SVR

from sklearn.svm import SVR # slow when the training set grows large
from sklearn.svm import LinearSVR # linearly with the size of the training size

import numpy as np

np.random.seed(42)
m = 50
X = 2 * np.random.rand(m, 1)
y = (4 + 3 * X + np.random.randn(m, 1)).ravel()

from sklearn.svm import LinearSVR

svm_reg = LinearSVR(epsilon=1.5, random_state=42)
svm_reg.fit(X, y)

LinearSVR(C=1.0, dual=True, epsilon=1.5, fit_intercept=True,
          intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,
          random_state=42, tol=0.0001, verbose=0)

def find_support_vectors(svm_reg, X, y):
    y_pred = svm_reg.predict(X)
    off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)
    return np.argwhere(off_margin)

svm_reg.support_ = find_support_vectors(svm_reg, X, y)

import matplotlib.pyplot as plt
x1s = np.linspace(0, 2, 100).reshape(100, 1)
y_pred = svm_reg.predict(x1s)
plt.plot(x1s, y_pred, "k-", linewidth=2, label=r"$\hat{y}$")

plt.plot(x1s, y_pred + svm_reg.epsilon, "k--")
plt.plot(x1s, y_pred - svm_reg.epsilon, "k--")
plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')
plt.plot(X, y, "bo")

[<matplotlib.lines.Line2D at 0x1a1ca1b450>]

Reference

• Hands-On Machine Learning with Scikit-Learn, Keras & TensorFlow, 2nd Edition