black_friday_modeling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "from sklearn.decomposition import PCA, FactorAnalysis\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "import zipfile\n",
    "from zipfile import ZipFile\n",
    "import warnings\n",
    "import xgboost as xgb\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choose Modeling Dataset to Use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def read_model_dataset(chosen, combine_cats = False):\n",
    "    non_features = ['u_id', 'p_id']\n",
    "    demo_cols = []\n",
    "    predictor = ['pur']\n",
    "    file_name = \"\"\n",
    "\n",
    "    if chosen == 0:\n",
    "        file_name = \"minimal_preprocess.csv\"\n",
    "        demo_cols = ['gender', 'age', 'years_in_city', 'married', 'city', 'occ']\n",
    "    elif chosen == 1:\n",
    "        file_name = \"some_one_hot.csv\"\n",
    "        demo_cols = ['gender', 'age', 'years_in_city', 'married', 'occ_0', 'occ_1', 'occ_10',\n",
    "               'occ_11', 'occ_12', 'occ_13', 'occ_14', 'occ_15', 'occ_16', 'occ_17',\n",
    "               'occ_18', 'occ_19', 'occ_2', 'occ_20', 'occ_3', 'occ_4', 'occ_5',\n",
    "               'occ_6', 'occ_7', 'occ_8', 'occ_9', 'city_A', 'city_B', 'city_C']\n",
    "    elif chosen == 2:\n",
    "        file_name = \"all_one_hot.csv\"\n",
    "        demo_cols = ['gender', 'married', 'age_0', 'age_1', 'age_2', 'age_3', 'age_4',\n",
    "               'age_5', 'age_6', 'occ_0', 'occ_1', 'occ_10', 'occ_11', 'occ_12',\n",
    "               'occ_13', 'occ_14', 'occ_15', 'occ_16', 'occ_17', 'occ_18', 'occ_19',\n",
    "               'occ_2', 'occ_20', 'occ_3', 'occ_4', 'occ_5', 'occ_6', 'occ_7', 'occ_8',\n",
    "               'occ_9', 'city_0', 'city_1', 'city_2',\n",
    "               'years_in_city_0', 'years_in_city_1', 'years_in_city_2',\n",
    "               'years_in_city_3', 'years_in_city_4']\n",
    "    else:\n",
    "        file_name = \"minimal_preprocess.csv\"\n",
    "        demo_cols = ['gender', 'age', 'years_in_city', 'married', 'city', 'occ']\n",
    "    \n",
    "    if combine_cats and chosen != 0:\n",
    "        modeldf = pd.read_csv(\"inputs/p_combined_\" + file_name)\n",
    "    else:\n",
    "        modeldf = pd.read_csv(\"inputs/\" + file_name)\n",
    "    modeldf = modeldf.drop(non_features, axis = 1)\n",
    "    # line below removes purchase outliers from modeldf\n",
    "    # modeldf = modeldf[modeldf[\"pur\"] < modeldf[\"pur\"].quantile(0.99)]\n",
    "    X = modeldf.drop(predictor, axis = 1)\n",
    "    y = modeldf[predictor]\n",
    "    \n",
    "    return modeldf, X, y, predictor, demo_cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>years_in_city</th>\n",
       "      <th>married</th>\n",
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       "<p>5 rows × 81 columns</p>\n",
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      "text/plain": [
       "   gender  age  years_in_city  married    pur  occ_0  occ_1  occ_10  occ_11  \\\n",
       "0       0    0              2        0   8370      0      0       1       0   \n",
       "1       0    0              2        0  15200      0      0       1       0   \n",
       "2       0    0              2        0   1422      0      0       1       0   \n",
       "3       0    0              2        0   1057      0      0       1       0   \n",
       "4       1    6              4        0   7969      0      0       0       0   \n",
       "\n",
       "   occ_12    ...      p_cat_3_15  p_cat_3_16  p_cat_3_17  p_cat_3_18  \\\n",
       "0       0    ...               0           0           0           0   \n",
       "1       0    ...               0           0           0           0   \n",
       "2       0    ...               0           0           0           0   \n",
       "3       0    ...               0           0           0           0   \n",
       "4       0    ...               0           0           0           0   \n",
       "\n",
       "   p_cat_3_3  p_cat_3_4  p_cat_3_5  p_cat_3_6  p_cat_3_8  p_cat_3_9  \n",
       "0          0          0          0          0          0          0  \n",
       "1          0          0          0          0          0          0  \n",
       "2          0          0          0          0          0          0  \n",
       "3          0          0          0          0          0          0  \n",
       "4          0          0          0          0          0          0  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# minimal_preprocess = 0\n",
    "# some_one_hot = 1\n",
    "# all_one_hot = 2\n",
    "# defaults to minimal_preprocess\n",
    "\n",
    "modeldf, X, y, predictor, demo_cols = read_model_dataset(1, combine_cats = False)\n",
    "modeldf.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principle Componenet Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_pca_modeldf(X, model_cols, per_variance_captured = .95):\n",
    "    \n",
    "    all_X = X\n",
    "    X = X[model_cols]\n",
    "    X = StandardScaler().fit_transform(X)\n",
    "    pca = PCA()\n",
    "    pca.fit(StandardScaler().fit_transform(X))\n",
    "    plt.subplots(2,1, figsize=(15,5))\n",
    "    ax1 = plt.subplot(1,2,1)\n",
    "    plt.plot(pca.explained_variance_ratio_, '-o')\n",
    "    plt.xlabel(\"Principal Component\")\n",
    "    plt.ylabel(\"Pro. Variance Explained\")\n",
    "    ax1 = plt.subplot(1,2,2)\n",
    "    plt.plot(np.cumsum(pca.explained_variance_ratio_), '-o')\n",
    "    plt.xlabel(\"Principal Component\")\n",
    "    plt.ylabel(\"Cumulative Pro. Variance Explained\")\n",
    "    plt.show()\n",
    "    \n",
    "    n_components = np.where(np.cumsum(pca.explained_variance_ratio_)>=per_variance_captured)[0][0] + 1\n",
    "    print('%0.2f of variance explained by %d principal components' % (per_variance_captured, n_components))\n",
    "    \n",
    "    principalComponents = pca.transform(X)[:, 0:n_components]\n",
    "    X_pca = pd.DataFrame(data = principalComponents, columns = ['pc_' + str(x) for x in range(n_components)])\n",
    "    pca_cols = X_pca.columns\n",
    "    X_pca = X_pca.join(all_X.drop(model_cols, axis = 1))\n",
    "    \n",
    "    return X_pca, pca_cols\n",
    "\n",
    "def plot_top3pca(X_pca, color = 'blue'):\n",
    "    start = 0\n",
    "    n_cols = 3\n",
    "    n_rows = 1\n",
    "    fig, axs = plt.subplots(n_rows, n_cols, figsize = (18,4 * n_rows))\n",
    "    for i, num in enumerate(range(start, start + 3)):\n",
    "        axes = axs[i]\n",
    "        first = 'pc_%d' % num\n",
    "        second = 'pc_%d' % (num+1)\n",
    "        axes.scatter(X_pca[first], X_pca[second], color = color)\n",
    "        axes.set_xlabel(first)\n",
    "        axes.set_ylabel(second)\n",
    "    plt.show()\n",
    "    \n",
    "    fig = plt.figure(figsize = (10,10))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    ax.scatter(X_pca['pc_0'], X_pca['pc_1'],  X_pca['pc_2'], color = color)\n",
    "\n",
    "    ax.set_xlabel(\"pc_0\")\n",
    "    ax.set_ylabel(\"pc_1\")\n",
    "    ax.set_zlabel(\"pc_2\")\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.95 of variance explained by 24 principal components\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pc_0</th>\n",
       "      <th>pc_1</th>\n",
       "      <th>pc_2</th>\n",
       "      <th>pc_3</th>\n",
       "      <th>pc_4</th>\n",
       "      <th>pc_5</th>\n",
       "      <th>pc_6</th>\n",
       "      <th>pc_7</th>\n",
