update week 45
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mhjensen
@@ -1148,184 +1148,6 @@ the context of bagging classification trees, we can add up the total
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amount that the Gini index is decreased by splits over a given
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predictor, averaged over all $B$ trees.
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!split
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===== Simple Voting Example, head or tail =====
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!bc pycod
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heads_proba = 0.51
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coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
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cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
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plt.figure(figsize=(8,3.5))
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plt.plot(cumulative_heads_ratio)
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plt.plot([0, 10000], [0.51, 0.51], "k--", linewidth=2, label="51%")
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plt.plot([0, 10000], [0.5, 0.5], "k-", label="50%")
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plt.xlabel("Number of coin tosses")
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plt.ylabel("Heads ratio")
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plt.legend(loc="lower right")
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plt.axis([0, 10000, 0.42, 0.58])
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save_fig("votingsimple")
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plt.show()
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!ec
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!split
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===== Using the Voting Classifier =====
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!bc pycod
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from sklearn.model_selection import train_test_split
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from sklearn.datasets import make_moons
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X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
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X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
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from sklearn.ensemble import RandomForestClassifier
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from sklearn.ensemble import VotingClassifier
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from sklearn.linear_model import LogisticRegression
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from sklearn.svm import SVC
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log_clf = LogisticRegression(solver="liblinear", random_state=42)
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rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
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svm_clf = SVC(gamma="auto", random_state=42)
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voting_clf = VotingClassifier(
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estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
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voting='hard')
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voting_clf.fit(X_train, y_train)
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from sklearn.metrics import accuracy_score
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for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
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clf.fit(X_train, y_train)
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y_pred = clf.predict(X_test)
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print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
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log_clf = LogisticRegression(solver="liblinear", random_state=42)
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rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
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svm_clf = SVC(gamma="auto", probability=True, random_state=42)
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voting_clf = VotingClassifier(
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estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
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voting='soft')
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voting_clf.fit(X_train, y_train)
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from sklearn.metrics import accuracy_score
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for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
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clf.fit(X_train, y_train)
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y_pred = clf.predict(X_test)
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print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
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!ec
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!split
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===== Please, not the moons again! Voting and Bagging =====
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!bc pycod
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from sklearn.model_selection import train_test_split
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from sklearn.datasets import make_moons
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X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
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X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
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from sklearn.ensemble import RandomForestClassifier
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from sklearn.ensemble import VotingClassifier
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from sklearn.linear_model import LogisticRegression
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from sklearn.svm import SVC
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log_clf = LogisticRegression(random_state=42)
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rnd_clf = RandomForestClassifier(random_state=42)
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svm_clf = SVC(random_state=42)
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voting_clf = VotingClassifier(
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estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
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voting='hard')
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voting_clf.fit(X_train, y_train)
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!ec
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!bc pycod
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from sklearn.metrics import accuracy_score
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for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
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clf.fit(X_train, y_train)
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y_pred = clf.predict(X_test)
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print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
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!ec
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!bc pycod
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log_clf = LogisticRegression(random_state=42)
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rnd_clf = RandomForestClassifier(random_state=42)
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svm_clf = SVC(probability=True, random_state=42)
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voting_clf = VotingClassifier(
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estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
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voting='soft')
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voting_clf.fit(X_train, y_train)
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!ec
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!bc pycod
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from sklearn.metrics import accuracy_score
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for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
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clf.fit(X_train, y_train)
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y_pred = clf.predict(X_test)
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print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
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!ec
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!split
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===== Bagging Examples =====
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!bc pycod
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from sklearn.ensemble import BaggingClassifier
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from sklearn.tree import DecisionTreeClassifier
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bag_clf = BaggingClassifier(
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DecisionTreeClassifier(random_state=42), n_estimators=500,
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max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
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bag_clf.fit(X_train, y_train)
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y_pred = bag_clf.predict(X_test)
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!ec
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!bc pycod
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from sklearn.metrics import accuracy_score
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print(accuracy_score(y_test, y_pred))
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!ec
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!bc pycod
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tree_clf = DecisionTreeClassifier(random_state=42)
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tree_clf.fit(X_train, y_train)
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y_pred_tree = tree_clf.predict(X_test)
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print(accuracy_score(y_test, y_pred_tree))
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!ec
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!bc pycod
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from matplotlib.colors import ListedColormap
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def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
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x1s = np.linspace(axes[0], axes[1], 100)
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x2s = np.linspace(axes[2], axes[3], 100)
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x1, x2 = np.meshgrid(x1s, x2s)
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X_new = np.c_[x1.ravel(), x2.ravel()]
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y_pred = clf.predict(X_new).reshape(x1.shape)
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custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
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plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
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if contour:
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custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
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plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
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plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
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plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
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plt.axis(axes)
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plt.xlabel(r"$x_1$", fontsize=18)
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plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
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plt.figure(figsize=(11,4))
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plt.subplot(121)
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plot_decision_boundary(tree_clf, X, y)
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plt.title("Decision Tree", fontsize=14)
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plt.subplot(122)
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plot_decision_boundary(bag_clf, X, y)
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plt.title("Decision Trees with Bagging", fontsize=14)
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save_fig("baggingtree")
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plt.show()
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!ec
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!split
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@@ -1342,9 +1164,9 @@ from sklearn.pipeline import make_pipeline
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from sklearn.utils import resample
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from sklearn.tree import DecisionTreeRegressor
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n = 100
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n = 1000
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n_boostraps = 100
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maxdepth = 8
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maxdepth = 10
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# Make data set.
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x = np.linspace(-3, 3, n).reshape(-1, 1)
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@@ -1355,23 +1177,17 @@ variance = np.zeros(maxdepth)
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polydegree = np.zeros(maxdepth)
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X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
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from sklearn.preprocessing import StandardScaler
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scaler = StandardScaler()
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scaler.fit(X_train)
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X_train_scaled = scaler.transform(X_train)
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X_test_scaled = scaler.transform(X_test)
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# we produce a simple tree first as benchmark
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# we produce a simple tree first as benchmark, no scaling
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simpletree = DecisionTreeRegressor(max_depth=3)
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simpletree.fit(X_train_scaled, y_train)
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simpleprediction = simpletree.predict(X_test_scaled)
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simpletree.fit(X_train, y_train)
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simpleprediction = simpletree.predict(X_test)
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for degree in range(1,maxdepth):
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model = DecisionTreeRegressor(max_depth=degree)
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y_pred = np.empty((y_test.shape[0], n_boostraps))
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for i in range(n_boostraps):
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x_, y_ = resample(X_train_scaled, y_train)
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x_, y_ = resample(X_train, y_train)
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model.fit(x_, y_)
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y_pred[:, i] = model.predict(X_test_scaled)#.ravel()
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y_pred[:, i] = model.predict(X_test)#.ravel()
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polydegree[degree] = degree
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error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )
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@@ -1383,7 +1199,7 @@ for degree in range(1,maxdepth):
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print('Var:', variance[degree])
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print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
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mse_simpletree= np.mean( np.mean((y_test - simpleprediction)**2)
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mse_simpletree= np.mean( np.mean((y_test - simpleprediction)**2))
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print(mse_simpletree)
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plt.xlim(1,maxdepth)
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plt.plot(polydegree, error, label='MSE')
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