cohorts/2022/06-trees/homework_6.ipynb

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      "source": [
        "**HOMEWORK**  \n",
        "\n",
        "The goal of this homework is to create a regression model for predicting housing prices (column 'median_house_value').  \n",
        "\n",
        "In this homework we'll again use the California Housing Prices dataset - the same one we used in homework 2 and 3.\n",
        "\n",
        "You can take it from [Kaggle](https://www.kaggle.com/datasets/camnugent/california-housing-prices) or download using wget link mentioned below:\n",
        "\n",
        "```\n",
        "wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv\n",
        "\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "nLosiCNJUjDM"
      },
      "outputs": [],
      "source": [
        "#@ IMPORTING LIBRARIES AND DEPENDENCIES:\n",
        "import re\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import xgboost as xgb\n",
        "import matplotlib.pyplot as plt\n",
        "from tqdm.auto import tqdm\n",
        "from sklearn.tree import DecisionTreeRegressor\n",
        "from sklearn.tree import export_text\n",
        "from sklearn.feature_extraction import DictVectorizer\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.ensemble import RandomForestRegressor\n",
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4Psk224nnyIF",
        "outputId": "ae1fa704-079b-49ac-f3b2-71818155798f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "--2022-10-08 09:15:25--  https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.111.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 1423529 (1.4M) [text/plain]\n",
            "Saving to: ‘housing.csv.4’\n",
            "\n",
            "\rhousing.csv.4         0%[                    ]       0  --.-KB/s               \rhousing.csv.4       100%[===================>]   1.36M  --.-KB/s    in 0.05s   \n",
            "\n",
            "2022-10-08 09:15:26 (24.7 MB/s) - ‘housing.csv.4’ saved [1423529/1423529]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "#@ DOWNLOADING THE DATASET: UNCOMMENT BELOW:\n",
        "!wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "492Hn6-3n08G"
      },
      "outputs": [],
      "source": [
        "#@ READING DATASET:\n",
        "PATH = \"./housing.csv\"\n",
        "select_cols = [\"longitude\", \"latitude\", \"housing_median_age\", \"total_rooms\", \"total_bedrooms\", \"population\", \"households\", \n",
        "               \"median_income\", \"median_house_value\", \"ocean_proximity\"]\n",
        "df = pd.read_csv(PATH, usecols=select_cols)\n",
        "df.total_bedrooms = df.total_bedrooms.fillna(0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OqXppJ_Ro0H0"
      },
      "source": [
        "- Apply the log transform to `median_house_value`. \n",
        "- Do train/validation/test split with 60%/20%/20% distribution.\n",
        "- Use the `train_test_split` function and set the `random_state parameter` to 1."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "W1MmdcRDpHS1"
      },
      "outputs": [],
      "source": [
        "#@ SPLITTING THE DATASET FOR TRAINING AND TEST:\n",
        "df_full_train, df_test = train_test_split(df, test_size=0.2, random_state=1)\n",
        "df_train, df_val = train_test_split(df_full_train, test_size=0.25, random_state=1)\n",
        "\n",
        "df_train = df_train.reset_index(drop=True)\n",
        "df_val = df_val.reset_index(drop=True)\n",
        "df_test = df_test.reset_index(drop=True)\n",
        "\n",
        "y_train = np.log1p(df_train.median_house_value.values)\n",
        "y_val = np.log1p(df_val.median_house_value.values)\n",
        "y_test = np.log1p(df_test.median_house_value.values)\n",
        "\n",
        "del df_train['median_house_value']\n",
        "del df_val['median_house_value']\n",
        "del df_test['median_house_value']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5VKq8FX7qIVM"
      },
      "source": [
        "- We will use `DictVectorizer` to turn train and validation into matrices."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "mwcyh9FPqP2-"
      },
      "outputs": [],
      "source": [
        "#@ INITIALIZING TRAINING FEATURES:\n",
        "features = [\"longitude\", \"latitude\", \"housing_median_age\", \"total_rooms\", \"total_bedrooms\", \"population\", \"households\", \n",
        "               \"median_income\", \"ocean_proximity\"]\n",
        "train_dicts = df_train[features].to_dict(orient='records')\n",
        "val_dicts = df_val[features].to_dict(orient='records')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "WnfFrWe9qtuc"
      },
      "outputs": [],
      "source": [
        "#@ IMPLEMENTATION OF DICTVECTORIZER:\n",
        "dv = DictVectorizer(sparse=False)\n",
        "X_train = dv.fit_transform(train_dicts)\n",