       "      <th>pc_8</th>\n",
       "      <th>pc_9</th>\n",
       "      <th>...</th>\n",
       "      <th>p_cat_3_15</th>\n",
       "      <th>p_cat_3_16</th>\n",
       "      <th>p_cat_3_17</th>\n",
       "      <th>p_cat_3_18</th>\n",
       "      <th>p_cat_3_3</th>\n",
       "      <th>p_cat_3_4</th>\n",
       "      <th>p_cat_3_5</th>\n",
       "      <th>p_cat_3_6</th>\n",
       "      <th>p_cat_3_8</th>\n",
       "      <th>p_cat_3_9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.320668</td>\n",
       "      <td>-1.762538</td>\n",
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       "      <td>0.208613</td>\n",
       "      <td>0.471076</td>\n",
       "      <td>-1.288151</td>\n",
       "      <td>2.805856</td>\n",
       "      <td>0.184317</td>\n",
       "      <td>-0.869306</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.320668</td>\n",
       "      <td>-1.762538</td>\n",
       "      <td>0.988307</td>\n",
       "      <td>1.951671</td>\n",
       "      <td>0.208613</td>\n",
       "      <td>0.471076</td>\n",
       "      <td>-1.288151</td>\n",
       "      <td>2.805856</td>\n",
       "      <td>0.184317</td>\n",
       "      <td>-0.869306</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3.320668</td>\n",
       "      <td>-1.762538</td>\n",
       "      <td>0.988307</td>\n",
       "      <td>1.951671</td>\n",
       "      <td>0.208613</td>\n",
       "      <td>0.471076</td>\n",
       "      <td>-1.288151</td>\n",
       "      <td>2.805856</td>\n",
       "      <td>0.184317</td>\n",
       "      <td>-0.869306</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-3.320668</td>\n",
       "      <td>-1.762538</td>\n",
       "      <td>0.988307</td>\n",
       "      <td>1.951671</td>\n",
       "      <td>0.208613</td>\n",
       "      <td>0.471076</td>\n",
       "      <td>-1.288151</td>\n",
       "      <td>2.805856</td>\n",
       "      <td>0.184317</td>\n",
       "      <td>-0.869306</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.541531</td>\n",
       "      <td>-0.919767</td>\n",
       "      <td>0.610573</td>\n",
       "      <td>-0.790028</td>\n",
       "      <td>-0.398485</td>\n",
       "      <td>-0.129828</td>\n",
       "      <td>1.227845</td>\n",
       "      <td>-0.287828</td>\n",
       "      <td>-0.725582</td>\n",
       "      <td>-0.637972</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 76 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       pc_0      pc_1      pc_2      pc_3      pc_4      pc_5      pc_6  \\\n",
       "0 -3.320668 -1.762538  0.988307  1.951671  0.208613  0.471076 -1.288151   \n",
       "1 -3.320668 -1.762538  0.988307  1.951671  0.208613  0.471076 -1.288151   \n",
       "2 -3.320668 -1.762538  0.988307  1.951671  0.208613  0.471076 -1.288151   \n",
       "3 -3.320668 -1.762538  0.988307  1.951671  0.208613  0.471076 -1.288151   \n",
       "4  2.541531 -0.919767  0.610573 -0.790028 -0.398485 -0.129828  1.227845   \n",
       "\n",
       "       pc_7      pc_8      pc_9    ...      p_cat_3_15  p_cat_3_16  \\\n",
       "0  2.805856  0.184317 -0.869306    ...               0           0   \n",
       "1  2.805856  0.184317 -0.869306    ...               0           0   \n",
       "2  2.805856  0.184317 -0.869306    ...               0           0   \n",
       "3  2.805856  0.184317 -0.869306    ...               0           0   \n",
       "4 -0.287828 -0.725582 -0.637972    ...               0           0   \n",
       "\n",
       "   p_cat_3_17  p_cat_3_18  p_cat_3_3  p_cat_3_4  p_cat_3_5  p_cat_3_6  \\\n",
       "0           0           0          0          0          0          0   \n",
       "1           0           0          0          0          0          0   \n",
       "2           0           0          0          0          0          0   \n",
       "3           0           0          0          0          0          0   \n",
       "4           0           0          0          0          0          0   \n",
       "\n",
       "   p_cat_3_8  p_cat_3_9  \n",
       "0          0          0  \n",
       "1          0          0  \n",
       "2          0          0  \n",
       "3          0          0  \n",
       "4          0          0  \n",
       "\n",
       "[5 rows x 76 columns]"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_pca, pca_cols = create_pca_modeldf(X, demo_cols, per_variance_captured = .95)\n",
    "X_pca.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factor Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_fa_modeldf(X, model_cols, per_variance_captured = .95):\n",
    "    \n",
    "    all_X = X\n",
    "    X = X[model_cols]\n",
    "    X = StandardScaler().fit_transform(X)\n",
    "    fa = FactorAnalysis()\n",
    "    fa.fit(X)\n",
    "    \n",
    "    m = fa.components_\n",
    "    n = fa.noise_variance_\n",
    "    \n",
    "    m1 = m**2\n",
    "    m2 = np.sum(m1, axis = 1)\n",
    "    \n",
    "    pvar = (100*m2)/(np.sum(m2)+np.sum(n))\n",
    "    pvar = pvar/np.cumsum(pvar)[len(pvar) - 1]\n",
    "    \n",
    "    plt.subplots(2,1, figsize=(15,5))\n",
    "    ax1 = plt.subplot(1,2,1)\n",
    "    plt.plot(pvar, '-o')\n",
    "    plt.xlabel(\"Principal Component\")\n",
    "    plt.ylabel(\"Pro. Variance Explained\")\n",
    "    ax1 = plt.subplot(1,2,2)\n",
    "    plt.plot(np.cumsum(pvar), '-o')\n",
    "    plt.xlabel(\"Principal Component\")\n",
    "    plt.ylabel(\"Cumulative Pro. Variance Explained\")\n",
    "    plt.show()\n",
    "    \n",
    "    n_components = np.where(np.cumsum(pvar)>=per_variance_captured)[0][0] + 1\n",
    "    print('%0.2f of variance explained by %d principal components' % (per_variance_captured, n_components))\n",
    "    \n",
    "    components = fa.transform(X)[:, 0:n_components]\n",
    "    X_fa = pd.DataFrame(data = components, columns = ['f' + str(x) for x in range(n_components)])\n",
    "    fa_cols = X_fa.columns\n",
    "    X_fa = X_fa.join(all_X.drop(model_cols, axis = 1))\n",
    "    \n",
    "    return X_fa, fa_cols\n",
    "\n",
    "def plot_top3fa(X_fa, color = 'blue'):\n",
    "    start = 0\n",
    "    n_cols = 3\n",
    "    n_rows = 1\n",
    "    fig, axs = plt.subplots(n_rows, n_cols, figsize = (18,4 * n_rows))\n",
    "    for i, num in enumerate(range(start, start + 3)):\n",
    "        axes = axs[i]\n",
    "        first = 'f%d' % num\n",
    "        second = 'f%d' % (num+1)\n",
    "        axes.scatter(X_fa[first], X_fa[second], color = color)\n",
    "        axes.set_xlabel(first)\n",
    "        axes.set_ylabel(second)\n",
    "    plt.show()\n",
    "    \n",
    "    fig = plt.figure(figsize = (10,10))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    ax.scatter(X_fa['f0'], X_fa['f1'],  X_fa['f2'], color = color)\n",
    "\n",
    "    ax.set_xlabel(\"f0\")\n",
    "    ax.set_ylabel(\"f1\")\n",
    "    ax.set_zlabel(\"f2\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.95 of variance explained by 17 principal components\n"
     ]
    },
    {
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       "      <td>-0.153652</td>\n",
       "      <td>-0.326405</td>\n",
       "      <td>0.684448</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 69 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         f0        f1        f2        f3        f4        f5        f6  \\\n",
       "0 -0.208597 -1.979441  0.694416  0.885650  0.772876  1.407854 -0.463428   \n",
