gradient-boosting/gradient_boost_step_by_step.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "gradient-boost-step-by-step.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "uZCSNIawbQKr"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IfLejin3bVGL"
      },
      "source": [
        "np.random.seed(42)\n",
        "X = np.random.rand(100, 1) - 0.5\n",
        "y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sMHXeN3kbWlw"
      },
      "source": [
        "import pandas as pd"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0jJoztbUbYW7"
      },
      "source": [
        "df = pd.DataFrame()"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHEpruVAbbG3"
      },
      "source": [
        "df['X'] = X.reshape(100)\n",
        "df['y'] = y"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "p4nfMcL1beac",
        "outputId": "14ca3bed-3869-43a5-9784-6c37e9ff5e2b"
      },
      "source": [
        "df"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.125460</td>\n",
              "      <td>0.051573</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.450714</td>\n",
              "      <td>0.594480</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.098658</td>\n",
              "      <td>-0.070178</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.343981</td>\n",
              "      <td>0.343986</td>\n",
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              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "      <td>-0.040675</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>0.022733</td>\n",
              "      <td>-0.002305</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.072459</td>\n",
              "      <td>0.032809</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.474581</td>\n",
              "      <td>0.689516</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.392109</td>\n",
              "      <td>0.502607</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           X         y\n",
              "0  -0.125460  0.051573\n",
              "1   0.450714  0.594480\n",
              "2   0.231994  0.166052\n",
              "3   0.098658 -0.070178\n",
              "4  -0.343981  0.343986\n",
              "..       ...       ...\n",
              "95 -0.006204 -0.040675\n",
              "96  0.022733 -0.002305\n",
              "97 -0.072459  0.032809\n",
              "98 -0.474581  0.689516\n",
              "99 -0.392109  0.502607\n",
              "\n",
              "[100 rows x 2 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "jpHtK8R1BNtN",
        "outputId": "23ba6686-ba3b-472f-b83a-18e10e2e7901"
      },
      "source": [
        "plt.scatter(df['X'],df['y'])\n",
        "plt.title('X vs Y')"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'X vs Y')"
            ]
          },
          "metadata": {},
          "execution_count": 40
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GbiTrFJZbiWY"
      },
      "source": [
        "df['pred1'] = df['y'].mean()"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "8XuACSn-bvev",
        "outputId": "d846369b-013a-4e7f-ed2d-b6cde34a4b8d"
      },
      "source": [
        "df"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>y</th>\n",
              "      <th>pred1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.125460</td>\n",
              "      <td>0.051573</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.450714</td>\n",
              "      <td>0.594480</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.231994</td>\n",
              "      <td>0.166052</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.098658</td>\n",
              "      <td>-0.070178</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.343981</td>\n",
              "      <td>0.343986</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>-0.006204</td>\n",
              "      <td>-0.040675</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>0.022733</td>\n",
              "      <td>-0.002305</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.072459</td>\n",
              "      <td>0.032809</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.474581</td>\n",
              "      <td>0.689516</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.392109</td>\n",
              "      <td>0.502607</td>\n",
              "      <td>0.265458</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           X         y     pred1\n",
              "0  -0.125460  0.051573  0.265458\n",
              "1   0.450714  0.594480  0.265458\n",
              "2   0.231994  0.166052  0.265458\n",
              "3   0.098658 -0.070178  0.265458\n",
              "4  -0.343981  0.343986  0.265458\n",
              "..       ...       ...       ...\n",
              "95 -0.006204 -0.040675  0.265458\n",
              "96  0.022733 -0.002305  0.265458\n",
              "97 -0.072459  0.032809  0.265458\n",
              "98 -0.474581  0.689516  0.265458\n",
              "99 -0.392109  0.502607  0.265458\n",
              "\n",
              "[100 rows x 3 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dUIy2RxobwVr"
      },
      "source": [
        "df['res1'] = df['y'] - df['pred1']"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "38KvYW9Sb5B-",
        "outputId": "a3040a9b-80a8-4587-a0d0-8515b8a9fc8f"
      },
      "source": [