        "X_val = dv.transform(val_dicts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qvxmhaD5hmAK"
      },
      "source": [
        "**Question 1**\n",
        "\n",
        "Let's train a decision tree regressor to predict the `median_house_value` variable.\n",
        "\n",
        "Train a model with `max_depth=1`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cqBcSbpIq7kJ",
        "outputId": "bf5e44a7-b5a4-4802-bc4d-3e484994edb3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "DecisionTreeRegressor(max_depth=1)"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ TRAINING THE REGRESSION MODEL:\n",
        "dt = DecisionTreeRegressor(max_depth=1)\n",
        "dt.fit(X_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sLAnqRwuikqQ",
        "outputId": "0a674274-5dbb-4008-9761-fea8fb003629"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "|--- ocean_proximity=INLAND <= 0.50\n",
            "|   |--- value: [12.31]\n",
            "|--- ocean_proximity=INLAND >  0.50\n",
            "|   |--- value: [11.61]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "#@ INSPECTION:\n",
        "print(export_text(dt, feature_names=dv.feature_names_))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JNBm-qeRp6aZ"
      },
      "source": [
        "- Which feature is used for splitting the data?\n",
        "\n",
        "- Answer: `ocean_proximity=INLAND`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xhnbdy-CqQoB"
      },
      "source": [
        "**Question 2**\n",
        "\n",
        "Train a random forest model with these parameters:\n",
        "\n",
        "- `n_estimators=10`  \n",
        "- `random_state=1`  \n",
        "- `n_jobs=-1` (optional-to make training faster)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2w-YSGYMisFt",
        "outputId": "2a156b02-7dd2-4bb4-cb10-8b7747d44bb6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "RandomForestRegressor(n_estimators=10, n_jobs=-1, random_state=1)"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ TRAINING RANDOM FOREST MODEL:\n",
        "rf = RandomForestRegressor(n_estimators=10, random_state=1, n_jobs=-1)\n",
        "rf.fit(X_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jCxUAO2Rq1Ps",
        "outputId": "4b03b32f-198d-46b1-fb41-e27e868edf9f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.24566012875324933"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ CALCULATING MEAN SQUARED ERROR:\n",
        "y_pred = rf.predict(X_val)\n",
        "np.sqrt(mean_squared_error(y_val, y_pred))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jfcDllHxrTqu"
      },
      "source": [
        "- What's the RMSE of this model on validation?\n",
        "\n",
        "- Answer: 0.25"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7K69bFSrg_V"
      },
      "source": [
        "**Question 3**\n",
        "\n",
        "Now, let's experiment with the `n_estimators` parameter.\n",
        "\n",
        "- Try different values of this parameter from 10 to 200 with step 10.\n",
        "- Set `random_state` to 1.\n",
        "- Evaluate the model on the validation dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
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        "colab": {
          "base_uri": "https://localhost:8080/",
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        "id": "-oUFCQwOrQNN",
        "outputId": "b1168dae-e700-4297-e34a-e8d226e3f3a4"
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      "outputs": [
        {
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              "  0%|          | 0/20 [00:00<?, ?it/s]"
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      ],
      "source": [
        "#@ TRAINING THE RANDOM FOREST MODEL:\n",
        "scores = []\n",
        "\n",
        "for n in tqdm(range(10, 201, 10)):\n",
        "    rf = RandomForestRegressor(n_estimators=n, random_state=1, n_jobs=-1)\n",
        "    rf.fit(X_train, y_train)\n",
        "    \n",
        "    y_pred = rf.predict(X_val)\n",
        "    score = np.sqrt(mean_squared_error(y_val, y_pred))\n",
        "    \n",
        "    scores.append((n, score))\n",
        "\n",
        "df_scores = pd.DataFrame(scores, columns=['n_estimators', 'rmse'])"
      ]
    },
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      "cell_type": "code",
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        "colab": {
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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ INSPECTING THE RMSE SCORES:\n",
        "plt.plot(df_scores.n_estimators, df_scores.rmse.round(3))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAXZcW3AuC-d"
      },
      "source": [
        "- After which value of `n_estimators` does RMSE stop improving?\n",
        "\n",
        "- Answer: 70"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "e86d0336042e4d13ab7580faf05382a0",