       "1 -0.208597 -1.979441  0.694416  0.885650  0.772876  1.407854 -0.463428   \n",
       "2 -0.208597 -1.979441  0.694416  0.885650  0.772876  1.407854 -0.463428   \n",
       "3 -0.208597 -1.979441  0.694416  0.885650  0.772876  1.407854 -0.463428   \n",
       "4  1.324356  1.013547 -0.024387 -0.432656 -0.236465 -0.174523 -0.124989   \n",
       "\n",
       "         f7        f8        f9    ...      p_cat_3_15  p_cat_3_16  \\\n",
       "0 -0.160788 -0.240930  0.525191    ...               0           0   \n",
       "1 -0.160788 -0.240930  0.525191    ...               0           0   \n",
       "2 -0.160788 -0.240930  0.525191    ...               0           0   \n",
       "3 -0.160788 -0.240930  0.525191    ...               0           0   \n",
       "4 -0.153652 -0.326405  0.684448    ...               0           0   \n",
       "\n",
       "   p_cat_3_17  p_cat_3_18  p_cat_3_3  p_cat_3_4  p_cat_3_5  p_cat_3_6  \\\n",
       "0           0           0          0          0          0          0   \n",
       "1           0           0          0          0          0          0   \n",
       "2           0           0          0          0          0          0   \n",
       "3           0           0          0          0          0          0   \n",
       "4           0           0          0          0          0          0   \n",
       "\n",
       "   p_cat_3_8  p_cat_3_9  \n",
       "0          0          0  \n",
       "1          0          0  \n",
       "2          0          0  \n",
       "3          0          0  \n",
       "4          0          0  \n",
       "\n",
       "[5 rows x 69 columns]"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_fa, fa_cols = create_fa_modeldf(X, demo_cols, per_variance_captured = .95)\n",
    "X_fa.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Optimal K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_elbow_method(X_frame, demo_cols, max_K = 10): # can change to PCA dataset\n",
    "    kmeansdf = X_frame[demo_cols]\n",
    "    distortions = []\n",
    "\n",
    "    K = range(1, max_K + 1)\n",
    "    for k in K:\n",
    "        kmean = KMeans(n_clusters=k, n_init = 10, precompute_distances = True, n_jobs = -1).fit(kmeansdf)\n",
    "        dist = sum(np.min(cdist(kmeansdf, kmean.cluster_centers_, 'euclidean'), axis=1)) / kmeansdf.shape[0]\n",
    "        print(\"Distorition for %d clusters: %0.3f\" % (k, dist))\n",
    "        distortions.append(dist)\n",
    "\n",
    "    plt.plot(K, distortions, 'bx-')\n",
    "    plt.xlabel('k')\n",
    "    plt.ylabel('Distortion')\n",
    "    plt.title('The Elbow Method showing the optimal k')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Model Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distorition for 1 clusters: 2.260\n",
      "Distorition for 2 clusters: 1.975\n",
      "Distorition for 3 clusters: 1.760\n",
      "Distorition for 4 clusters: 1.691\n",
      "Distorition for 5 clusters: 1.635\n",
      "Distorition for 6 clusters: 1.600\n",
      "Distorition for 7 clusters: 1.564\n",
      "Distorition for 8 clusters: 1.518\n",
      "Distorition for 9 clusters: 1.489\n",
      "Distorition for 10 clusters: 1.473\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### DON'T RUN UNLESS YOU WANT TO FIND OPTIMAL K FOR K MEANS ###\n",
    "### TAKES A LONG TIME TO RUN ###\n",
    "\n",
    "# Model dataframe elbow method\n",
    "run_elbow_method(X, demo_cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distorition for 1 clusters: 4.924\n",
      "Distorition for 2 clusters: 4.744\n",
      "Distorition for 3 clusters: 4.578\n",
      "Distorition for 4 clusters: 4.530\n",
      "Distorition for 5 clusters: 4.368\n",
      "Distorition for 6 clusters: 4.214\n",
      "Distorition for 7 clusters: 4.018\n",
      "Distorition for 8 clusters: 3.998\n",
      "Distorition for 9 clusters: 3.770\n",
      "Distorition for 10 clusters: 3.638\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### DON'T RUN UNLESS YOU WANT TO FIND OPTIMAL K FOR K MEANS ###\n",
    "### TAKES A LONG TIME TO RUN ###\n",
    "\n",
    "#PCA elbow method\n",
    "run_elbow_method(X_pca, pca_cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FA Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distorition for 1 clusters: 1.897\n",
      "Distorition for 2 clusters: 1.723\n",
      "Distorition for 3 clusters: 1.568\n",
      "Distorition for 4 clusters: 1.509\n",
      "Distorition for 5 clusters: 1.492\n",
      "Distorition for 6 clusters: 1.439\n",
      "Distorition for 7 clusters: 1.403\n",
      "Distorition for 8 clusters: 1.379\n",
      "Distorition for 9 clusters: 1.345\n",
      "Distorition for 10 clusters: 1.309\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### DON'T RUN UNLESS YOU WANT TO FIND OPTIMAL K FOR K MEANS ###\n",
    "### TAKES A LONG TIME TO RUN ###\n",
    "\n",
    "#PCA elbow method\n",
    "run_elbow_method(X_fa, fa_cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Clustered Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Generates k-means cluster datasets\n",
    "# returns whole dataframe with clusters and cluster split dataframes\n",
    "def create_cluster_modeldfs(X_frame, y, frame_demo_cols, n_clusters = 3):\n",
    "    kmeansdf = StandardScaler().fit_transform(X_frame[frame_demo_cols])\n",
    "    \n",
    "    kmeans = KMeans(n_clusters = n_clusters, random_state = 42, n_init = 30, precompute_distances = True, n_jobs = -1).fit(kmeansdf) # testing shows that 2-3 clussters works the best\n",
    "    cluster_nums = kmeans.predict(kmeansdf)\n",
    "\n",
    "    # Single dataset for clusters\n",
    "    X_cl = pd.DataFrame(cluster_nums, columns = ['cluster_num']).join(X_frame)\n",
    "    \n",
    "    # Seperate datasets based on clusters\n",
    "    temp = X_cl.join(y)\n",
    "    X_cls = [temp[temp['cluster_num'] == x] for x in range(max(temp['cluster_num']) + 1)]\n",
    "    X_cls = [cluster.drop('cluster_num', axis = 1) for cluster in X_cls]\n",
    "    \n",
    "    # one hot encode cluster numbers\n",
    "    ranges = pd.unique(pd.Series(X_cl['cluster_num']))\n",
    "    ranges.sort()\n",
    "    mapped = ['cluster_num_' + str(x) for x in ranges]\n",
    "    saved_cluster_num = X_cl['cluster_num']\n",
    "    X_cl['cluster_num'] = X_cl['cluster_num'].map(dict(zip(ranges, mapped)))\n",
    "    one_hot = pd.get_dummies(X_cl['cluster_num'])\n",
    "    #X_cl = X_cl.drop('cluster_num', axis = 1)\n",
    "    X_cl['cluster_num'] = saved_cluster_num\n",
    "    X_cl = X_cl.join(one_hot) \n",
    "    \n",
    "    return X_cl, X_cls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_PCA_clusters(X_pca_clusters):\n",
    "    colors = ['green', 'blue', 'red']\n",
    "    labels = ['cluster 0', 'cluster 1', 'cluster 2']\n",
    "\n",
    "    fig = plt.figure(figsize = (10,10))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for cluster, color, label in zip(X_pca_clusters, colors, labels):\n",
    "        ax.scatter(cluster['pc_0'], cluster['pc_1'],  cluster['pc_2'], color = color, label = label)\n",
    "\n",
    "    ax.set_xlabel(\"pc_0\")\n",
    "    ax.set_ylabel(\"pc_1\")\n",
    "    ax.set_zlabel(\"pc_2\")\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "    \n",
    "def plot_FA_clusters(X_fa_clusters):\n",
    "    colors = ['green', 'blue', 'red']\n",
    "    labels = ['cluster 0', 'cluster 1', 'cluster 2']\n",
    "\n",
    "    fig = plt.figure(figsize = (10,10))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for cluster, color, label in zip(X_fa_clusters, colors, labels):\n",
