Random_Forests_Limitations.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python",
      "version": "3.6.5",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "kernel_info": {
      "name": "python3"
    },
    "nteract": {
      "version": "0.14.5"
    },
    "colab": {
      "name": "Random_Forests_Limitations_v0.1.ipynb",
      "provenance": []
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:25.760406Z",
          "start_time": "2019-08-29T10:55:19.582404Z"
        },
        "id": "HuWovt4qFDHK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.ensemble import RandomForestRegressor"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1gCrtgTXFDHN",
        "colab_type": "text"
      },
      "source": [
        "## Random forests: Limitations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qGM1C0BgFDHN",
        "colab_type": "text"
      },
      "source": [
        "[Alonso Silva](http://www.dim.uchile.cl/~alsilva/) [(@alonsosilva)](https://twitter.com/alonsosilva) | 2019/09/05"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yiTo01zlFDHO",
        "colab_type": "text"
      },
      "source": [
        "The purpose of this notebook is to show that random forests cannot extrapolate.\n",
        "\n",
        "First, consider a dependent variable $y$ that depends linearly on $x$ plus some random noise, that is:\n",
        "$$\n",
        "y = x +\\varepsilon\\quad\\textrm{where}\\quad\\varepsilon\\sim\\mathcal{N}(0,1).\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:25.809445Z",
          "start_time": "2019-08-29T10:55:25.764949Z"
        },
        "id": "iIVhXyTDFDHP",
        "colab_type": "code",
        "outputId": "70b90c95-9b21-48fd-8a38-c0a917bd192a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        }
      },
      "source": [
        "np.random.seed(42)\n",
        "x = np.linspace(0,10)\n",
        "y = x + np.random.normal(0, 1, x.shape)\n",
        "\n",
        "plt.figure(figsize=(6, 6))\n",
        "plt.scatter(x,y)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Dsxynq3IMTKBkBEGLdu8Y16E92zU+OiJLGh8d0aE925NOd+R4951jYAIlY42gZbk1NNs8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\nAIDKEQQAUDmCAAAqRxAAQOUIAgCo3P8D+I2fjCBC770AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJoPSCegFDHS",
        "colab_type": "text"
      },
      "source": [
        "There are $50$ observations (the default value in [numpy.linspace](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html))\n",
        "\n",
        "Split the train/valid datasets: for train the first 40 points, and for valid the last 10 points"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:26.296236Z",
          "start_time": "2019-08-29T10:55:26.281066Z"
        },
        "id": "rWaP0UabFDHT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x1 = x[...,None] # we add a dimension so that RandomForestRegressor doesn't complain"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:26.312861Z",
          "start_time": "2019-08-29T10:55:26.297625Z"
        },
        "id": "rSadsy62FDHV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_trn, x_val = x1[:40], x1[40:]\n",
        "y_trn, y_val = y[:40], y[40:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:26.352878Z",
          "start_time": "2019-08-29T10:55:26.314300Z"
        },
        "scrolled": true,
        "id": "92DVR_V4FDHa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "m = RandomForestRegressor(n_estimators=100).fit(x_trn, y_trn)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aguUUl8CFDHc",
        "colab_type": "text"
      },
      "source": [
        "Function to plot predictions vs actuals"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:26.494639Z",
          "start_time": "2019-08-29T10:55:26.354566Z"
        },
        "scrolled": true,
        "id": "7w5DC201FDHd",
        "colab_type": "code",
        "outputId": "05e592a8-184d-478d-f185-2e2198aaa37b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        }
      },
      "source": [
        "plt.figure(figsize=(6, 6))\n",
        "plt.xlabel('true target')\n",
        "plt.ylabel('prediction')\n",
        "plt.xlim(-1, 9)\n",
        "plt.ylim(-1, 9)\n",
        "plt.plot(np.linspace(-1,9), np.linspace(-1,9))\n",
        "plt.scatter(y_trn, m.predict(x_trn))\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mg9yzeC0Du7RmwZR4YptH+12SBIHutBWRs7yx4QD3L01jSLc2zJsUT5uYJn6XJEGiwBeR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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OuUhNOV6FDHf",
        "colab_type": "text"
      },
      "source": [
        "In the training set, the predictions work well (as expected)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-08-29T10:55:26.661377Z",
          "start_time": "2019-08-29T10:55:26.496083Z"
        },
        "id": "2OmmTz9SFDHf",
        "colab_type": "code",
        "outputId": "e6b485ff-284f-4fbc-ddd2-219b1f2fb7ee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        }
      },
      "source": [
        "plt.figure(figsize=(6, 6))\n",
        "plt.xlabel('true target')\n",
        "plt.ylabel('prediction')\n",
        "plt.xlim(7, 10)\n",
        "plt.ylim(7, 10)\n",
        "plt.plot(np.linspace(7,10), np.linspace(7,10))\n",
        "plt.scatter(y_val, m.predict(x_val))\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ercxv9jNm+gKa1q3OnHGJtKxfw+tIIlFLZSJh6csN+xg3I4uW9auTlpJEs7rV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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NEsNLG14FDHh",
        "colab_type": "text"
      },
      "source": [
        "Holy cow! In the test set, the predictions are completely off!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sthg5LwoFDHi",
        "colab_type": "text"
      },
      "source": [
        "Sources:\n",
        "\n",
        "This example is taken from Lesson6 of [FastAI ML](http://course18.fast.ai/ml.html). To check it out, see this [direct link](https://youtu.be/BFIYUvBRTpE?t=5086)."
      ]
    }
  ]
}