notebooks/ML/Linear Regression/Reguralization_https_www.kaggle.com-code-apapiu-regularized-linear-models.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3c2830f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from random import random\n",
    "#from mpl_toolkits.mplot3d import axes3d\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "\n",
    "from scipy.stats import skew"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d731f9c9",
   "metadata": {},
   "source": [
    "<h1> Reguralization <h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f8611f58",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#load dataset kaggle competitions download -c house-prices-advanced-regression-techniques\n",
    "train= pd.read_csv(\"../../../resources/data/train_pricing_house.csv\")  \n",
    "test= pd.read_csv(\"../../../resources/data/test_pricing_house.csv\")  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "97dda631",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Alley</th>\n",
       "      <th>LotShape</th>\n",
       "      <th>LandContour</th>\n",
       "      <th>Utilities</th>\n",
       "      <th>...</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>Fence</th>\n",
       "      <th>MiscFeature</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SaleType</th>\n",
       "      <th>SaleCondition</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>208500</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>181500</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>Pave</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "      <td>140000</td>\n",
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       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 81 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
       "0   1          60       RL         65.0     8450   Pave   NaN      Reg   \n",
       "1   2          20       RL         80.0     9600   Pave   NaN      Reg   \n",
       "2   3          60       RL         68.0    11250   Pave   NaN      IR1   \n",
       "3   4          70       RL         60.0     9550   Pave   NaN      IR1   \n",
       "4   5          60       RL         84.0    14260   Pave   NaN      IR1   \n",
       "\n",
       "  LandContour Utilities  ... PoolArea PoolQC Fence MiscFeature MiscVal MoSold  \\\n",
       "0         Lvl    AllPub  ...        0    NaN   NaN         NaN       0      2   \n",
       "1         Lvl    AllPub  ...        0    NaN   NaN         NaN       0      5   \n",
       "2         Lvl    AllPub  ...        0    NaN   NaN         NaN       0      9   \n",
       "3         Lvl    AllPub  ...        0    NaN   NaN         NaN       0      2   \n",
       "4         Lvl    AllPub  ...        0    NaN   NaN         NaN       0     12   \n",
       "\n",
       "  YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0   2008        WD         Normal     208500  \n",
       "1   2007        WD         Normal     181500  \n",
       "2   2008        WD         Normal     223500  \n",
       "3   2006        WD        Abnorml     140000  \n",
       "4   2008        WD         Normal     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
      ]
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     "execution_count": 16,
     "metadata": {},
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   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56e916ab",
   "metadata": {},
   "source": [
    "<h2> Data preprosesing </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "952e7027",
   "metadata": {},
   "source": [
    "* First I'll transform the skewed numeric features by taking log(feature + 1) - this will make the features more normal\n",
    "* Create Dummy variables for the categorical features\n",
    "* Replace the numeric missing values (NaN's) with the mean of their respective columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cc8fbdfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (12.0, 6.0)\n",
    "prices = pd.DataFrame({\"price\": train[\"SalePrice\"],\"log(price+1)\": np.log1p(train[\"SalePrice\"])})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b7c9515c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>price</th>\n",
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      "text/plain": [
       "       price  log(price+1)\n",
       "0     208500     12.247699\n",
       "1     181500     12.109016\n",
       "2     223500     12.317171\n",
       "3     140000     11.849405\n",
       "4     250000     12.429220\n",
       "...      ...           ...\n",
       "1455  175000     12.072547\n",
       "1456  210000     12.254868\n",
       "1457  266500     12.493133\n",
       "1458  142125     11.864469\n",
       "1459  147500     11.901590\n",
       "\n",
       "[1460 rows x 2 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "056ac5fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'price'}>,\n",
       "        <AxesSubplot:title={'center':'log(price+1)'}>]], dtype=object)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prices.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "70b7b767",
   "metadata": {},
   "outputs": [],
   "source": [
    "#log transform the target:\n",
    "train[\"SalePrice\"] = np.log1p(train['SalePrice'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b64fe9b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>MSZoning</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>Street</th>\n",
       "      <th>Alley</th>\n",
       "      <th>LotShape</th>\n",
       "      <th>LandContour</th>\n",
       "      <th>Utilities</th>\n",
       "      <th>LotConfig</th>\n",
       "      <th>...</th>\n",
       "      <th>ScreenPorch</th>\n",
       "      <th>PoolArea</th>\n",
       "      <th>PoolQC</th>\n",
       "      <th>Fence</th>\n",