    "        ax.scatter(cluster['f0'], cluster['f1'],  cluster['f2'], color = color, label = label)\n",
    "\n",
    "    ax.set_xlabel(\"f0\")\n",
    "    ax.set_ylabel(\"f1\")\n",
    "    ax.set_zlabel(\"f2\")\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Model Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clustering\n",
      "\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Clustering\\n\")\n",
    "    X_cluster, X_clusters = create_cluster_modeldfs(X, y, demo_cols, n_clusters = 3)\n",
    "    print(\"Done!\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clustering Using PCAs\n",
      "\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Clustering Using PCAs\\n\")\n",
    "    X_pca_cluster, X_pca_clusters = create_cluster_modeldfs(X_pca, y, pca_cols, n_clusters = 3)\n",
    "    print(\"Done!\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FA Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clustering Using FA\n",
      "\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Clustering Using FA\\n\")\n",
    "    X_fa_cluster, X_fa_clusters = create_cluster_modeldfs(X_fa, y, fa_cols, n_clusters = 3)\n",
    "    print(\"Done!\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predictive Modeling "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Training and Test Datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train and testing data for model dataset\n",
    "def split_model_data(X, y, scale = False): # can specify different\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X,y,test_size = 0.25, random_state=30)\n",
    "    y_train = np.array(y_train).T.reshape(1, -1)[0]\n",
    "    y_test = np.array(y_test).T.reshape(1, -1)[0]\n",
    "    return X_train, X_test, y_train, y_test\n",
    "def create_dataframe_split(X_data, y_data, scale = False):\n",
    "    try:\n",
    "        data_splits = (split_model_data(X_data, y_data, scale = scale))\n",
    "        print(\"Dataframe shape:\", data_splits[0].shape, data_splits[1].shape, data_splits[2].shape, data_splits[3].shape)      \n",
    "        return data_splits[0], data_splits[1], data_splits[2], data_splits[3]\n",
    "    except:\n",
    "        print (\"Create model dataframe first!\")\n",
    "        return [], [], [], []\n",
    "def create_cluster_dataframe_split(clusters):\n",
    "    try:\n",
    "        X_cl_trains = []\n",
    "        X_cl_tests = [] \n",
    "        y_cl_trains = []\n",
    "        y_cl_tests = []\n",
    "        for i, clusterdf in enumerate(clusters):\n",
    "            X_frame = clusterdf.drop(predictor, axis = 1)\n",
    "            y_frame = clusterdf[predictor]\n",
    "            X_cl_train, X_cl_test, y_cl_train, y_cl_test = train_test_split(X_frame, y_frame, test_size = 0.25, random_state=30)\n",
    "            y_cl_train = np.array(y_cl_train).T.reshape(1, -1)[0]\n",
    "            y_cl_test = np.array(y_cl_test).T.reshape(1, -1)[0]\n",
    "            X_cl_trains.append(X_cl_train)\n",
    "            X_cl_tests.append(X_cl_test)\n",
    "            y_cl_trains.append(y_cl_train)\n",
    "            y_cl_tests.append(y_cl_test)\n",
    "            print(\"Cluster num\", i, \":\" , X_cl_trains[i].shape, X_cl_tests[i].shape, y_cl_trains[i].shape, y_cl_tests[i].shape)\n",
    "        return X_cl_trains, X_cl_tests, y_cl_trains, y_cl_tests\n",
    "    except:\n",
    "        print (\"Create model dataframe first!\")\n",
    "        print(\"\")\n",
    "        return [], [], [], []\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Dataset\n",
      "Dataframe shape: (403182, 80) (134395, 80) (403182,) (134395,)\n",
      "\n",
      "PCA Dataset\n",
      "Dataframe shape: (403182, 76) (134395, 76) (403182,) (134395,)\n",
      "\n",
      "FA Dataset\n",
      "Dataframe shape: (403182, 69) (134395, 69) (403182,) (134395,)\n",
      "\n",
      "Cluster Dataset\n",
      "Dataframe shape: (403182, 83) (134395, 83) (403182,) (134395,)\n",
      "\n",
      "PCA Cluster Dataset\n",
      "Dataframe shape: (403182, 79) (134395, 79) (403182,) (134395,)\n",
      "\n",
      "FA Cluster Dataset\n",
      "Dataframe shape: (403182, 73) (134395, 73) (403182,) (134395,)\n",
      "\n",
      "Split Cluster Dataset\n",
      "Cluster num 0 : (169869, 80) (56624, 80) (169869,) (56624,)\n",
      "Cluster num 1 : (108478, 80) (36160, 80) (108478,) (36160,)\n",
      "Cluster num 2 : (124834, 80) (41612, 80) (124834,) (41612,)\n",
      "\n",
      "Split PCA Cluster Dataset\n",
      "Cluster num 0 : (108478, 76) (36160, 76) (108478,) (36160,)\n",
      "Cluster num 1 : (124834, 76) (41612, 76) (124834,) (41612,)\n",
      "Cluster num 2 : (169869, 76) (56624, 76) (169869,) (56624,)\n",
      "\n",
      "Split FA Cluster Dataset\n",
      "Cluster num 0 : (121210, 69) (40404, 69) (121210,) (40404,)\n",
      "Cluster num 1 : (173493, 69) (57832, 69) (173493,) (57832,)\n",
      "Cluster num 2 : (108478, 69) (36160, 69) (108478,) (36160,)\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Model Dataset\")\n",
    "    X_train, X_test, y_train, y_test = create_dataframe_split(X, y)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Dataset\")\n",
    "    X_pca_train, X_pca_test, y_pca_train, y_pca_test = create_dataframe_split(X_pca, y)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nFA Dataset\")\n",
    "    X_fa_train, X_fa_test, y_fa_train, y_fa_test = create_dataframe_split(X_fa, y)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")    \n",
    "    \n",
    "try:\n",
    "    print(\"\\nCluster Dataset\")\n",
    "    X_cl_train, X_cl_test, y_cl_train, y_cl_test = create_dataframe_split(X_cluster.drop('cluster_num', axis = 1), y)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:\n",
    "    print(\"\\nPCA Cluster Dataset\")\n",
    "    X_pca_cl_train, X_pca_cl_test, y_pca_cl_train, y_pca_cl_test = create_dataframe_split(X_pca_cluster.drop('cluster_num', axis = 1), y) \n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:\n",
    "    print(\"\\nFA Cluster Dataset\")\n",
    "    X_fa_cl_train, X_fa_cl_test, y_fa_cl_train, y_fa_cl_test = create_dataframe_split(X_fa_cluster.drop('cluster_num', axis = 1), y) \n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "#--------------------------------------------------------\n",
    "\n",
    "try:    \n",
    "    print(\"\\nSplit Cluster Dataset\")\n",
    "    X_cl_trains, X_cl_tests, y_cl_trains, y_cl_tests = create_cluster_dataframe_split(X_clusters)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nSplit PCA Cluster Dataset\")\n",
    "    X_pca_cl_trains, X_pca_cl_tests, y_pca_cl_trains, y_pca_cl_tests = create_cluster_dataframe_split(X_pca_clusters)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:    \n",
    "    print(\"\\nSplit FA Cluster Dataset\")\n",
    "    X_fa_cl_trains, X_fa_cl_tests, y_fa_cl_trains, y_fa_cl_tests = create_cluster_dataframe_split(X_fa_clusters)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_reg_data(X_tr, y_tr, X_te, y_te):\n",
    "    reg = LinearRegression().fit(X_tr, y_tr)\n",
    "    pred = reg.predict(X_te)\n",
    "    print(\"MAE: \", mean_absolute_error(pred, y_te))\n",
    "    print(\"RMSE: \", np.sqrt(mean_squared_error(pred, y_te)))\n",
    "def MLP_data(X_tr, y_tr, X_te, y_te, verbose = False, show_plot = False):  \n",
    "    mlp = MLPRegressor(activation = 'identity',\n",
    "                   hidden_layer_sizes = (25, 1),\n",
    "                   solver = 'adam',\n",