        "df"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>y</th>\n",
              "      <th>pred1</th>\n",
              "      <th>res1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.125460</td>\n",
              "      <td>0.051573</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.213885</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.450714</td>\n",
              "      <td>0.594480</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.329021</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.231994</td>\n",
              "      <td>0.166052</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.099407</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.098658</td>\n",
              "      <td>-0.070178</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.335636</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.343981</td>\n",
              "      <td>0.343986</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.078528</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>-0.006204</td>\n",
              "      <td>-0.040675</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.306133</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>0.022733</td>\n",
              "      <td>-0.002305</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.267763</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.072459</td>\n",
              "      <td>0.032809</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.232650</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.474581</td>\n",
              "      <td>0.689516</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.424057</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.392109</td>\n",
              "      <td>0.502607</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.237148</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 4 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           X         y     pred1      res1\n",
              "0  -0.125460  0.051573  0.265458 -0.213885\n",
              "1   0.450714  0.594480  0.265458  0.329021\n",
              "2   0.231994  0.166052  0.265458 -0.099407\n",
              "3   0.098658 -0.070178  0.265458 -0.335636\n",
              "4  -0.343981  0.343986  0.265458  0.078528\n",
              "..       ...       ...       ...       ...\n",
              "95 -0.006204 -0.040675  0.265458 -0.306133\n",
              "96  0.022733 -0.002305  0.265458 -0.267763\n",
              "97 -0.072459  0.032809  0.265458 -0.232650\n",
              "98 -0.474581  0.689516  0.265458  0.424057\n",
              "99 -0.392109  0.502607  0.265458  0.237148\n",
              "\n",
              "[100 rows x 4 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "38eiADY1BaJO",
        "outputId": "75610e5a-4f41-4aee-eca4-4ab2daa727b4"
      },
      "source": [
        "plt.scatter(df['X'],df['y'])\n",
        "plt.plot(df['X'],df['pred1'],color='red')"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f40df5f2d90>]"
            ]
          },
          "metadata": {},
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w-ocxPrbb5_N"
      },
      "source": [
        "from sklearn.tree import DecisionTreeRegressor"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AHu918SIcS9v"
      },
      "source": [
        "tree1 = DecisionTreeRegressor(max_leaf_nodes=8)"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RsGgZjNAcXz3",
        "outputId": "74ae2153-25a7-44f1-b249-58cb45ea9a24"
      },
      "source": [
        "tree1.fit(df['X'].values.reshape(100,1),df['res1'].values)"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=None,\n",
              "                      max_features=None, max_leaf_nodes=8,\n",
              "                      min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                      min_samples_leaf=1, min_samples_split=2,\n",
              "                      min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                      random_state=None, splitter='best')"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "qah9L_-aJ4_f",
        "outputId": "47802410-9870-4c74-e695-8f38cdef03ce"
      },
      "source": [
        "from sklearn.tree import plot_tree\n",
        "plot_tree(tree1)\n",
        "plt.show()"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IdFPanXnciQ3"
      },
      "source": [
        "# generating X_test\n",
        "X_test = np.linspace(-0.5, 0.5, 500)"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tzu0mK9Xe8dn"
      },
      "source": [
        "y_pred = 0.265458 + tree1.predict(X_test.reshape(500, 1))"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "88mvQQ_UfVBO",
        "outputId": "77c6554f-cbd0-46fe-d6e8-1c18c24c5178"
      },
      "source": [
        "plt.figure(figsize=(14,4))\n",
        "plt.subplot(121)\n",
        "plt.plot(X_test, y_pred, linewidth=2,color='red')\n",
        "plt.scatter(df['X'],df['y'])"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f40df5ee810>"
            ]
          },
          "metadata": {},
          "execution_count": 51
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NXhf93RSfnfO"
      },
      "source": [
        "df['pred2'] = 0.265458 + tree1.predict(df['X'].values.reshape(100,1))"
      ],
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "YKf7AMhwidKy",