            "f18a93e874be419c92d0a037a3c5600e",
            "8be473b1becd48a8a2c544f4e0424879",
            "d6e432d4a16d4ff392d4dc903279edb7",
            "be00ae7ff4764cd1be7ceee608421bcd",
            "9166c89c2c5e40ed8cc2f5b97fff93eb",
            "f8986d027aeb4c179bf7693af51b49bc",
            "d30991a5930e4100a118f67a32e45675",
            "99bfd95a9c194f3b968ca813d4233f4e",
            "c3dae3f105b5453abcb2cb0043e7e5ec",
            "522742d7234447619f84116446e74483"
          ]
        },
        "id": "A6WYsNYRtzyh",
        "outputId": "9b68dc76-1a91-44bd-d861-eafa4e1f74d9"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "e86d0336042e4d13ab7580faf05382a0",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "  0%|          | 0/20 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ TRAINING THE RANDOM FOREST MODEL:\n",
        "scores = []\n",
        "\n",
        "rf = RandomForestRegressor(n_estimators=0,\n",
        "                           random_state=1, n_jobs=-1,\n",
        "                           warm_start=True)\n",
        "\n",
        "for n in tqdm(range(10, 201, 10)):\n",
        "    rf.n_estimators = n\n",
        "    rf.fit(X_train, y_train)\n",
        "    \n",
        "    y_pred = rf.predict(X_val)\n",
        "    score = np.sqrt(mean_squared_error(y_val, y_pred))\n",
        "    \n",
        "    scores.append((n, score))\n",
        "\n",
        "df_scores = pd.DataFrame(scores, columns=['n_estimators', 'rmse'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "OiPiv87Pushd",
        "outputId": "aa6c8e89-396d-4190-aef5-bd1be5ce7193"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ INSPECTING THE RMSE SCORES:\n",
        "plt.plot(df_scores.n_estimators, df_scores.rmse.round(3))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CYhRv3kEvWjK"
      },
      "source": [
        "**Question 4**\n",
        "\n",
        "Let's select the best `max_depth`:\n",
        "\n",
        "- Try different values of `max_depth`: [10, 15, 20, 25].\n",
        "- For each of these values, try different values of n_estimators from 10 till 200 (with step 10).\n",
        "- Fix the random seed: `random_state=1`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 177,
          "referenced_widgets": [
            "1e45abfcf0a1435ba21e3c48eeebd3b1",
            "6c782fa06d2a4014b4e2dc55672ae59e",
            "958a59dede26406eb0f2c5562372952a",
            "026946586d7d45329360ec25dd0db930",
            "e321c1a91e4a4c439c437076946f9cc0",
            "ea90bf9bafb54ee8bd452a9e99167bb2",
            "4bc9e21ca7314431b695229c937b54d0",
            "0e2e99b623014943ae54454b4b1c86f0",
            "0dbd521db75f4eacb17409864ff0bfe2",
            "3626d9c1527d4b05be14a5359fb60e94",
            "1a7c2145019f4595b5dfc73dcabf9dc4",
            "595941dff8ca467d91bb36f8bfa01635",
            "306cefb79f1a462683a6d0cb55ac9853",
            "2d8f2f78c5b54c48b69fdd5d6763939d",
            "856b6fc4c87c4597bac26526a5dd6856",
            "4f61199f6c9e4c5cbdd5cfd57d30389f",
            "482986cfdd174c52a16903ec84cbd501",
            "d11fd568700540399f781611b4e098f7",
            "391b003e3fbd4e058cd130130aa76def",
            "3286e5433b2f4aec8d333affc841aff6",
            "ad861cf36d764489959adb539b4dcd18",
            "59427cf29f664be897ba695a04e9bb9c",
            "6355b3f71a254fb8858b274148d26069",
            "4683ea7340954818a38363f93f7a8e0c",
            "c1855905940243a1a510528f5b35c9a8",
            "15e9b4e9b29f4f7499885ac32a2372a0",
            "e534fe9ebad44b03b8b2a7a29e894b81",
            "d7aea086539c44139ae316abf1925c34",
            "fa20cc42ac1a4ed6a0e5b1ee4c602700",
            "ae6b07968da44caf9aa59bf45aef3d1b",
            "8a109d9ef7f049f5a94fffa8c458770e",
            "142efe5644c244e6a894ca0b0fae58ae",
            "80bbb1bd3f7248a79d44bbdeed7ecda2",
            "f7663ca0b2fc4d539fdb97672e14d088",
            "3122f7055bd647af82b2047de08b514a",
            "30875f5780644350918231c158892e6f",
            "12ec1f6b1db74a92bf3597a31f63f81d",
            "cc94a3d22aa641aa9c5aa415e0f16a7f",
            "c2104ed9eadb4aa0a6a35a415799d51e",
            "5e451874af0c4b618db80d5e442d4525",
            "b8afa965629a4d0388d821c5c2ff8187",
            "f132ea450da642b8bbff0a96619b9551",
            "519906af5513473abcf1899a5c1cb26e",
            "af8ae4f90e6a4e169f6d07e2ac83649d",
            "18cb064fb7f04dda84eda73d321fcbd9",
            "0a5e8c8d5d1f49029366ffe8c7afbedb",
            "878cccec427a433a90083a11e21d507e",
            "e9209f21b7214e43a6755a330a92f243",
            "f8ba1f648f8b4e308b6a5f1df1ea0280",
            "3508e505a1734244b8af20e59a7b3ef3",
            "65dff98afdd844f8a97cbdb819ecfd8c",
            "926a52a845d64688bdc9829ffa74c690",
            "d464b6598ea94ed3903a4f68590ccee0",
            "3d748f291d894e97bfcc1c9cf9709d91",
