Plot the contours of the three penalties.
All of the above are supported by sklearn.linear_model.stochastic_gradient.
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 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | from __future__ import divisionprint(__doc__)import numpy as npimport matplotlib.pyplot as pltdef l1(xs): return np.array([np.sqrt((1 - np.sqrt(x ** 2.0)) ** 2.0) for x in xs])def l2(xs): return np.array([np.sqrt(1.0 - x ** 2.0) for x in xs])def el(xs, z): return np.array([(2 - 2 * x - 2 * z + 4 * x * z - (4 * z ** 2 - 8 * x * z ** 2 + 8 * x ** 2 * z ** 2 - 16 * x ** 2 * z ** 3 + 8 * x * z ** 3 + 4 * x ** 2 * z ** 4) ** (1. / 2) - 2 * x * z ** 2) / (2 - 4 * z) for x in xs])def cross(ext): plt.plot([-ext, ext], [0, 0], "k-") plt.plot([0, 0], [-ext, ext], "k-")xs = np.linspace(0, 1, 100)alpha = 0.501 # 0.5 division throuh zerocross(1.2)l1_color = "navy"l2_color = "c"elastic_net_color = "darkorange"lw = 2plt.plot(xs, l1(xs), color=l1_color, label="L1", lw=lw)plt.plot(xs, -1.0 * l1(xs), color=l1_color, lw=lw)plt.plot(-1 * xs, l1(xs), color=l1_color, lw=lw)plt.plot(-1 * xs, -1.0 * l1(xs), color=l1_color, lw=lw)plt.plot(xs, l2(xs), color=l2_color, label="L2", lw=lw)plt.plot(xs, -1.0 * l2(xs), color=l2_color, lw=lw)plt.plot(-1 * xs, l2(xs), color=l2_color, lw=lw)plt.plot(-1 * xs, -1.0 * l2(xs), color=l2_color, lw=lw)plt.plot(xs, el(xs, alpha), color=elastic_net_color, label="Elastic Net", lw=lw)plt.plot(xs, -1.0 * el(xs, alpha), color=elastic_net_color, lw=lw)plt.plot(-1 * xs, el(xs, alpha), color=elastic_net_color, lw=lw)plt.plot(-1 * xs, -1.0 * el(xs, alpha), color=elastic_net_color, lw=lw)plt.xlabel(r"$w_0$")plt.ylabel(r"$w_1$")plt.legend()plt.axis("equal")plt.show() |
Total running time of the script: (0 minutes 0.078 seconds)
Download Python source code:
plot_sgd_penalties.py
Download IPython notebook:
plot_sgd_penalties.ipynb
Please login to continue.