       "      <th>MiscFeature</th>\n",
       "      <th>MiscVal</th>\n",
       "      <th>MoSold</th>\n",
       "      <th>YrSold</th>\n",
       "      <th>SaleType</th>\n",
       "      <th>SaleCondition</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>65.0</td>\n",
       "      <td>8450</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20</td>\n",
       "      <td>RL</td>\n",
       "      <td>80.0</td>\n",
       "      <td>9600</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>FR2</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2007</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>68.0</td>\n",
       "      <td>11250</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Corner</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>84.0</td>\n",
       "      <td>14260</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR1</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>FR2</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1454</th>\n",
       "      <td>160</td>\n",
       "      <td>RM</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1936</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1455</th>\n",
       "      <td>160</td>\n",
       "      <td>RM</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1894</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1456</th>\n",
       "      <td>20</td>\n",
       "      <td>RL</td>\n",
       "      <td>160.0</td>\n",
       "      <td>20000</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1457</th>\n",
       "      <td>85</td>\n",
       "      <td>RL</td>\n",
       "      <td>62.0</td>\n",
       "      <td>10441</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>MnPrv</td>\n",
       "      <td>Shed</td>\n",
       "      <td>700</td>\n",
       "      <td>7</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1458</th>\n",
       "      <td>60</td>\n",
       "      <td>RL</td>\n",
       "      <td>74.0</td>\n",
       "      <td>9627</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
       "      <td>AllPub</td>\n",
       "      <td>Inside</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2919 rows × 79 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
       "0             60       RL         65.0     8450   Pave   NaN      Reg   \n",
       "1             20       RL         80.0     9600   Pave   NaN      Reg   \n",
       "2             60       RL         68.0    11250   Pave   NaN      IR1   \n",
       "3             70       RL         60.0     9550   Pave   NaN      IR1   \n",
       "4             60       RL         84.0    14260   Pave   NaN      IR1   \n",
       "...          ...      ...          ...      ...    ...   ...      ...   \n",
       "1454         160       RM         21.0     1936   Pave   NaN      Reg   \n",
       "1455         160       RM         21.0     1894   Pave   NaN      Reg   \n",
       "1456          20       RL        160.0    20000   Pave   NaN      Reg   \n",
       "1457          85       RL         62.0    10441   Pave   NaN      Reg   \n",
       "1458          60       RL         74.0     9627   Pave   NaN      Reg   \n",
       "\n",
       "     LandContour Utilities LotConfig  ... ScreenPorch PoolArea PoolQC  Fence  \\\n",
       "0            Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "1            Lvl    AllPub       FR2  ...           0        0    NaN    NaN   \n",
       "2            Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "3            Lvl    AllPub    Corner  ...           0        0    NaN    NaN   \n",
       "4            Lvl    AllPub       FR2  ...           0        0    NaN    NaN   \n",
       "...          ...       ...       ...  ...         ...      ...    ...    ...   \n",
       "1454         Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "1455         Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "1456         Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "1457         Lvl    AllPub    Inside  ...           0        0    NaN  MnPrv   \n",
       "1458         Lvl    AllPub    Inside  ...           0        0    NaN    NaN   \n",
       "\n",
       "     MiscFeature MiscVal  MoSold  YrSold  SaleType  SaleCondition  \n",
       "0            NaN       0       2    2008        WD         Normal  \n",
       "1            NaN       0       5    2007        WD         Normal  \n",
       "2            NaN       0       9    2008        WD         Normal  \n",
       "3            NaN       0       2    2006        WD        Abnorml  \n",
       "4            NaN       0      12    2008        WD         Normal  \n",
       "...          ...     ...     ...     ...       ...            ...  \n",
       "1454         NaN       0       6    2006        WD         Normal  \n",
       "1455         NaN       0       4    2006        WD        Abnorml  \n",
       "1456         NaN       0       9    2006        WD        Abnorml  \n",
       "1457        Shed     700       7    2006        WD         Normal  \n",
       "1458         NaN       0      11    2006        WD         Normal  \n",
       "\n",
       "[2919 rows x 79 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#log transform skewed numeric features:\n",
    "all_data = pd.concat((train.loc[:,'MSSubClass':'SaleCondition'],\n",
    "                      test.loc[:,'MSSubClass':'SaleCondition']))\n",
    "all_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "64d1fd4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MSSubClass         int64\n",
       "MSZoning          object\n",
       "LotFrontage      float64\n",
       "LotArea            int64\n",
       "Street            object\n",
       "                  ...   \n",
       "MiscVal            int64\n",
       "MoSold             int64\n",
       "YrSold             int64\n",
