Assignment_2.ipynb

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    "# Linear Regression - Ridge Regression   \n",
    "-------------------------\n",
    "\n",
    "_Authors: Khal Makhoul, W.P.G.Peterson_  \n",
    "\n",
    "## Project Guide  \n",
    "\n",
    "--------------------\n",
    "- [Project Overview](#overview)  \n",
    "- [Data Review](#data)  \n",
    "- [Coding Ridge Regression](#code)\n",
    "- [Ridge Regression in `sklearn`](#sklearn)  \n",
    "\n",
    "<a id = \"overview\"></a>\n",
    "## Project Overview  \n",
    "-------------\n",
    "#### EXPECTED TIME 2.5 HRS  \n",
    "\n",
    "This assignment will test your ability to code your own version of ridge-regularized regression in `Python`. This assignment draws upon and presupposed the knowledge found in the lectures for Week 2. If ever a theoretical questions arises as to \"why\" we are doing something, please refer back to those lectures.  \n",
    "\n",
    "The assignment also builds upon the work performed in assignment 1 \"*Linear Regression - Least Squares*\". The data used will be the same. Though the last assignment tested your ability to read data into `Pandas` from a `.csv`. Those fundamental processes will not be directly tested here.\n",
    "\n",
    "In coding Ridge Regression you will be asked to:  \n",
    "- Mean center target variable and mean center / standardize observation  \n",
    "- Calculate Ridge Regression weights using linear algebra\n",
    "- Create a  hyperparameter tuning process   \n",
    "\n",
    "**Motivation**: Ridge Regression offers a way to mitigate some of the weaknesses of Least Squares Linear Regression to build more robust models.  \n",
    "\n",
    "**Objectives**: This assignmet will -  \n",
    "\n",
    "- Test `Python` competency and mathematical understandings of Ridge Regression\n",
    "- Begin to introduce the concept of hyper-parameter tuning  \n",
    "\n",
    "**Problem**: Using housing data, we will attempt to predict house price using living area with a regression model.  \n",
    "\n",
    "**Data**: Data comes from [Kaggle's House Prices Dataset](https://www.kaggle.com/c/house-prices-advanced-regression-techniques/data).  \n",
    "\n",
    "See above link for Description of data.\n",
    "\n",
    "<a id = \"data\"></a>  \n",
    "### Data Exploration\n",
    "\n",
    "Below provides a review of the \"Housing\" dataset."
   ]
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       "<div>\n",
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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",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\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>...</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",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\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>...</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",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <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",
       "      <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",
       "      <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",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2006</td>\n",
       "      <td>WD</td>\n",
       "      <td>Abnorml</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\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>...</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",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 81 columns</p>\n",
       "</div>"
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      "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  \\\n",
       "0         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "1         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "2         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "3         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "4         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
       "\n",
       "  MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0      2   2008        WD         Normal     208500  \n",
       "1      5   2007        WD         Normal     181500  \n",
       "2      9   2008        WD         Normal     223500  \n",
       "3      2   2006        WD        Abnorml     140000  \n",
       "4     12   2008        WD         Normal     250000  \n",
       "\n",
       "[5 rows x 81 columns]"
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    "### This cell imports the necessary modules and sets a few plotting parameters for display\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (20.0, 10.0)  \n",
    "\n",
    "### Read in the data\n",
    "tr_path = '../resource/asnlib/publicdata/train.csv'\n",
    "test_path = '../resource/asnlib/publicdata/test.csv'\n",
    "\n",
    "data = pd.read_csv(tr_path)  \n",
    "\n",
    "### The .head() function shows the first few lines of data for perspecitve\n",
    "data.head()"
   ]
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   "source": [
    "#### Question 1"
   ]
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     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1460 entries, 0 to 1459\n",
      "Data columns (total 81 columns):\n",
      "Id               1460 non-null int64\n",
