svm_regression_1d.ipynb

Kernel: Unknown Kernel

# SVM for regression in 1d
# Code is based on
# https://github.com/ageron/handson-ml2/blob/master/05_support_vector_machines.ipynb


import numpy as np
import matplotlib.pyplot as plt

try:
    from sklearn.pipeline import Pipeline
except ModuleNotFoundError:
    %pip install -qq scikit-learn
    from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler

from sklearn.svm import LinearSVR
from sklearn.svm import SVR


def plot_svm_regression(svm_reg, X, y, axes):
    x1s = np.linspace(axes[0], axes[1], 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")
    plt.xlabel(r"$x_1$", fontsize=18)
    # plt.legend(loc="upper left", fontsize=18)
    plt.axis(axes)


np.random.seed(42)
m = 100
X = 2 * np.random.rand(m, 1) - 1
# y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()
y = (0.2 + 0.1 * X + 0.5 * X**2 + 0.1 * X**3 + np.random.randn(m, 1) / 10).ravel()

epsilons = [0.1, 0.05]
eps_names = ["0p1", "0p05"]
for i, eps in enumerate(epsilons):
    # svm_poly_reg1 = SVR(kernel="poly", degree=5, C=1e3, epsilon=eps, gamma="scale")
    # svm_poly_reg2 = SVR(kernel="poly", degree=5, C=1e-3, epsilon=eps, gamma="scale")
    svm_reg1 = SVR(kernel="rbf", gamma=1, C=100, epsilon=eps)
    svm_reg2 = SVR(kernel="rbf", gamma=1, C=0.01, epsilon=eps)

    svm_reg1.fit(X, y)
    svm_reg2.fit(X, y)

    fig, axes = plt.subplots(ncols=2, figsize=(9, 4), sharey=True)
    plt.sca(axes[0])
    plot_svm_regression(svm_reg1, X, y, [-1, 1, 0, 1])
    plt.title(r"$C={}, \epsilon = {}$".format(svm_reg1.C, svm_reg1.epsilon), fontsize=18)
    plt.ylabel(r"$y$", fontsize=18, rotation=0)
    plt.sca(axes[1])
    plot_svm_regression(svm_reg2, X, y, [-1, 1, 0, 1])
    plt.title(r"$C={}, \epsilon = {}$".format(svm_reg2.C, svm_reg2.epsilon), fontsize=18)
    fname = "figures/svm_regression_e{}.pdf".format(eps_names[i])
    plt.savefig(fname, dpi=300)
    plt.show()