67 lines
1.5 KiB
Python
67 lines
1.5 KiB
Python
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"""
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=========================================================
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Logistic function
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=========================================================
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Shown in the plot is how the logistic regression would, in this
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synthetic dataset, classify values as either 0 or 1,
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i.e. class one or two, using the logistic curve.
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"""
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# Code source: Gael Varoquaux
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# License: BSD 3 clause
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy.special import expit
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from sklearn.linear_model import LinearRegression, LogisticRegression
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# Generate a toy dataset, it's just a straight line with some Gaussian noise:
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xmin, xmax = -5, 5
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n_samples = 100
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np.random.seed(0)
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X = np.random.normal(size=n_samples)
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y = (X > 0).astype(float)
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X[X > 0] *= 4
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X += 0.3 * np.random.normal(size=n_samples)
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X = X[:, np.newaxis]
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# Fit the classifier
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clf = LogisticRegression(C=1e5)
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clf.fit(X, y)
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# and plot the result
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plt.figure(1, figsize=(4, 3))
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plt.clf()
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plt.scatter(X.ravel(), y, label="example data", color="black", zorder=20)
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X_test = np.linspace(-5, 10, 300)
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loss = expit(X_test * clf.coef_ + clf.intercept_).ravel()
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plt.plot(X_test, loss, label="Logistic Regression Model", color="red", linewidth=3)
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ols = LinearRegression()
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ols.fit(X, y)
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plt.plot(
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X_test,
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ols.coef_ * X_test + ols.intercept_,
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label="Linear Regression Model",
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linewidth=1,
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)
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plt.axhline(0.5, color=".5")
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plt.ylabel("y")
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plt.xlabel("X")
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plt.xticks(range(-5, 10))
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plt.yticks([0, 0.5, 1])
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plt.ylim(-0.25, 1.25)
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plt.xlim(-4, 10)
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plt.legend(
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loc="lower right",
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fontsize="small",
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)
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plt.tight_layout()
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plt.show()
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