       "SaleType          object\n",
       "SaleCondition     object\n",
       "Length: 79, dtype: object"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6d43243a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['MSSubClass', 'LotFrontage', 'LotArea', 'OverallQual', 'OverallCond',\n",
       "       'YearBuilt', 'YearRemodAdd', 'MasVnrArea', 'BsmtFinSF1', 'BsmtFinSF2',\n",
       "       'BsmtUnfSF', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', 'LowQualFinSF',\n",
       "       'GrLivArea', 'BsmtFullBath', 'BsmtHalfBath', 'FullBath', 'HalfBath',\n",
       "       'BedroomAbvGr', 'KitchenAbvGr', 'TotRmsAbvGrd', 'Fireplaces',\n",
       "       'GarageYrBlt', 'GarageCars', 'GarageArea', 'WoodDeckSF', 'OpenPorchSF',\n",
       "       'EnclosedPorch', '3SsnPorch', 'ScreenPorch', 'PoolArea', 'MiscVal',\n",
       "       'MoSold', 'YrSold'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_feats = all_data.dtypes[all_data.dtypes != \"object\"].index\n",
    "numeric_feats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "bf289c0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['MSSubClass', 'LotFrontage', 'LotArea', 'MasVnrArea', 'BsmtFinSF1',\n",
       "       'BsmtFinSF2', 'BsmtUnfSF', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF',\n",
       "       'LowQualFinSF', 'GrLivArea', 'BsmtHalfBath', 'KitchenAbvGr',\n",
       "       'WoodDeckSF', 'OpenPorchSF', 'EnclosedPorch', '3SsnPorch',\n",
       "       'ScreenPorch', 'PoolArea', 'MiscVal'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skewed_feats = train[numeric_feats].apply(lambda x: skew(x.dropna())) #compute skewness\n",
    "skewed_feats = skewed_feats[skewed_feats > 0.75]\n",
    "skewed_feats = skewed_feats.index\n",
    "skewed_feats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "924c7fe5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MSSubClass</th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>OverallCond</th>\n",
       "      <th>YearBuilt</th>\n",
       "      <th>YearRemodAdd</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <th>...</th>\n",
       "      <th>SaleType_ConLw</th>\n",
       "      <th>SaleType_New</th>\n",
       "      <th>SaleType_Oth</th>\n",
       "      <th>SaleType_WD</th>\n",
       "      <th>SaleCondition_Abnorml</th>\n",
       "      <th>SaleCondition_AdjLand</th>\n",
       "      <th>SaleCondition_Alloca</th>\n",
       "      <th>SaleCondition_Family</th>\n",
       "      <th>SaleCondition_Normal</th>\n",
       "      <th>SaleCondition_Partial</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.967505</td>\n",
       "      <td>0.973301</td>\n",
       "      <td>1.195975</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2003</td>\n",
       "      <td>2003</td>\n",
       "      <td>1.043057</td>\n",
       "      <td>1.106252</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.874370</td>\n",
       "      <td>0.987819</td>\n",
       "      <td>1.199786</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>1976</td>\n",
       "      <td>1976</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.120099</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.967505</td>\n",
       "      <td>0.976519</td>\n",
       "      <td>1.204436</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2001</td>\n",
       "      <td>2002</td>\n",
       "      <td>1.032210</td>\n",
       "      <td>1.089386</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.978567</td>\n",
       "      <td>0.967505</td>\n",
       "      <td>1.199631</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1915</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.048424</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</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>0.967505</td>\n",
       "      <td>0.991126</td>\n",
       "      <td>1.211219</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>2000</td>\n",
       "      <td>2000</td>\n",
       "      <td>1.073575</td>\n",
       "      <td>1.102955</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1454</th>\n",
       "      <td>1.031488</td>\n",
       "      <td>0.879129</td>\n",
       "      <td>1.146811</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>1970</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1455</th>\n",
       "      <td>1.031488</td>\n",
       "      <td>0.879129</td>\n",
       "      <td>1.145997</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>1970</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.056722</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</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>1456</th>\n",
       "      <td>0.874370</td>\n",
       "      <td>1.031488</td>\n",
       "      <td>1.220561</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1960</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.129201</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</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>1457</th>\n",
       "      <td>0.991922</td>\n",
       "      <td>0.969893</td>\n",
       "      <td>1.202260</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1992</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.071688</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1458</th>\n",
       "      <td>0.967505</td>\n",
       "      <td>0.982453</td>\n",
       "      <td>1.199869</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>1993</td>\n",
       "      <td>1994</td>\n",
       "      <td>0.998606</td>\n",
       "      <td>1.109338</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2919 rows × 288 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      MSSubClass  LotFrontage   LotArea  OverallQual  OverallCond  YearBuilt  \\\n",
       "0       0.967505     0.973301  1.195975            7            5       2003   \n",