            "46711ae90e944f55b57a7fd541d2d5c4"
          ]
        },
        "id": "fO9TackKvKcS",
        "outputId": "be476cb9-a6a8-4ee4-a05d-c69fa7886828"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "1e45abfcf0a1435ba21e3c48eeebd3b1",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "  0%|          | 0/4 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "595941dff8ca467d91bb36f8bfa01635",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "  0%|          | 0/20 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "6355b3f71a254fb8858b274148d26069",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
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            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "f7663ca0b2fc4d539fdb97672e14d088",
              "version_major": 2,
              "version_minor": 0
            },
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            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "18cb064fb7f04dda84eda73d321fcbd9",
              "version_major": 2,
              "version_minor": 0
            },
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            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ TRAINING THE MODEL WITH DEPTH:\n",
        "scores = []\n",
        "\n",
        "for d in tqdm([10, 15, 20, 25]):\n",
        "    rf = RandomForestRegressor(n_estimators=0,\n",
        "                               max_depth=d,\n",
        "                               random_state=1, n_jobs=-1,\n",
        "                               warm_start=True)\n",
        "\n",
        "    for n in tqdm(range(10, 201, 10)):\n",
        "        rf.n_estimators = n\n",
        "        rf.fit(X_train, y_train)\n",
        "\n",
        "        y_pred = rf.predict(X_val)\n",
        "        score = np.sqrt(mean_squared_error(y_val, y_pred))\n",
        "\n",
        "        scores.append((d, n, score))\n",
        "\n",
        "columns = ['max_depth', 'n_estimators', 'rmse']\n",
        "df_scores = pd.DataFrame(scores, columns=columns)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "rqajbG4pwPly",
        "outputId": "da4d80ce-927f-4967-e8e1-b7f8d9372dca"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ PLOTTING THE GRAPH:\n",
        "for d in [10, 15, 20, 25]:\n",
        "    df_subset = df_scores[df_scores.max_depth == d]\n",
        "    plt.plot(df_subset.n_estimators, df_subset.rmse, label=d)\n",
        "\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eCRCaKlSwp7D"
      },
      "source": [
        "- What's the best `max_depth`:\n",
        "\n",
        "- Answer: 25"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BDLbx3N5xAoY"
      },
      "source": [
        "**Question 5**\n",
        "\n",
        "We can extract feature importance information from tree-based models.\n",
        "\n",
        "At each step of the decision tree learning algorith, it finds the best split. When doint it, we can calculate \"gain\" - the reduction in impurity before and after the split. This gain is quite useful in understanding what are the imporatant features for tree-based models.\n",
        "\n",
        "In Scikit-Learn, tree-based models contain this information in the `feature_importances_` field.\n",
        "\n",
        "For this homework question, we'll find the most important feature:\n",
        "\n",
        "Train the model with these parametes:\n",
        "- `n_estimators=10`,\n",
        "- `max_depth=20`,\n",
        "- `random_state=1`,\n",
        "- `n_jobs=-1` (optional)\n",
        "\n",
        "Get the feature importance information from this model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UICqST2Qwhbj",
        "outputId": "a21fe5b2-90ab-472b-f420-4b240f86e8e2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "RandomForestRegressor(max_depth=20, n_estimators=10, n_jobs=-1, random_state=1)"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ TRAINING THE RANDOM FOREST MODEL:\n",
        "rf = RandomForestRegressor(n_estimators=10, max_depth=20, \n",
        "                           random_state=1, n_jobs=-1)\n",
        "rf.fit(X_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JgI6w1Etx2g5",
        "outputId": "cf0c0cf6-5cf9-480c-f8a8-c04619375d82"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1.63873827e-02, 3.31454580e-02, 1.01255849e-01, 9.64702137e-02,\n",
              "       3.63325843e-01, 2.48880276e-03, 3.10900842e-01, 3.56806263e-04,\n",
              "       4.80369796e-04, 4.69876693e-03, 3.07769212e-02, 1.91716318e-02,\n",
              "       2.05411131e-02])"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ INSPECTING FEATURE IMPORTANCE:\n",
        "rf.feature_importances_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "fkPGLPpUx9XC",
        "outputId": "8e27e350-1759-48dd-aa59-45ec14e6ec80"
      },
      "outputs": [
        {