      "MSSubClass       1460 non-null int64\n",
      "MSZoning         1460 non-null object\n",
      "LotFrontage      1201 non-null float64\n",
      "LotArea          1460 non-null int64\n",
      "Street           1460 non-null object\n",
      "Alley            91 non-null object\n",
      "LotShape         1460 non-null object\n",
      "LandContour      1460 non-null object\n",
      "Utilities        1460 non-null object\n",
      "LotConfig        1460 non-null object\n",
      "LandSlope        1460 non-null object\n",
      "Neighborhood     1460 non-null object\n",
      "Condition1       1460 non-null object\n",
      "Condition2       1460 non-null object\n",
      "BldgType         1460 non-null object\n",
      "HouseStyle       1460 non-null object\n",
      "OverallQual      1460 non-null int64\n",
      "OverallCond      1460 non-null int64\n",
      "YearBuilt        1460 non-null int64\n",
      "YearRemodAdd     1460 non-null int64\n",
      "RoofStyle        1460 non-null object\n",
      "RoofMatl         1460 non-null object\n",
      "Exterior1st      1460 non-null object\n",
      "Exterior2nd      1460 non-null object\n",
      "MasVnrType       1452 non-null object\n",
      "MasVnrArea       1452 non-null float64\n",
      "ExterQual        1460 non-null object\n",
      "ExterCond        1460 non-null object\n",
      "Foundation       1460 non-null object\n",
      "BsmtQual         1423 non-null object\n",
      "BsmtCond         1423 non-null object\n",
      "BsmtExposure     1422 non-null object\n",
      "BsmtFinType1     1423 non-null object\n",
      "BsmtFinSF1       1460 non-null int64\n",
      "BsmtFinType2     1422 non-null object\n",
      "BsmtFinSF2       1460 non-null int64\n",
      "BsmtUnfSF        1460 non-null int64\n",
      "TotalBsmtSF      1460 non-null int64\n",
      "Heating          1460 non-null object\n",
      "HeatingQC        1460 non-null object\n",
      "CentralAir       1460 non-null object\n",
      "Electrical       1459 non-null object\n",
      "1stFlrSF         1460 non-null int64\n",
      "2ndFlrSF         1460 non-null int64\n",
      "LowQualFinSF     1460 non-null int64\n",
      "GrLivArea        1460 non-null int64\n",
      "BsmtFullBath     1460 non-null int64\n",
      "BsmtHalfBath     1460 non-null int64\n",
      "FullBath         1460 non-null int64\n",
      "HalfBath         1460 non-null int64\n",
      "BedroomAbvGr     1460 non-null int64\n",
      "KitchenAbvGr     1460 non-null int64\n",
      "KitchenQual      1460 non-null object\n",
      "TotRmsAbvGrd     1460 non-null int64\n",
      "Functional       1460 non-null object\n",
      "Fireplaces       1460 non-null int64\n",
      "FireplaceQu      770 non-null object\n",
      "GarageType       1379 non-null object\n",
      "GarageYrBlt      1379 non-null float64\n",
      "GarageFinish     1379 non-null object\n",
      "GarageCars       1460 non-null int64\n",
      "GarageArea       1460 non-null int64\n",
      "GarageQual       1379 non-null object\n",
      "GarageCond       1379 non-null object\n",
      "PavedDrive       1460 non-null object\n",
      "WoodDeckSF       1460 non-null int64\n",
      "OpenPorchSF      1460 non-null int64\n",
      "EnclosedPorch    1460 non-null int64\n",
      "3SsnPorch        1460 non-null int64\n",
      "ScreenPorch      1460 non-null int64\n",
      "PoolArea         1460 non-null int64\n",
      "PoolQC           7 non-null object\n",
      "Fence            281 non-null object\n",
      "MiscFeature      54 non-null object\n",
      "MiscVal          1460 non-null int64\n",
      "MoSold           1460 non-null int64\n",
      "YrSold           1460 non-null int64\n",
      "SaleType         1460 non-null object\n",
      "SaleCondition    1460 non-null object\n",
      "SalePrice        1460 non-null int64\n",
      "dtypes: float64(3), int64(35), object(43)\n",
      "memory usage: 924.0+ KB\n"
     ]
    }
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    "data.info()"
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    "### GRADED\n",
    "### Which column has the most \"null\" values? assign name as string to ans1.\n",
    "### ### CAPITALIZATION/SPELLING MATTERS e.g. 'Street' != 'street'\n",
    "### How many nulls are in that column? assign number as int to ans2\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "ans1 = 'PoolQC'\n",
    "ans2 = 1460 - 7"
   ]
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    "#\n",
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OvqFdOTxyLCdOnmp6aQAAfa34R+mEwcHBeuTIkaaXAQA9055BtXtgZ/bvGciBQyM5PHIs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\nYAYjLgyVoOXno0TmbjeH01cX+MBkQFqMq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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9914ed5c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot('GrLivArea', 'SalePrice', kind = 'scatter', marker = 'x');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "#### Question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### In building regressions below, a subset of our data will be used.\n",
    "\n",
    "### Practice subsetting a DataFrame below.\n",
    "### Create a DataFrame only containing the \"Street\" and \"Alley\" columns from \n",
    "### the `data` DataFrame.\n",