        "outputId": "b3e58d2e-6c75-4416-abd3-ffa0c1abcc19"
      },
      "source": [
        "df"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>y</th>\n",
              "      <th>pred1</th>\n",
              "      <th>res1</th>\n",
              "      <th>pred2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.125460</td>\n",
              "      <td>0.051573</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.213885</td>\n",
              "      <td>0.018319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.450714</td>\n",
              "      <td>0.594480</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.329021</td>\n",
              "      <td>0.605884</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.231994</td>\n",
              "      <td>0.166052</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.099407</td>\n",
              "      <td>0.215784</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.098658</td>\n",
              "      <td>-0.070178</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.335636</td>\n",
              "      <td>0.018319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.343981</td>\n",
              "      <td>0.343986</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.078528</td>\n",
              "      <td>0.305964</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>-0.006204</td>\n",
              "      <td>-0.040675</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.306133</td>\n",
              "      <td>0.018319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>0.022733</td>\n",
              "      <td>-0.002305</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.267763</td>\n",
              "      <td>0.018319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.072459</td>\n",
              "      <td>0.032809</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.232650</td>\n",
              "      <td>0.018319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.474581</td>\n",
              "      <td>0.689516</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.424057</td>\n",
              "      <td>0.660912</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.392109</td>\n",
              "      <td>0.502607</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.237148</td>\n",
              "      <td>0.487796</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 5 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           X         y     pred1      res1     pred2\n",
              "0  -0.125460  0.051573  0.265458 -0.213885  0.018319\n",
              "1   0.450714  0.594480  0.265458  0.329021  0.605884\n",
              "2   0.231994  0.166052  0.265458 -0.099407  0.215784\n",
              "3   0.098658 -0.070178  0.265458 -0.335636  0.018319\n",
              "4  -0.343981  0.343986  0.265458  0.078528  0.305964\n",
              "..       ...       ...       ...       ...       ...\n",
              "95 -0.006204 -0.040675  0.265458 -0.306133  0.018319\n",
              "96  0.022733 -0.002305  0.265458 -0.267763  0.018319\n",
              "97 -0.072459  0.032809  0.265458 -0.232650  0.018319\n",
              "98 -0.474581  0.689516  0.265458  0.424057  0.660912\n",
              "99 -0.392109  0.502607  0.265458  0.237148  0.487796\n",
              "\n",
              "[100 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HPRqolQ8ih7t"
      },
      "source": [
        "df['res2'] = df['y'] - df['pred2']"
      ],
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "oFaReIF6i5XV",
        "outputId": "28b9e320-cbb1-44c6-e516-2c1a1389b7ee"
      },
      "source": [
        "df"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>y</th>\n",
              "      <th>pred1</th>\n",
              "      <th>res1</th>\n",
              "      <th>pred2</th>\n",
              "      <th>res2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.125460</td>\n",
              "      <td>0.051573</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.213885</td>\n",
              "      <td>0.018319</td>\n",
              "      <td>0.033254</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.450714</td>\n",
              "      <td>0.594480</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.329021</td>\n",
              "      <td>0.605884</td>\n",
              "      <td>-0.011404</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.231994</td>\n",
              "      <td>0.166052</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.099407</td>\n",
              "      <td>0.215784</td>\n",
              "      <td>-0.049732</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.098658</td>\n",
              "      <td>-0.070178</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.335636</td>\n",
              "      <td>0.018319</td>\n",
              "      <td>-0.088497</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.343981</td>\n",
              "      <td>0.343986</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.078528</td>\n",
              "      <td>0.305964</td>\n",
              "      <td>0.038022</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>-0.006204</td>\n",
              "      <td>-0.040675</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.306133</td>\n",
              "      <td>0.018319</td>\n",