    "                   learning_rate = 'constant',\n",
    "                   random_state = 42,\n",
    "                   batch_size = 3000,\n",
    "                   verbose = verbose,\n",
    "                   learning_rate_init = 1).fit(X_tr, y_tr)\n",
    "    pred = mlp.predict(X_te)\n",
    "    print(\"MAE: \", mean_absolute_error(pred, y_te))\n",
    "    print(\"RMSE: \", np.sqrt(mean_squared_error(pred, y_te)))\n",
    "    if show_plot:\n",
    "        plt.plot(np.sqrt(mlp.loss_curve_))\n",
    "        plt.xlabel(\"epoch\")\n",
    "        plt.ylabel(\"MAE\")\n",
    "        plt.show()\n",
    "def xgboost_data(X_tr, y_tr, X_te, y_te):\n",
    "    param = {\n",
    "        'booster': 'dart',\n",
    "        'eta': .75,  # the training step for each iteration\n",
    "        'silent': 1,  # logging mode - quiet\n",
    "        'grow_policy' : 'depthwise',\n",
    "        'tree_method' : 'hist',\n",
    "        'eval_metric': 'rmse',\n",
    "        'max_depth' : 10,\n",
    "        'rate_drop': 0.1,\n",
    "        'skip_drop': 0.5,\n",
    "        'seed': 42}\n",
    "    num_round = 30  # the number of training iterations\n",
    "    \n",
    "    dtrain = xgb.DMatrix(X_tr, label=y_tr)\n",
    "    dtest = xgb.DMatrix(X_te, label=y_te)\n",
    "\n",
    "    bst = xgb.train(param, dtrain, num_round)\n",
    "    pred = bst.predict(dtest, ntree_limit=num_round)\n",
    "    rmse = np.sqrt(mean_squared_error(pred, y_te))\n",
    "    print(\"MAE: \", mean_absolute_error(pred, y_te))\n",
    "    print(\"RMSE: \", np.sqrt(mean_squared_error(pred, y_te)))\n",
    "    return bst, rmse\n",
    "\n",
    "def xgboost_cluster_data(X_cl_trs, X_cl_tes, y_cl_trs, y_cl_tes):\n",
    "    param = {\n",
    "        'booster': 'dart',\n",
    "        'eta': .75,  # the training step for each iteration\n",
    "        'silent': 1,  # logging mode - quiet\n",
    "        'grow_policy' : 'depthwise',\n",
    "        'tree_method' : 'hist',\n",
    "        'eval_metric': 'rmse',\n",
    "        'max_depth' : 10,\n",
    "        'rate_drop': 0.1,\n",
    "        'skip_drop': 0.5,\n",
    "        'seed': 42}\n",
    "    bsts = []\n",
    "    num_round = 30  # the number of training iterations\n",
    "    mean_mae = 0\n",
    "\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_cl_trs)), X_cl_trs, X_cl_tes, y_cl_trs, y_cl_tes):\n",
    "        dtrain = xgb.DMatrix(X_cl_tr, label=y_cl_tr)\n",
    "        dtest = xgb.DMatrix(X_cl_te, label=y_cl_te)\n",
    "\n",
    "        bst = xgb.train(param, dtrain, num_round)\n",
    "        pred = bst.predict(dtest)\n",
    "        temp_mae = mean_absolute_error(pred, y_cl_te)\n",
    "        mean_mae = mean_mae + temp_mae\n",
    "        \n",
    "        print(\"MAE for cluster\", i, \":\", temp_mae)\n",
    "        print(\"RMSE for Cluster:\", i, \":\", np.sqrt(mean_squared_error(pred, y_cl_te)))\n",
    "        print(\"\")\n",
    "        bsts.append(bst)\n",
    "    print(\"\\nAverage MAE for all clusters:\", mean_mae/len(X_cl_trs))\n",
    "    return bsts\n",
    "\n",
    "def update_best_model(best_bst, best_rmse, best_name, bst, rmse, name):\n",
    "    if best_rmse == -1 or best_rmse > rmse:\n",
    "        best_rmse = rmse\n",
    "        best_bst = bst\n",
    "        best_name = name\n",
    "    return best_bst, best_rmse, best_name\n",
    "\n",
    "def get_best_data(best_name):\n",
    "    if best_name == 'Model':\n",
    "        return X\n",
    "    elif best_name == 'PCA':\n",
    "        return X_pca\n",
    "    elif best_name == 'FA':\n",
    "        return X_fa\n",
    "    elif best_name == 'Cluster':\n",
    "        return X_cluster\n",
    "    elif best_name == 'PCA Cluster':\n",
    "        return X_pca_cluster\n",
    "    elif best_name == 'FA Cluster':\n",
    "        return X_fa_cluster\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Dataset\n",
      "MAE:  2262.835475417612\n",
      "RMSE:  2990.954371855573\n",
      "\n",
      "PCA Dataset\n",
      "MAE:  2263.3288254771383\n",
      "RMSE:  2991.4735948970642\n",
      "\n",
      "FA Dataset\n",
      "MAE:  2264.3159697161354\n",
      "RMSE:  2992.258885540102\n",
      "\n",
      "Cluster Dataset\n",
      "MAE:  2262.6752139216487\n",
      "RMSE:  2990.799890574183\n",
      "\n",
      "PCA Cluster Dataset\n",
      "MAE:  2262.8558065776256\n",
      "RMSE:  2990.9975766820176\n",
      "\n",
      "FA Cluster Dataset\n",
      "MAE:  2264.0032999739574\n",
      "RMSE:  2992.1082780589995\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Model Dataset\")\n",
    "    linear_reg_data(X_train, y_train, X_test, y_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Dataset\")\n",
    "    linear_reg_data(X_pca_train, y_pca_train, X_pca_test, y_pca_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nFA Dataset\")\n",
    "    linear_reg_data(X_fa_train, y_fa_train, X_fa_test, y_fa_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")    \n",
    "    \n",
    "try:\n",
    "    print(\"\\nCluster Dataset\")\n",
    "    linear_reg_data(X_cl_train, y_cl_train, X_cl_test, y_cl_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Cluster Dataset\")\n",
    "    linear_reg_data(X_pca_cl_train, y_pca_cl_train, X_pca_cl_test, y_pca_cl_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:    \n",
    "    print(\"\\nFA Cluster Dataset\")\n",
    "    linear_reg_data(X_fa_cl_train, y_fa_cl_train, X_fa_cl_test, y_fa_cl_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Split Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2135.0795216198776\n",
      "RMSE:  2823.803718852458\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2247.717755954284\n",
      "RMSE:  2969.5367245089856\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2281.8974258812755\n",
      "RMSE:  3013.9057745380633\n",
      "\n",
      "\n",
      "Split PCA Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2226.389637522198\n",
      "RMSE:  2943.552088059883\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2251.3302673852213\n",
      "RMSE:  2962.681427073759\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2274.603370470344\n",
      "RMSE:  2998.717524701019\n",
      "\n",
      "\n",
      "Split FA Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2252.879360644986\n",
      "RMSE:  2992.831420506857\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2241.8097744328397\n",
      "RMSE:  2957.755893460205\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2293.3356125553096\n",
      "RMSE:  3019.0622726309534\n",
      "\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"\\nSplit Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_cl_trains)), X_cl_trains, X_cl_tests, y_cl_trains, y_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        linear_reg_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:\n",
    "    print(\"\\nSplit PCA Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_pca_cl_trains)), X_pca_cl_trains, X_pca_cl_tests, y_pca_cl_trains, y_pca_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        linear_reg_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:\n",
    "    print(\"\\nSplit FA Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_fa_cl_trains)), X_fa_cl_trains, X_fa_cl_tests, y_fa_cl_trains, y_fa_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        linear_reg_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLP Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Dataset\n",