          "data": {
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              "<style scoped>\n",
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              "\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>feature</th>\n",
              "      <th>importance</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>households</td>\n",
              "      <td>0.016387</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>housing_median_age</td>\n",
              "      <td>0.033145</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>latitude</td>\n",
              "      <td>0.101256</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>longitude</td>\n",
              "      <td>0.096470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>median_income</td>\n",
              "      <td>0.363326</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>ocean_proximity=&lt;1H OCEAN</td>\n",
              "      <td>0.002489</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>ocean_proximity=INLAND</td>\n",
              "      <td>0.310901</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>ocean_proximity=ISLAND</td>\n",
              "      <td>0.000357</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>ocean_proximity=NEAR BAY</td>\n",
              "      <td>0.000480</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>ocean_proximity=NEAR OCEAN</td>\n",
              "      <td>0.004699</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>population</td>\n",
              "      <td>0.030777</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>total_bedrooms</td>\n",
              "      <td>0.019172</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>total_rooms</td>\n",
              "      <td>0.020541</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "                       feature  importance\n",
              "0                   households    0.016387\n",
              "1           housing_median_age    0.033145\n",
              "2                     latitude    0.101256\n",
              "3                    longitude    0.096470\n",
              "4                median_income    0.363326\n",
              "5    ocean_proximity=<1H OCEAN    0.002489\n",
              "6       ocean_proximity=INLAND    0.310901\n",
              "7       ocean_proximity=ISLAND    0.000357\n",
              "8     ocean_proximity=NEAR BAY    0.000480\n",
              "9   ocean_proximity=NEAR OCEAN    0.004699\n",
              "10                  population    0.030777\n",
              "11              total_bedrooms    0.019172\n",
              "12                 total_rooms    0.020541"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ INSPECTING FEATURE IMPORTANCES:\n",
        "df_importances = pd.DataFrame()\n",
        "df_importances['feature'] = dv.feature_names_\n",
        "df_importances['importance'] = rf.feature_importances_\n",
        "df_importances"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "vZ8J6YzfyFyq",
        "outputId": "fe57bbef-8c69-4fff-8a7c-493d9a2c34c9"
      },
      "outputs": [
        {
          "data": {
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              "\n",
              "  <div id=\"df-4d7613d8-bad0-4738-8a5e-06dd54a1ef62\">\n",
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              "      <div>\n",
              "<style scoped>\n",
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              "    }\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>feature</th>\n",
              "      <th>importance</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>median_income</td>\n",
              "      <td>0.363326</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>ocean_proximity=INLAND</td>\n",
              "      <td>0.310901</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>latitude</td>\n",
              "      <td>0.101256</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>longitude</td>\n",
              "      <td>0.096470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>housing_median_age</td>\n",
              "      <td>0.033145</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-4d7613d8-bad0-4738-8a5e-06dd54a1ef62 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4d7613d8-bad0-4738-8a5e-06dd54a1ef62');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "                  feature  importance\n",
              "4           median_income    0.363326\n",
              "6  ocean_proximity=INLAND    0.310901\n",
              "2                latitude    0.101256\n",
              "3               longitude    0.096470\n",
              "1      housing_median_age    0.033145"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#@ SORTING THE VALUES:\n",
        "df_importances.sort_values(by='importance', ascending=False).head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kSCqlx9jye1s"
