble on the test set. For each image in the test set, make predictions with all your classifiers, then feed the predictions to the blender to get the ensemble's predictions. How does it compare to the voting classifier you trained earlier?
In [80]:
X_test_predictions = np.empty((len(X_test), len(estimators)), dtype=np.float32)
for index, estimator in enumerate(estimators):
X_test_predictions[:, index] = estimator.predict(X_test)
In [81]:
y_pred = rnd_forest_blender.predict(X_test_predictions)
In [82]:
from sklearn.metrics import accuracy_score
In [83]:
accuracy_score(y_test, y_pred)
Out[83]:
0.9601
This stacking ensemble does not perform as well as the soft voting classifier we trained earlier, it's just as good as the best individual classifier.