A plot that compares the various convex loss functions supported by sklearn.linear_model.SGDClassifier .
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | print(__doc__)import numpy as npimport matplotlib.pyplot as pltdef modified_huber_loss(y_true, y_pred): z = y_pred * y_true loss = -4 * z loss[z >= -1] = (1 - z[z >= -1]) ** 2 loss[z >= 1.] = 0 return lossxmin, xmax = -4, 4xx = np.linspace(xmin, xmax, 100)lw = 2plt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color='gold', lw=lw, label="Zero-one loss")plt.plot(xx, np.where(xx < 1, 1 - xx, 0), color='teal', lw=lw, label="Hinge loss")plt.plot(xx, -np.minimum(xx, 0), color='yellowgreen', lw=lw, label="Perceptron loss")plt.plot(xx, np.log2(1 + np.exp(-xx)), color='cornflowerblue', lw=lw, label="Log loss")plt.plot(xx, np.where(xx < 1, 1 - xx, 0) ** 2, color='orange', lw=lw, label="Squared hinge loss")plt.plot(xx, modified_huber_loss(xx, 1), color='darkorchid', lw=lw, linestyle='--', label="Modified Huber loss")plt.ylim((0, 8))plt.legend(loc="upper right")plt.xlabel(r"Decision function $f(x)$")plt.ylabel("$L(y, f(x))$")plt.show() |
Total running time of the script: (0 minutes 0.069 seconds)
Download Python source code:
plot_sgd_loss_functions.py
Download IPython notebook:
plot_sgd_loss_functions.ipynb
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