50 lines
1.2 KiB
Python
50 lines
1.2 KiB
Python
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"""
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==========================
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SGD: convex loss functions
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==========================
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A plot that compares the various convex loss functions supported by
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:class:`~sklearn.linear_model.SGDClassifier` .
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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def modified_huber_loss(y_true, y_pred):
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z = y_pred * y_true
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loss = -4 * z
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loss[z >= -1] = (1 - z[z >= -1]) ** 2
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loss[z >= 1.0] = 0
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return loss
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xmin, xmax = -4, 4
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xx = np.linspace(xmin, xmax, 100)
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lw = 2
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plt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color="gold", lw=lw, label="Zero-one loss")
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plt.plot(xx, np.where(xx < 1, 1 - xx, 0), color="teal", lw=lw, label="Hinge loss")
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plt.plot(xx, -np.minimum(xx, 0), color="yellowgreen", lw=lw, label="Perceptron loss")
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plt.plot(xx, np.log2(1 + np.exp(-xx)), color="cornflowerblue", lw=lw, label="Log loss")
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plt.plot(
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xx,
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np.where(xx < 1, 1 - xx, 0) ** 2,
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color="orange",
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lw=lw,
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label="Squared hinge loss",
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)
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plt.plot(
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xx,
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modified_huber_loss(xx, 1),
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color="darkorchid",
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lw=lw,
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linestyle="--",
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label="Modified Huber loss",
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)
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plt.ylim((0, 8))
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plt.legend(loc="upper right")
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plt.xlabel(r"Decision function $f(x)$")
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plt.ylabel("$L(y=1, f(x))$")
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plt.show()
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