       "1       0.874370     0.987819  1.199786            6            8       1976   \n",
       "2       0.967505     0.976519  1.204436            7            5       2001   \n",
       "3       0.978567     0.967505  1.199631            7            5       1915   \n",
       "4       0.967505     0.991126  1.211219            8            5       2000   \n",
       "...          ...          ...       ...          ...          ...        ...   \n",
       "1454    1.031488     0.879129  1.146811            4            7       1970   \n",
       "1455    1.031488     0.879129  1.145997            4            5       1970   \n",
       "1456    0.874370     1.031488  1.220561            5            7       1960   \n",
       "1457    0.991922     0.969893  1.202260            5            5       1992   \n",
       "1458    0.967505     0.982453  1.199869            7            5       1993   \n",
       "\n",
       "      YearRemodAdd  MasVnrArea  BsmtFinSF1  BsmtFinSF2  ...  SaleType_ConLw  \\\n",
       "0             2003    1.043057    1.106252         0.0  ...               0   \n",
       "1             1976    0.000000    1.120099         0.0  ...               0   \n",
       "2             2002    1.032210    1.089386         0.0  ...               0   \n",
       "3             1970    0.000000    1.048424         0.0  ...               0   \n",
       "4             2000    1.073575    1.102955         0.0  ...               0   \n",
       "...            ...         ...         ...         ...  ...             ...   \n",
       "1454          1970    0.000000    0.000000         0.0  ...               0   \n",
       "1455          1970    0.000000    1.056722         0.0  ...               0   \n",
       "1456          1996    0.000000    1.129201         0.0  ...               0   \n",
       "1457          1992    0.000000    1.071688         0.0  ...               0   \n",
       "1458          1994    0.998606    1.109338         0.0  ...               0   \n",
       "\n",
       "      SaleType_New  SaleType_Oth  SaleType_WD  SaleCondition_Abnorml  \\\n",
       "0                0             0            1                      0   \n",
       "1                0             0            1                      0   \n",
       "2                0             0            1                      0   \n",
       "3                0             0            1                      1   \n",
       "4                0             0            1                      0   \n",
       "...            ...           ...          ...                    ...   \n",
       "1454             0             0            1                      0   \n",
       "1455             0             0            1                      1   \n",
       "1456             0             0            1                      1   \n",
       "1457             0             0            1                      0   \n",
       "1458             0             0            1                      0   \n",
       "\n",
       "      SaleCondition_AdjLand  SaleCondition_Alloca  SaleCondition_Family  \\\n",
       "0                         0                     0                     0   \n",
       "1                         0                     0                     0   \n",
       "2                         0                     0                     0   \n",
       "3                         0                     0                     0   \n",
       "4                         0                     0                     0   \n",
       "...                     ...                   ...                   ...   \n",
       "1454                      0                     0                     0   \n",
       "1455                      0                     0                     0   \n",
       "1456                      0                     0                     0   \n",
       "1457                      0                     0                     0   \n",
       "1458                      0                     0                     0   \n",
       "\n",
       "      SaleCondition_Normal  SaleCondition_Partial  \n",
       "0                        1                      0  \n",
       "1                        1                      0  \n",
       "2                        1                      0  \n",
       "3                        0                      0  \n",
       "4                        1                      0  \n",
       "...                    ...                    ...  \n",
       "1454                     1                      0  \n",
       "1455                     0                      0  \n",
       "1456                     0                      0  \n",
       "1457                     1                      0  \n",
       "1458                     1                      0  \n",
       "\n",
       "[2919 rows x 288 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_data[skewed_feats] = np.log1p(all_data[skewed_feats])\n",
    "all_data = pd.get_dummies(all_data)\n",
    "all_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "26f24367",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data.mean()\n",
    "all_data = all_data.fillna(all_data.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "03f6f5ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = all_data[:train.shape[0]] #train.shape[0]]\n",
    "X_test = all_data[train.shape[0]:]\n",
    "y = train.SalePrice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "04fc5022",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train.to_csv('train-data-price.csv', index=False)\n",
    "X_test.to_csv('train-data-price.csv', index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6688ca2",
   "metadata": {},
   "source": [
    "Models\n",
