148 lines
4.5 KiB
Python
148 lines
4.5 KiB
Python
"""
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================================================
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Varying regularization in Multi-layer Perceptron
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================================================
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A comparison of different values for regularization parameter 'alpha' on
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synthetic datasets. The plot shows that different alphas yield different
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decision functions.
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Alpha is a parameter for regularization term, aka penalty term, that combats
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overfitting by constraining the size of the weights. Increasing alpha may fix
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high variance (a sign of overfitting) by encouraging smaller weights, resulting
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in a decision boundary plot that appears with lesser curvatures.
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Similarly, decreasing alpha may fix high bias (a sign of underfitting) by
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encouraging larger weights, potentially resulting in a more complicated
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decision boundary.
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"""
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# Author: Issam H. Laradji
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# License: BSD 3 clause
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import numpy as np
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from matplotlib import pyplot as plt
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from matplotlib.colors import ListedColormap
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from sklearn.datasets import make_circles, make_classification, make_moons
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from sklearn.model_selection import train_test_split
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from sklearn.neural_network import MLPClassifier
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from sklearn.pipeline import make_pipeline
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from sklearn.preprocessing import StandardScaler
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h = 0.02 # step size in the mesh
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alphas = np.logspace(-1, 1, 5)
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classifiers = []
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names = []
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for alpha in alphas:
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classifiers.append(
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make_pipeline(
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StandardScaler(),
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MLPClassifier(
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solver="lbfgs",
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alpha=alpha,
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random_state=1,
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max_iter=2000,
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early_stopping=True,
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hidden_layer_sizes=[10, 10],
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),
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)
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)
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names.append(f"alpha {alpha:.2f}")
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X, y = make_classification(
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n_features=2, n_redundant=0, n_informative=2, random_state=0, n_clusters_per_class=1
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)
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rng = np.random.RandomState(2)
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X += 2 * rng.uniform(size=X.shape)
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linearly_separable = (X, y)
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datasets = [
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make_moons(noise=0.3, random_state=0),
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make_circles(noise=0.2, factor=0.5, random_state=1),
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linearly_separable,
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]
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figure = plt.figure(figsize=(17, 9))
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i = 1
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# iterate over datasets
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for X, y in datasets:
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# split into training and test part
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X_train, X_test, y_train, y_test = train_test_split(
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X, y, test_size=0.4, random_state=42
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)
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x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
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y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
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xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
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# just plot the dataset first
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cm = plt.cm.RdBu
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cm_bright = ListedColormap(["#FF0000", "#0000FF"])
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ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
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# Plot the training points
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ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
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# and testing points
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ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
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ax.set_xlim(xx.min(), xx.max())
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ax.set_ylim(yy.min(), yy.max())
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ax.set_xticks(())
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ax.set_yticks(())
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i += 1
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# iterate over classifiers
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for name, clf in zip(names, classifiers):
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ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
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clf.fit(X_train, y_train)
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score = clf.score(X_test, y_test)
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# Plot the decision boundary. For that, we will assign a color to each
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# point in the mesh [x_min, x_max] x [y_min, y_max].
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if hasattr(clf, "decision_function"):
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Z = clf.decision_function(np.column_stack([xx.ravel(), yy.ravel()]))
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else:
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Z = clf.predict_proba(np.column_stack([xx.ravel(), yy.ravel()]))[:, 1]
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# Put the result into a color plot
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Z = Z.reshape(xx.shape)
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ax.contourf(xx, yy, Z, cmap=cm, alpha=0.8)
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# Plot also the training points
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ax.scatter(
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X_train[:, 0],
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X_train[:, 1],
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c=y_train,
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cmap=cm_bright,
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edgecolors="black",
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s=25,
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)
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# and testing points
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ax.scatter(
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X_test[:, 0],
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X_test[:, 1],
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c=y_test,
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cmap=cm_bright,
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alpha=0.6,
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edgecolors="black",
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s=25,
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)
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ax.set_xlim(xx.min(), xx.max())
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ax.set_ylim(yy.min(), yy.max())
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ax.set_xticks(())
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ax.set_yticks(())
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ax.set_title(name)
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ax.text(
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xx.max() - 0.3,
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yy.min() + 0.3,
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f"{score:.3f}".lstrip("0"),
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size=15,
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horizontalalignment="right",
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)
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i += 1
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figure.subplots_adjust(left=0.02, right=0.98)
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plt.show()
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