# SGD: convex loss functions¶

A plot that compares the various convex loss functions supported by SGDClassifier .

import matplotlib.pyplot as plt
import numpy as np

def 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] = 0
return loss

xmin, xmax = -4, 4
xx = np.linspace(xmin, xmax, 100)
lw = 2
plt.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("$L(y=1, f(x))$")
plt.show()


Total running time of the script: (0 minutes 0.099 seconds)

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