    "Now we are going to use regularized linear regression models from the scikit learn module. I'm going to try both l_1(Lasso) and l_2(Ridge) regularization. I'll also define a function that returns the cross-validation rmse error so we can evaluate our models and pick the best tuning par"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "f458bbd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge, RidgeCV, ElasticNet, LassoCV, LassoLarsCV\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "1a46af1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "58504446",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ridge = Ridge()\n",
    "alphas = [0.05, 0.1, 0.3, 1, 3, 5, 10, 15, 30, 50, 75]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "d648baf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "rmse= np.sqrt(-cross_val_score(model_ridge, X_train, y, scoring=\"neg_mean_squared_error\", cv = 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fe0db721",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01030121, 0.01198328, 0.01180427, 0.00965649, 0.01228641])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "264f71e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.06114922e-04, -1.43598921e-04, -1.39340714e-04, -9.32478735e-05,\n",
       "       -1.50955803e-04])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(model_ridge, X_train, y, scoring=\"neg_mean_squared_error\", cv = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "c8062974",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def rmse_cv(model):\n",
    "    rmse= np.sqrt(-cross_val_score(model, X_train, y, scoring=\"neg_mean_squared_error\", cv = 5))\n",
    "    return(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef97f1fa",
   "metadata": {},
   "source": [
    "The main tuning parameter for the Ridge model is alpha - a regularization parameter that measures how flexible our model is. The higher the regularization the less prone our model will be to overfit. However it will also lose flexibility and might not capture all of the signal in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "80158b30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.011137775956204429,\n",
       " 0.011206399140055896,\n",
       " 0.011299822809983094,\n",
       " 0.01120633085517515,\n",
       " 0.011021809345886391,\n",
       " 0.010950013403660397,\n",
       " 0.010893762031479539,\n",
       " 0.01088911468584063,\n",
       " 0.010940033311288629,\n",
       " 0.01103179175472883,\n",
       " 0.011140578731117384]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = [0.05, 0.1, 0.3, 1, 3, 5, 10, 15, 30, 50, 75]\n",
    "cv_ridge = [rmse_cv(Ridge(alpha = alpha)).mean() \n",
    "            for alpha in alphas]\n",
    "cv_ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "36795705",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'rmse')"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "cv_ridge = pd.Series(cv_ridge, index = alphas)\n",
    "cv_ridge.plot(title = \"Validation - Just Do It\")\n",
    "plt.xlabel(\"alpha\")\n",
    "plt.ylabel(\"rmse\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdc4118e",
   "metadata": {},
   "source": [
    "So for the Ridge regression we get a rmsle of about 0.127\n",
    "\n",
    "Let' try out the Lasso model. We will do a slightly different approach here and use the built in Lasso CV to figure out the best alpha for us. For some reason the alphas in Lasso CV are really the inverse or the alphas in Ridge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "050faae3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012495387466705279"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_lasso = LassoCV(alphas = [1, 0.1, 0.001, 0.0005]).fit(X_train, y)\n",
    "rmse_cv(model_lasso).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "570fb610",
   "metadata": {},
   "outputs": [],
   "source": [
    "coef = pd.Series(model_lasso.coef_, index = X_train.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "8461ad20",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso picked 21 variables and eliminated the other 267 variables\n"
     ]
    }
   ],
   "source": [
    "print(\"Lasso picked \" + str(sum(coef != 0)) + \" variables and eliminated the other \" +  str(sum(coef == 0)) + \" variables\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "367a4ab7",
   "metadata": {},
   "source": [
    "Good job Lasso. One thing to note here however is that the features selected are not necessarily the \"correct\" ones - especially since there are a lot of collinear features in this dataset. One idea to try here is run Lasso a few times on boostrapped samples and see how stable the feature selection is."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6431a68",
   "metadata": {},
   "source": [
    "We can also take a look directly at what the most important coefficients are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "a328d756",
   "metadata": {},
   "outputs": [],
   "source": [
    "imp_coef = pd.concat([coef.sort_values().head(10),\n",
    "                     coef.sort_values().tail(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "fc83b925",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Coefficients in the Lasso Model')"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (8.0, 10.0)\n",
    "imp_coef.plot(kind = \"barh\")\n",
    "plt.title(\"Coefficients in the Lasso Model\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7370610",
   "metadata": {},
   "source": [
    "https://www.kaggle.com/code/apapiu/regularized-linear-models <br>\n",
    "\n",
    "https://web.stanford.edu/~hastie/StatLearnSparsity_files/SLS.pdf <br>\n",
    "\n",
    "https://www.cs.mcgill.ca/~dprecup/courses/ML/Lectures/ml-lecture02.pdf"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}