      "MAE:  2246.6227078802553\n",
      "RMSE:  3029.516435437649\n",
      "\n",
      "PCA Dataset\n",
      "MAE:  2324.077174133776\n",
      "RMSE:  3031.3322226588807\n",
      "\n",
      "FA Dataset\n",
      "MAE:  2258.586969553854\n",
      "RMSE:  3004.188170814923\n",
      "\n",
      "Cluster Dataset\n",
      "MAE:  2241.540325635304\n",
      "RMSE:  3021.913035733147\n",
      "\n",
      "PCA Cluster Dataset\n",
      "MAE:  2301.8827606728278\n",
      "RMSE:  3014.93917705603\n",
      "\n",
      "FA Cluster Dataset\n",
      "MAE:  2305.4185400394963\n",
      "RMSE:  3018.1252728536497\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Model Dataset\")\n",
    "    MLP_data(X_train, y_train, X_test, y_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Dataset\")\n",
    "    MLP_data(X_pca_train, y_pca_train, X_pca_test, y_pca_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nFA Dataset\")\n",
    "    MLP_data(X_fa_train, y_fa_train, X_fa_test, y_fa_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")    \n",
    "    \n",
    "try:\n",
    "    print(\"\\nCluster Dataset\")\n",
    "    MLP_data(X_cl_train, y_cl_train, X_cl_test, y_cl_test)\n",
    "\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Cluster Dataset\")\n",
    "    MLP_data(X_pca_cl_train, y_pca_cl_train, X_pca_cl_test, y_pca_cl_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:    \n",
    "    print(\"\\nFA Cluster Dataset\")\n",
    "    MLP_data(X_fa_cl_train, y_fa_cl_train, X_fa_cl_test, y_fa_cl_test)\n",
    "except:\n",
    "    print (\"Create model dataframe first!\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Split Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2127.7660937863525\n",
      "RMSE:  2830.764630492819\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2251.7510280705033\n",
      "RMSE:  2974.1146729368406\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2317.2862615650142\n",
      "RMSE:  3030.0839655565246\n",
      "\n",
      "\n",
      "Split PCA Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2253.1129553270735\n",
      "RMSE:  2964.4549338730008\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2274.8661208702865\n",
      "RMSE:  2972.5139128770784\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2324.2920630778463\n",
      "RMSE:  3031.4843013216578\n",
      "\n",
      "\n",
      "Split FA Cluster Dataset\n",
      "-------------\n",
      "Cluster num: 0\n",
      "MAE:  2213.6072154559847\n",
      "RMSE:  3010.4310532089194\n",
      "\n",
      "Cluster num: 1\n",
      "MAE:  2295.8482821645343\n",
      "RMSE:  3007.329016491799\n",
      "\n",
      "Cluster num: 2\n",
      "MAE:  2318.404298350742\n",
      "RMSE:  3039.7182420250006\n",
      "\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"\\nSplit Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_cl_trains)), X_cl_trains, X_cl_tests, y_cl_trains, y_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        MLP_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:\n",
    "    print(\"\\nSplit PCA Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_pca_cl_trains)), X_pca_cl_trains, X_pca_cl_tests, y_pca_cl_trains, y_pca_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        MLP_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:\n",
    "    print(\"\\nSplit FA Cluster Dataset\\n-------------\")\n",
    "    for i, X_cl_tr, X_cl_te, y_cl_tr, y_cl_te in zip(range(len(X_fa_cl_trains)), X_fa_cl_trains, X_fa_cl_tests, y_fa_cl_trains, y_fa_cl_tests):\n",
    "        print(\"Cluster num:\", i)\n",
    "        MLP_data(X_cl_tr, y_cl_tr, X_cl_te, y_cl_te)\n",
    "        print(\"\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### XGBoost Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Dataset\n",
      "[08:06:47] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2152.5959621798224\n",
      "RMSE:  2885.963515566603\n",
      "\n",
      "PCA Dataset\n",
      "[08:07:01] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2141.2540774039203\n",
      "RMSE:  2879.381052974568\n",
      "\n",
      "FA Dataset\n",
      "[08:07:20] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2135.425510224956\n",
      "RMSE:  2871.144101988556\n",
      "\n",
      "Cluster Dataset\n",
      "[08:07:37] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2152.5959621798224\n",
      "RMSE:  2885.963515566603\n",
      "\n",
      "PCA Cluster Dataset\n",
      "[08:07:51] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2139.603933422567\n",
      "RMSE:  2876.118001857127\n",
      "\n",
      "FA Cluster Dataset\n",
      "[08:08:10] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2144.820282749555\n",
      "RMSE:  2884.7616940605208\n",
      "\n",
      "--------------------\n",
      "Best Dataset: FA\n",
      "Best RMSE: 2871.144101988556\n"
     ]
    }
   ],
   "source": [
    "best_bst = xgb.Booster({'nthread': 4})\n",
    "best_rmse = -1\n",
    "best_name = \"\"\n",
    "\n",
    "try:\n",
    "    print(\"Model Dataset\")\n",
    "    bst, rmse = xgboost_data(X_train, y_train, X_test, y_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"Model\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Dataset\")\n",
    "    bst, rmse = xgboost_data(X_pca_train, y_pca_train, X_pca_test, y_pca_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"PCA\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nFA Dataset\")\n",
    "    bst, rmse = xgboost_data(X_fa_train, y_fa_train, X_fa_test, y_fa_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"FA\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")    \n",
    "    \n",
    "try:\n",
    "    print(\"\\nCluster Dataset\")\n",
    "    bst, rmse = xgboost_data(X_cl_train, y_cl_train, X_cl_test, y_cl_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"Cluster\")\n",
    "\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:    \n",
    "    print(\"\\nPCA Cluster Dataset\")\n",
    "    bst, rmse = xgboost_data(X_pca_cl_train, y_pca_cl_train, X_pca_cl_test, y_pca_cl_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"PCA Cluster\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "try:    \n",
    "    print(\"\\nFA Cluster Dataset\")\n",
    "    bst, rmse = xgboost_data(X_fa_cl_train, y_fa_cl_train, X_fa_cl_test, y_fa_cl_test)\n",
    "    best_bst, best_rmse, best_name = update_best_model(best_bst, best_rmse, best_name, bst, rmse, \"FA Cluster\")\n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "    \n",
    "print(\"\\n--------------------\\nBest Dataset:\", best_name)\n",
    "print(\"Best RMSE:\", best_rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Split Cluster Dataset\n",
      "Cluster 0\n",
      "[08:08:27] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2131.906846385313\n",
      "RMSE:  2858.3778081175615\n",
      "Cluster 1\n",
      "[08:08:34] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2146.914476866796\n",
      "RMSE:  2893.2398201651467\n",
      "Cluster 2\n",
      "[08:08:39] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2172.750778835954\n",
      "RMSE:  2928.4275711799346\n",
      "\n",
      "Split PCA Cluster Dataset\n",
      "PCA Cluster 0\n",
      "[08:08:44] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2139.7543129654587\n",
      "RMSE:  2898.462014911795\n",
      "PCA Cluster 1\n",
      "[08:08:51] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2169.453574340481\n",