      },
      "source": [
        "- What's the most important feature?\n",
        "\n",
        "- Answer: `median_income`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K5KEdiTMzPaI"
      },
      "source": [
        "**Question 6**\n",
        "\n",
        "Now let's train an XGBoost model! For this question, we'll tune the eta parameter:\n",
        "\n",
        "- Install XGBoost.\n",
        "- Create DMatrix for train and validation\n",
        "- Create a watchlist\n",
        "- Train a model with these parameters for 100 rounds:\n",
        "\n",
        "```\n",
        "xgb_params = {  \n",
        "    'eta': 0.3,  \n",
        "    'max_depth': 6,  \n",
        "    'min_child_weight': 1,  \n",
        "\n",
        "    'objective': 'reg:squarederror',\n",
        "    'nthread': 8,\n",
        "\n",
        "    'seed': 1,\n",
        "    'verbosity': 1,\n",
        "}\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "TUP0uoL5yZTc"
      },
      "outputs": [],
      "source": [
        "#@ CREATING THE DMARTIX:\n",
        "features = dv.feature_names_\n",
        "\n",
        "regex = re.compile(r\"<\", re.IGNORECASE)\n",
        "features = [regex.sub(\"_\", col) if any(x in str(col) for x in set(('[', ']', '<'))) else col for col in features]\n",
        "\n",
        "dtrain = xgb.DMatrix(X_train, label=y_train, feature_names=features)\n",
        "dval = xgb.DMatrix(X_val, label=y_val, feature_names=features)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "h7L7ocjZ53EC"
      },
      "outputs": [],
      "source": [
        "#@ INITIALIZATION:\n",
        "watchlist = [(dtrain, 'train'), (dval, 'val')]\n",
        "scores = {}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "zYqIK1I76Wod"
      },
      "outputs": [],
      "source": [
        "#@ DEFINING THE FUNCTION:\n",
        "def parse_xgb_output(output):\n",
        "    results = []\n",
        "\n",
        "    for line in output.stdout.strip().split('\\n'):\n",
        "        it_line, train_line, val_line = line.split('\\t')\n",
        "\n",
        "        it = int(it_line.strip('[]'))\n",
        "        train = float(train_line.split(':')[1])\n",
        "        val = float(val_line.split(':')[1])\n",
        "\n",
        "        results.append((it, train, val))\n",
        "    \n",
        "    columns = ['num_iter', 'train_auc', 'val_auc']\n",
        "    df_results = pd.DataFrame(results, columns=columns)\n",
        "    return df_results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "xsET8Kgu6j7M"
      },
      "outputs": [],
      "source": [
        "%%capture output\n",
        "\n",
        "xgb_params = {\n",
        "    'eta': 0.3, \n",
        "    'max_depth': 6,\n",
        "    'min_child_weight': 1,\n",
        "\n",
        "    'objective': 'reg:squarederror',\n",
        "    'nthread': 8,\n",
        "\n",
        "    'seed': 1,\n",
        "    'verbosity': 1,\n",
        "}\n",
        "\n",
        "model = xgb.train(xgb_params, dtrain, num_boost_round=100,\n",
        "                  verbose_eval=5, evals=watchlist)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "XQDiUOiB6nsf"
      },
      "outputs": [],
      "source": [
        "#@ STORING:\n",
        "scores['eta=0.3'] = parse_xgb_output(output)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "uorkyEGi6w25"
      },
      "outputs": [],
      "source": [
        "%%capture output\n",
        "\n",
        "xgb_params = {\n",
        "    'eta': 0.1, \n",
        "    'max_depth': 6,\n",
        "    'min_child_weight': 1,\n",
        "\n",
        "    'objective': 'reg:squarederror',\n",
        "    'nthread': 8,\n",
        "\n",
        "    'seed': 1,\n",
        "    'verbosity': 1,\n",
        "}\n",
        "\n",
        "model = xgb.train(xgb_params, dtrain, num_boost_round=100,\n",
        "                  verbose_eval=5, evals=watchlist)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "ukbUfPNy7Ar8"
      },
      "outputs": [],
      "source": [
        "#@ STORING:\n",
        "scores['eta=0.1'] = parse_xgb_output(output)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "l0OJpOUd7Gpk",
        "outputId": "5c8c2ea1-7d47-4b15-e3ee-eb0544738a16"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "#@ INSPECTION:\n",
        "plt.plot(scores['eta=0.1'].num_iter, scores['eta=0.1'].val_auc,\n",
        "        label='0.1')\n",
        "plt.plot(scores['eta=0.3'].num_iter, scores['eta=0.3'].val_auc,\n",
        "        label='0.3')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yl6Xn6Zb76iH"
      },
      "source": [
        "- Which eta leads to the best RMSE score on the validation dataset?\n",
        "\n",
        "- Answer: Both gives same. "
      ]
    }
  ],
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