              "      <td>-0.058994</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>0.022733</td>\n",
              "      <td>-0.002305</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.267763</td>\n",
              "      <td>0.018319</td>\n",
              "      <td>-0.020624</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>97</th>\n",
              "      <td>-0.072459</td>\n",
              "      <td>0.032809</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>-0.232650</td>\n",
              "      <td>0.018319</td>\n",
              "      <td>0.014489</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>98</th>\n",
              "      <td>-0.474581</td>\n",
              "      <td>0.689516</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.424057</td>\n",
              "      <td>0.660912</td>\n",
              "      <td>0.028604</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>99</th>\n",
              "      <td>-0.392109</td>\n",
              "      <td>0.502607</td>\n",
              "      <td>0.265458</td>\n",
              "      <td>0.237148</td>\n",
              "      <td>0.487796</td>\n",
              "      <td>0.014810</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>100 rows × 6 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           X         y     pred1      res1     pred2      res2\n",
              "0  -0.125460  0.051573  0.265458 -0.213885  0.018319  0.033254\n",
              "1   0.450714  0.594480  0.265458  0.329021  0.605884 -0.011404\n",
              "2   0.231994  0.166052  0.265458 -0.099407  0.215784 -0.049732\n",
              "3   0.098658 -0.070178  0.265458 -0.335636  0.018319 -0.088497\n",
              "4  -0.343981  0.343986  0.265458  0.078528  0.305964  0.038022\n",
              "..       ...       ...       ...       ...       ...       ...\n",
              "95 -0.006204 -0.040675  0.265458 -0.306133  0.018319 -0.058994\n",
              "96  0.022733 -0.002305  0.265458 -0.267763  0.018319 -0.020624\n",
              "97 -0.072459  0.032809  0.265458 -0.232650  0.018319  0.014489\n",
              "98 -0.474581  0.689516  0.265458  0.424057  0.660912  0.028604\n",
              "99 -0.392109  0.502607  0.265458  0.237148  0.487796  0.014810\n",
              "\n",
              "[100 rows x 6 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6VfcebMZi6I1"
      },
      "source": [
        "tree2 = DecisionTreeRegressor(max_leaf_nodes=8)"
      ],
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4OLND2zyjD51",
        "outputId": "731793fc-ece4-4905-831b-e5fe992d73c8"
      },
      "source": [
        "tree2.fit(df['X'].values.reshape(100,1),df['res2'].values)"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=None,\n",
              "                      max_features=None, max_leaf_nodes=8,\n",
              "                      min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                      min_samples_leaf=1, min_samples_split=2,\n",
              "                      min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                      random_state=None, splitter='best')"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S_enS_gpjOlJ"
      },
      "source": [
        "y_pred = 0.265458 + sum(regressor.predict(X_test.reshape(-1, 1)) for regressor in [tree1,tree2])"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "tNz6xOm0jYa1",
        "outputId": "28dd7644-6415-4d66-aa3e-44ef0f6ba8cb"
      },
      "source": [
        "plt.figure(figsize=(14,4))\n",
        "plt.subplot(121)\n",
        "plt.plot(X_test, y_pred, linewidth=2,color='red')\n",
        "plt.scatter(df['X'],df['y'])\n",
        "plt.title('X vs y')"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'X vs y')"
            ]
          },
          "metadata": {},
          "execution_count": 59
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e744L8_QjbMZ"
      },
      "source": [
        "def gradient_boost(X,y,number,lr,count=1,regs=[],foo=None):\n",
        "\n",
        "  if number == 0:\n",
        "    return \n",
        "  else:\n",
        "    # do gradient boosting\n",
        "\n",
        "    if count > 1:\n",
        "      y = y - regs[-1].predict(X)\n",
        "    else:\n",
        "      foo = y\n",
        "\n",
        "    tree_reg = DecisionTreeRegressor(max_depth=5, random_state=42)\n",
        "    tree_reg.fit(X, y)\n",
        "\n",
        "    regs.append(tree_reg)\n",
        "\n",
        "    x1 = np.linspace(-0.5, 0.5, 500)\n",
        "    y_pred = sum(lr * regressor.predict(x1.reshape(-1, 1)) for regressor in regs)\n",
        "\n",
        "    print(number)\n",
        "    plt.figure()\n",
        "    plt.plot(x1, y_pred, linewidth=2)\n",
        "    plt.plot(X[:, 0], foo,\"r.\")\n",
        "    plt.show()\n",
        "\n",
        "    gradient_boost(X,y,number-1,lr,count+1,regs,foo=foo)\n"
      ],
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "TCWIe2xYCq5a",
        "outputId": "d0bfa589-d143-4ce5-d4a3-0808167dd31f"
      },
      "source": [
        "np.random.seed(42)\n",
        "X = np.random.rand(100, 1) - 0.5\n",
        "y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)\n",
        "gradient_boost(X,y,5,lr=1)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wx8rt90LCtTV"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}