      "RMSE:  2927.4705796513954\n",
      "PCA Cluster 2\n",
      "[08:08:59] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2128.240534579562\n",
      "RMSE:  2864.9991842174104\n",
      "\n",
      "Split FA Cluster Dataset\n",
      "FA Cluster 0\n",
      "[08:09:07] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2186.5843502439234\n",
      "RMSE:  2943.5309330259797\n",
      "FA Cluster 1\n",
      "[08:09:14] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2124.699776946237\n",
      "RMSE:  2853.8359983040637\n",
      "FA Cluster 2\n",
      "[08:09:22] Tree method is selected to be 'hist', which uses a single updater grow_fast_histmaker.\n",
      "MAE:  2142.193407637804\n",
      "RMSE:  2901.620966975743\n",
      "\n",
      "--------------------\n",
      "Best Dataset: Cluster\n",
      "Best RMSE: 2893.348399820881\n"
     ]
    }
   ],
   "source": [
    "best_bsts = []\n",
    "best_multi_name = \"\"\n",
    "best_avg_rmse = -1\n",
    "\n",
    "try:\n",
    "    print(\"Split Cluster Dataset\")\n",
    "\n",
    "    total_rmse = 0\n",
    "    bsts = []\n",
    "    for i in range(len(X_cl_trains)):\n",
    "        print(\"Cluster\", i)\n",
    "        bst, rmse = xgboost_data(X_cl_trains[i], y_cl_trains[i], X_cl_tests[i], y_cl_tests[i])\n",
    "        bsts.append(bst)\n",
    "        total_rmse = total_rmse + rmse\n",
    "\n",
    "    best_bsts, best_avg_rmse, best_multi_name = update_best_model(best_bsts, best_avg_rmse, best_multi_name, bsts, total_rmse/len(X_cl_trains), \"Cluster\")  \n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "\n",
    "try:\n",
    "    print(\"\\nSplit PCA Cluster Dataset\")\n",
    "\n",
    "    total_rmse = 0\n",
    "    bsts = []\n",
    "    for i in range(len(X_pca_cl_trains)):\n",
    "        print(\"PCA Cluster\", i)\n",
    "        bst, rmse = xgboost_data(X_pca_cl_trains[i], y_pca_cl_trains[i], X_pca_cl_tests[i], y_pca_cl_tests[i])\n",
    "        bsts.append(bst)\n",
    "        total_rmse = total_rmse + rmse\n",
    "\n",
    "    best_bsts, best_avg_rmse, best_multi_name = update_best_model(best_bsts, best_avg_rmse, best_multi_name, bsts, total_rmse/len(X_pca_cl_trains), \"PCA Cluster\")  \n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "try:\n",
    "    print(\"\\nSplit FA Cluster Dataset\")\n",
    "\n",
    "    total_rmse = 0\n",
    "    bsts = []\n",
    "    for i in range(len(X_fa_cl_trains)):\n",
    "        print(\"FA Cluster\", i)\n",
    "        bst, rmse = xgboost_data(X_fa_cl_trains[i], y_fa_cl_trains[i], X_fa_cl_tests[i], y_fa_cl_tests[i])\n",
    "        bsts.append(bst)\n",
    "        total_rmse = total_rmse + rmse\n",
    "\n",
    "    best_bsts, best_avg_rmse, best_multi_name = update_best_model(best_bsts, best_avg_rmse, best_multi_name, bsts, total_rmse/len(X_fa_cl_trains), \"PCA Cluster\")  \n",
    "except:\n",
    "    print (\"Create model dataframe first!\")\n",
    "\n",
    "print(\"\\n--------------------\\nBest Dataset:\", best_multi_name)\n",
    "print(\"Best RMSE:\", best_avg_rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Save Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save XGB Model and Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_data(name, split = False, cluster = False, split_index = 0):\n",
    "    if split:\n",
    "        if name in ['Model', 'Cluster']:\n",
    "            return (X_clusters[split_index].drop(predictor, axis = 1), X_clusters[split_index][predictor])\n",
    "        elif name in ['PCA', 'PCA Cluster']:\n",
    "            return (X_pca_clusters[split_index].drop(predictor, axis = 1), X_pca_clusters[split_index][predictor])\n",
    "        elif name in ['FA', 'FA Cluster']:\n",
    "            return (X_fa_clusters[split_index].drop(predictor, axis = 1), X_fa_clusters[split_index][predictor])\n",
    "    elif cluster:\n",
    "        if name in ['Model', 'Cluster']:\n",
    "            return X_cluster, y\n",
    "        elif name in ['PCA', 'PCA Cluster']:\n",
    "            return X_pca_cluster, y\n",
    "        elif name in ['FA', 'FA Cluster']:\n",
    "            return X_fa_cluster, y\n",
    "    else:\n",
    "        if name == 'Model':\n",
    "            return X, y\n",
    "        elif name == 'PCA':\n",
    "            return X_pca, y\n",
    "        elif name == 'FA':\n",
    "            return X_fa, y\n",
    "        elif name == 'Cluster':\n",
    "            return X_cluster.drop('cluster_num', axis = 1), y\n",
    "        elif name == 'PCA Cluster':\n",
    "            return X_pca_cluster.drop('cluster_num', axis = 1), y\n",
    "        elif name == 'FA Cluster':\n",
    "            return X_fa_cluster.drop('cluster_num', axis = 1), y\n",
    "\n",
    "def save_model_and_data(bst, name):\n",
    "    print(\"Zipping model and data\\n----------------\")\n",
    "    with ZipFile('outputs/xgb_model_and_data.zip', 'w', zipfile.ZIP_DEFLATED) as myzip:\n",
    "        X_data, y = get_data(name) \n",
    "        bst.save_model('outputs/xgb_model.bin') # saves model to local disk\n",
    "        xgb.DMatrix(X_data, label=y).save_binary('outputs/xgb_data.buffer') # saves model data to local disk\n",
    "        myzip.write('outputs/xgb_data.buffer') # saves model data to zip so it can be saved on github\n",
    "        myzip.write('outputs/xgb_model.bin')\n",
    "    print(\"Done!\")\n",
    "\n",
    "def save_multi_model_and_data(bsts, name):\n",
    "    print(\"Zipping models and data\\n----------------\")\n",
    "    with ZipFile('outputs/xgb_models_and_data.zip', 'w', zipfile.ZIP_DEFLATED) as myzip:\n",
    "        for i, bst in zip(range(len(bsts)), bsts):\n",
    "            print(\"Zipping for Cluster\", i)\n",
    "            X_data, y = get_data(name, split = True, split_index = i)\n",
    "            bst.save_model('outputs/xgb_model%d.bin' % i) # saves model to local disk\n",
    "            xgb.DMatrix(X_data, label=y).save_binary('outputs/xgb_data%d.buffer' % i) # saves model data to local disk\n",
    "            myzip.write('outputs/xgb_data%d.buffer' % i) # saves model data to zip so it can be saved on github\n",
    "            myzip.write('outputs/xgb_model%d.bin' % i)\n",
    "    print(\"----------------\\nDone!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zipping model and data\n",
      "----------------\n",
      "Done!\n",
      "\n",
      "Zipping models and data\n",
      "----------------\n",
      "Zipping for Cluster 0\n",
      "Zipping for Cluster 1\n",
      "Zipping for Cluster 2\n",
      "----------------\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    save_model_and_data(best_bst, best_name)\n",
    "except:\n",
    "    print(\"Run XGB modeling first!\")\n",
    "print(\"\")\n",
    "try:\n",
    "    save_multi_model_and_data(best_bsts, best_multi_name)\n",
    "except:\n",
    "    print(\"Run split XGB modeling first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save User Cluster Assignments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "# uses the minimal_preprocess dataset\n",
    "def write_cluster_dataset(X_cl, name):\n",
    "    min_df = pd.read_csv(\"inputs/minimal_preprocess.csv\")\n",
    "    min_demo = ['gender', 'age', 'years_in_city', 'married', 'city', 'occ']\n",
    "    start = pd.DataFrame(min_df['u_id']).join(min_df['p_id'])\n",
    "    outcluster = start.join(pd.DataFrame(X_cl['cluster_num'])).join(min_df.drop(['u_id', 'p_id'], axis = 1))\n",
    "    outcluster.to_csv(\"outputs/%s.csv\" % name, encoding='utf-8', index = False)\n",