    "\n",
    "### Assign to 'ans1'\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "\n",
    "ans1 = data[['Street','Alley']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 2",
     "locked": true,
     "points": "5",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "<a id = \"code\"></a>\n",
    "### Coding Ridge Regression   \n",
    "\n",
    "#### Preprocessing\n",
    "Before implementing Ridge Regression, it is important to mean-center our target variable and mean-center and standardize observations. We will do this according to the following:  \n",
    "#### Mean Center Target\n",
    "$$y_{cent} = y_0 - \\bar{y}$$\n",
    "\n",
    "#### Standardize Observations\n",
    "$$X_{std} = \\frac{X_0-\\bar{X}}{s_{X}}$$\n",
    "\n",
    "Where $\\bar{X}$ is the sample mean of X and $s_{X}$ is the sample standard deviation of X  \n",
    "\n",
    "#### Question 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Why are the centering / standardization transformations described above important for ridge regression?\n",
    "### 'a') Regression works best when values are unitless\n",
    "### 'b') The transformations makes the regression more interpretable\n",
    "### 'c') Ridge penalizes large coefficients; the transformations make the coefficients of similar scales\n",
    "### 'd') It isn't important\n",
    "\n",
    "### Assign character associated with your choice as a string to ans1\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "ans1 = 'c'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 3",
     "locked": true,
     "points": "2",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "#### Question 4:\n",
    "$$X_{std} = \\frac{X_0-\\bar{X}}{s_{X}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Code a function called \"standardize\" \n",
    "### ACCEPT one input, a list of numbers\n",
    "### RETURN a list where those values have been standardized.\n",
    "\n",
    "### To standardize, subtract the mean of the list and divide by standard deviation.\n",
    "### Please use np.std for calculating standard deviation\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "def standardize(num_list):\n",
    "    \"\"\"\n",
    "    Standardize the given list of numbers\n",
    "    \n",
    "    Positional arguments:\n",
    "        num_list -- a list of numbers\n",
    "    \n",
    "    Example:\n",
    "        num_list = [1,2,3,3,4,4,5,5,5,5,5]\n",
    "        nl_std = standardize(num_list)\n",
    "        print(np.round(nl_std,2))\n",
    "        #--> np.array([-2.11, -1.36, -0.61, -0.61,  \n",
    "                0.14,  0.14,  0.88,  0.88,  0.88,\n",
    "                0.88,  0.88])\n",
    "    \"\"\"\n",
    "    \n",
    "    return list((np.array(num_list) - np.mean(num_list))/ np.std(num_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 4",
     "locked": true,
     "points": "20",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Below we will create a function which will preprocess  our data by performing:\n",
    "* mean subtraction from $y$,\n",
    "* dimension standardization for $x$.\n",
    "\n",
    "Both according to the equations set out below.\n",
    "\n",
    "#### Mean Center Target\n",
    "$$y_{cent} = y_0 - \\bar{y}$$\n",
    "\n",
    "#### Standardize Observations\n",
    "$$X_{std} = \\frac{X_0-\\bar{X}}{s_{X}}$$\n",
    "\n",
    "#### Question 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def preprocess_for_regularization(data, y_column_name, x_column_names):\n",
    "    \"\"\"\n",
    "    Perform mean subtraction and dimension standardization on data\n",
    "        \n",
    "    Positional argument:\n",
    "        data -- a pandas dataframe of the data to pre-process\n",
    "        y_column_name -- the name (string) of the column that contains\n",
    "            the target of the training data.\n",
    "        x_column_names -- a *list* of the names of columns that contain the\n",
    "            observations to be standardized\n",
    "        \n",
    "    Returns:\n",
    "        Return a DataFrame consisting only of the columns included\n",
    "        in `y_column_name` and `x_column_names`.\n",
    "        Where the y_column has been mean-centered, and the\n",
    "        x_columns have been mean-centered/standardized.\n",
    "        \n",
    "        \n",
    "    Example:\n",
    "        data = pd.read_csv(tr_path).head()\n",
    "        prepro_data = preprocess_for_regularization(data,'SalePrice', ['GrLivArea','YearBuilt'])\n",
    "        \n",
    "        print(prepro_data) #-->\n",
    "                   GrLivArea  YearBuilt  SalePrice\n",
    "                0  -0.082772   0.716753     7800.0\n",
    "                1  -1.590161  -0.089594   -19200.0\n",
    "                2   0.172946   0.657024    22800.0\n",
    "                3  -0.059219  -1.911342   -60700.0\n",
    "                4   1.559205   0.627159    49300.0\n",
    "    \"\"\"\n",
    "    stdrd_x = data[x_column_names].apply(standardize)\n",
    "    stdrd_y = data[y_column_name].apply(lambda y: y - np.mean(data[y_column_name]))\n",
    "    return pd.concat([stdrd_x,stdrd_y],axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 5",
     "locked": true,
     "points": "20",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Next, you'll implement the equation for ridge regression using the closed form equation:  \n",
