Ridge_Coefficients.ipynb

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   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "\n",
    "# X is the 10x10 Hilbert matrix\n",
    "X = 1. / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])\n",
    "y = np.ones(10)\n",
    "\n",
    "###############################################################################\n",
    "# Compute paths\n",
    "\n",
    "n_alphas = 200\n",
    "alphas = np.logspace(-10, -2, n_alphas)\n",
    "clf = linear_model.Ridge(fit_intercept=False)\n",
    "\n",
    "coefs = []\n",
    "for i,a in enumerate(alphas):\n",
    "    clf.set_params(alpha=a)\n",
    "    clf.fit(X, y)\n",
    "    print(i)\n",
    "    coefs.append(clf.coef_)\n",
    "\n",
    "###############################################################################\n",
    "# Display results\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_color_cycle(['b', 'r', 'g', 'c', 'k', 'y', 'm'])\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
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