    "    return outcluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing User Cluster Assignments\n",
      "------------------\n",
      "Done!\n",
      "\n",
      "Writing Multi User Cluster Assignments\n",
      "------------------\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(\"Writing User Cluster Assignments\\n------------------\")\n",
    "    cluster_data, y = get_data(best_name, cluster = True)\n",
    "    write_cluster_dataset(cluster_data, \"user_cluster_assignments\")\n",
    "    print(\"Done!\")\n",
    "except:\n",
    "    print(\"Run XGB modeling first!\")\n",
    "\n",
    "print(\"\")  \n",
    "\n",
    "try:\n",
    "    print(\"Writing Multi User Cluster Assignments\\n------------------\")\n",
    "    cluster_data, y = get_data(best_multi_name, cluster = True)\n",
    "    cluster_data['colFromIndex'] = cluster_data.index\n",
    "    cluster_data = cluster_data.sort_values(['cluster_num', 'colFromIndex']).drop('colFromIndex', axis = 1)\n",
    "    write_cluster_dataset(cluster_data, \"user_multi_cluster_assignments\")\n",
    "    print(\"Done!\")\n",
    "except:\n",
    "    print(\"Run split XGB modeling first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gradient Boost Regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Iter       Train Loss   Remaining Time \n",
      "         1    16221645.0535            4.78m\n",
      "         2    13065914.7181            4.55m\n",
      "         3    10602313.8467            4.44m\n",
      "         4     9715728.7413            4.16m\n",
      "         5     9419597.2898            4.02m\n",
      "         6     9261543.8304            3.91m\n",
      "         7     9128276.0273            3.87m\n",
      "         8     9053171.4313            3.78m\n",
      "         9     8997516.7107            3.73m\n",
      "        10     8950024.7879            3.64m\n",
      "        11     8905513.6901            3.66m\n",
      "        12     8881135.2198            3.67m\n",
      "        13     8852741.0655            3.64m\n",
      "        14     8822221.0665            3.64m\n",
      "        15     8804191.9498            3.58m\n",
      "        16     8774665.4730            3.63m\n",
      "        17     8756341.4232            3.58m\n",
      "        18     8740436.5772            3.50m\n",
      "        19     8714358.7594            3.46m\n",
      "        20     8696167.5447            3.42m\n",
      "        21     8655346.9308            3.37m\n",
      "        22     8617291.5468            3.32m\n",
      "        23     8602176.7138            3.26m\n",
      "        24     8591183.9890            3.20m\n",
      "        25     8577617.8273            3.13m\n",
      "        26     8563417.0526            3.09m\n",
      "        27     8551720.7012            3.03m\n",
      "        28     8539861.3678            2.97m\n",
      "        29     8525573.8247            2.95m\n",
      "        30     8517069.9420            2.94m\n",
      "        31     8504173.5016            2.93m\n",
      "        32     8491340.5660            2.93m\n",
      "        33     8477162.6197            2.92m\n",
      "        34     8463270.5207            2.89m\n",
      "        35     8455249.8736            2.86m\n",
      "        36     8444674.6188            2.81m\n",
      "        37     8434674.2177            2.77m\n",
      "        38     8423686.3426            2.73m\n",
      "        39     8410031.9512            2.69m\n",
      "        40     8398777.4999            2.64m\n",
      "        41     8384904.7848            2.59m\n",
      "        42     8371828.2084            2.56m\n",
      "        43     8365418.0088            2.51m\n",
      "        44     8356192.3370            2.48m\n",
      "        45     8350134.6114            2.43m\n",
      "        46     8345070.4859            2.38m\n",
      "        47     8336997.3839            2.34m\n",
      "        48     8330735.2856            2.30m\n",
      "        49     8322985.3630            2.25m\n",
      "        50     8315258.2316            2.21m\n",
      "        51     8309954.0310            2.17m\n",
      "        52     8302662.5342            2.13m\n",
      "        53     8296914.4673            2.08m\n",
      "        54     8291131.2541            2.04m\n",
      "        55     8285391.4864            1.99m\n",
      "        56     8278772.5992            1.95m\n",
      "        57     8274366.1200            1.91m\n",
      "        58     8270495.0280            1.86m\n",
      "        59     8264505.9145            1.81m\n",
      "        60     8258686.8944            1.76m\n",
      "        61     8253418.1925            1.72m\n",
      "        62     8248719.8203            1.67m\n",
      "        63     8244052.4268            1.63m\n",
      "        64     8237858.0912            1.59m\n",
      "        65     8233893.8262            1.54m\n",
      "        66     8227781.3958            1.49m\n",
      "        67     8219153.1567            1.45m\n",
      "        68     8213149.4180            1.41m\n",
      "        69     8209218.7954            1.36m\n",
      "        70     8205759.8438            1.31m\n",
      "        71     8199655.9923            1.28m\n",
      "        72     8195812.4707            1.23m\n",
      "        73     8192009.5406            1.19m\n",
      "        74     8188335.7406            1.14m\n",
      "        75     8185355.8695            1.10m\n",
      "        76     8182044.6314            1.05m\n",
      "        77     8177560.9045            1.01m\n",
      "        78     8172825.3139           57.76s\n",
      "        79     8169315.8917           55.30s\n",
      "        80     8165415.5137           52.73s\n",
      "        81     8162393.4229           50.23s\n",
      "        82     8160139.4080           47.53s\n",
      "        83     8155139.1188           45.03s\n",
      "        84     8152659.1517           42.41s\n",
      "        85     8148845.8915           39.76s\n",
      "        86     8143148.1461           37.10s\n",
      "        87     8140502.0663           34.49s\n",
      "        88     8137733.3224           31.81s\n",
      "        89     8133817.8386           29.13s\n",
      "        90     8129631.6373           26.51s\n",
      "        91     8127874.1994           23.82s\n",
      "        92     8125353.1503           21.14s\n",
      "        93     8122017.3592           18.45s\n",
      "        94     8119540.0635           15.77s\n",
      "        95     8117487.4573           13.13s\n",
      "        96     8114118.0321           10.47s\n",
      "        97     8110256.5410            7.85s\n",
      "        98     8099787.3398            5.22s\n",
      "        99     8094875.3720            2.60s\n",
      "       100     8090867.1090            0.00s\n",
      "MAE:  2165.8501750058804\n",
      "R^2 Score:  0.5072244413344393\n"
     ]
    }
   ],
   "source": [
    "learning_rates = [1.5]\n",
    "for learning_rate in learning_rates:\n",
    "    gb = GradientBoostingRegressor(learning_rate = learning_rate, random_state = 42, max_leaf_nodes = 300, verbose = 2).fit(X_pca_train, y_pca_train)\n",
    "    pred = gb.predict(X_pca_test)\n",
    "    print(\"MAE: \", mean_absolute_error(pred, y_pca_test))\n",
    "    print(\"MSE: \", mean_squared_error(pred, y_pca_test))"
   ]
  }
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