57604.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "57604.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bmreiniger/datascience.stackexchange/blob/master/57604.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n_KNUZ9yMweM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[1, 1],[5**0.5, -5**0.5]])\n",
        "y = np.array([3,-5**0.5])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OAtYBmkaS2ww",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.linear_model import ElasticNet\n",
        "import matplotlib.pyplot as plt\n",
        "import itertools\n",
        "\n",
        "delta = 0.01\n",
        "xrange = np.arange(-1, 2.5, delta)\n",
        "yrange = np.arange(-1, 2.5, delta)\n",
        "xs, ys = np.meshgrid(xrange,yrange)\n",
        "\n",
        "def loss(a,b):\n",
        "  \"\"\"Unregularized loss, that is.\"\"\"\n",
        "  return np.linalg.norm(y.T-X@(np.array([a,b]).T))\n",
        "\n",
        "\n",
        "def plot_reg(reg_alpha, reg_lambda):\n",
        "  alpha = reg_alpha+reg_lambda\n",
        "  l1_ratio = reg_alpha/(reg_alpha+reg_lambda) if alpha > 0 else 0\n",
        "  model = ElasticNet(alpha=alpha, l1_ratio=l1_ratio, fit_intercept=False)\n",
        "  model.fit(X,y)\n",
        "  print(model.coef_.round(8))\n",
        "  ah, bh = model.coef_\n",
        "  opt_loss = loss(*model.coef_)\n",
        "  \n",
        "  plt.contour(xs, ys, np.array([[loss(a,b) for a in xrange] for b in yrange]), [opt_loss])\n",
        "  plt.plot([1],[2], '+')\n",
        "  plt.contourf(xs, ys, l1_ratio*(abs(xs)+abs(ys))+(1-l1_ratio)*(xs**2+ys**2), \n",
        "                    [0,l1_ratio*(abs(ah)+abs(bh))+(1-l1_ratio)*(ah**2+bh**2)])\n",
        "  plt.gca().set_aspect('equal', adjustable='box')\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t3yAVcUXTvyX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        },
        "outputId": "016a223d-b3c6-4d7e-84f4-6e79fb54faa0"
      },
      "source": [
        "plot_reg(0,0)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:19: UserWarning: With alpha=0, this algorithm does not converge well. You are advised to use the LinearRegression estimator\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/coordinate_descent.py:475: UserWarning: Coordinate descent with no regularization may lead to unexpected results and is discouraged.\n",
            "  positive)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[0.9999208 1.9999472]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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4TzcEviXJpgWOL4dxv/L/tiT3J/lWkjcvR4HuFvKtwN3zDo372hc11OPRQzXK18EPtf7g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\n9P+helIJSIbIHwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L94NZwNDS9IE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "f7c5edf0-a7f5-4557-fe80-fa4975908efb"
      },
      "source": [
        "plot_reg(0,5)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 4.999999999999998, tolerance: 0.0014\n",
            "  positive)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[0.  0.5]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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C+DcmU61xZQYv7q/Pj01Adz2SsWPFHgC9i1U6Z4xh+sDZzBwyjzqta9BvRo8MN07CHQ2K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\nW10AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5LckPOZmTs_-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "acf34b49-27cf-4fb0-ce8f-29c70dd950f8"
      },
      "source": [
        "plot_reg(0,10)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 5.757575757575756, tolerance: 0.0014\n",
            "  positive)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[-0.03030303  0.3030303 ]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wrTFmj4iMEpFnHM1mAoVFJBx4E/jXIdSsTAe5Vb7OkttbGWNCgJBb3hue4vlN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\nyikNCqWUUxoUSimn/h9WmJMjF0aq1QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FixVemp4TyML",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "eddfaecc-6680-4349-cc0a-4aa849f550e6"
      },
      "source": [
        "plot_reg(0,1)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 2.6666666666666665, tolerance: 0.0014\n",
            "  positive)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "[0.33333333 1.16666667]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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69H4vliqXXOB2WSYbthPoU9e1vpbjR/9g9bx1bpeSY0cPxvNW7Hv0qN+P/T8f5F8TevD6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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4JX7ts1Q17Jv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "0cf46c1d-14df-465c-e064-1964780ce770"
      },
      "source": [
        "plot_reg(1,0)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0. 1.]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0JJRbRGMfRQVgR7rHCaHn1DnSB4OGhHKT3FlNICLzgbIZvNQ3dEVzx4hId6B7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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fyH-s6hV19rN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "13afa8b1-e549-489f-c27c-0dc2905264ed"
      },
      "source": [
        "plot_reg(2,0)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.         0.66666667]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/Fph95QIiUlhE8rruhwC1gB0ethuQrOrcGhLK1zwNio+AB0VkD/CA6zEiEiki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\n0qBQSrmlQaGUckuDQinl1v8B0+zsf+CK0IQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ARGaSrEZ2Bou",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "259c564c-aade-4ac5-a699-dd118187937b"
      },
      "source": [
        "plot_reg(0.5,0)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.4999109 1.4999406]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Z2QznXHbS5YIIhZnVA9Y455yZnQy8TOEeRqmDBx2KjI9EMVVXbaPOu6uptWAze3bvoUq1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\ngV3pMFi90gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xe7zVrYwRtCe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "51033eeb-feaa-4d96-8bda-c428484840da"
      },
      "source": [
        "plot_reg(1,2)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.  0.6]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Go+0p5S7iyqTiIrIXaGiMOSUiwcBqY0wFJ39nOrDYGLPgTsuFhISYiIiIDNfm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\nSjn1f+CZ0uLh73pIAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}