    "\n",
    "$$w_{RR}=(\\lambda+X^TX)^{-1}X^Ty$$  \n",
    "\n",
    "The function will be very similar to the function you wrote for Least Squares Regression with a slightly different matrix to invert.  \n",
    "\n",
    "NB: Many `numpy` matrix functions will be useful. e.g. `np.matmul`, `np.linalg.inv`, `np.ones`, `np.transpose`, and`np.identity`.\n",
    "\n",
    "The main change from Least Squares Regression is that $\\lambda$ is a parameter *we* must set. This is different from the $w$ parameters that we calculate from either closed form or approximation algorithms.  \n",
    "\n",
    "We will address tuning parameters such as $\\lambda$ in the next section.  \n",
    "\n",
    "#### Question 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Code a function called \"ridge_regression_weights\"\n",
    "### ACCEPT three inputs:\n",
    "### Two matricies corresponding to the x inputs and y target\n",
    "### and a number (int or float) for the lambda parameter\n",
    "\n",
    "### RETURN a numpy array of regression weights\n",
    "\n",
    "### The following must be accomplished:\n",
    "\n",
    "### Ensure the number of rows of each the X matrix is greater than the number of columns.\n",
    "### ### If not, transpose the matrix.\n",
    "### Ultimately, the y input will have length n.\n",
    "### Thus the x input should be in the shape n-by-p\n",
    "\n",
    "### *Prepend* an n-by-1 column of ones to the input_x matrix\n",
    "\n",
    "### Use the above equation to calculate the least squares weights.\n",
    "### This will involve creating the lambda matrix---\n",
    "### ### a p+1-by-p+1 matrix with the \"lambda_param\" on the diagonal\n",
    "### ### p+1-by-p+1 because of the prepended \"ones\".\n",
    "\n",
    "### NB: Pay close attention to the expected format of the returned\n",
    "### weights. It is different / simplified from Assignment 1.\n",
    "\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "def ridge_regression_weights(input_x, output_y, lambda_param):\n",
    "    \"\"\"Calculate ridge regression least squares weights.\n",
    "    \n",
    "    Positional arguments:\n",
    "        input_x -- 2-d matrix of input data\n",
    "        output_y -- 1-d numpy array of target values\n",
    "        lambda_param -- lambda parameter that controls how heavily\n",
    "            to penalize large weight values\n",
    "        \n",
    "    Example:\n",
    "        training_y = np.array([208500, 181500, 223500, \n",
    "                                140000, 250000, 143000, \n",
    "                                307000, 200000, 129900, \n",
    "                                118000])\n",
    "                                \n",
    "        training_x = np.array([[1710, 1262, 1786, \n",
    "                                1717, 2198, 1362, \n",
    "                                1694, 2090, 1774, \n",
    "                                1077], \n",
    "                               [2003, 1976, 2001, \n",
    "                                1915, 2000, 1993, \n",
    "                                2004, 1973, 1931, \n",
    "                                1939]])\n",
    "        lambda_param = 10\n",
    "        \n",
    "        rrw = ridge_regression_weights(training_x, training_y, lambda_param)\n",
    "        \n",
    "        print(rrw) #--> np.array([-576.67947107,   77.45913349,   31.50189177])\n",
    "        print(rrw[2]) #--> 31.50189177\n",
    "        \n",
    "    Assumptions:\n",
    "        -- output_y is a vector whose length is the same as the\n",
    "        number of observations in input_x\n",
    "        -- lambda_param has a value greater than 0\n",
    "    \"\"\"\n",
    "    # Make sure that number of rows are greater than number of columns  \n",
    "        \n",
    "    if input_x.shape[0] < input_x.shape[1]:\n",
    "        input_x = np.transpose(input_x)\n",
    "    \n",
    "    if len(output_y) != input_x.shape[0]:\n",
    "        print(\"x and y are not match in length\")\n",
    "        \n",
    "    #prepend 1 to X\n",
    "    input_x = np.concatenate([np.ones((input_x.shape[0],1)),input_x],axis=1)\n",
    "    \n",
    "    #create lambda metrix\n",
    "    lambda_metrix = np.diag([lambda_param] * input_x.shape[1])\n",
    "    \n",
    "    # calculate Wrr\n",
    "    \n",
    "    Wrr = np.matmul(np.matmul(np.linalg.inv(lambda_metrix + np.matmul(np.transpose(input_x),input_x)),np.transpose(input_x)),output_y)\n",
    "    \n",
    "    return Wrr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 6",
     "locked": true,
     "points": "15",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "#### Selecting the $\\lambda$ parameter\n",
    "\n",
    "For our final function before looking at the `sklearn` implementation of ridge regression, we will create a hyper-parameter tuning algorithm.  \n",
    "\n",
    "In ridge regression, we must pick a value for $\\lambda$. We have some intuition about $\\lambda$ from the equations that define it: small values tend to emulate the results from Least Squares, while large values will reduce the dimensionality of the problem. But the choice of $\\lambda$ can motivated with a more precise quantitative treatment.\n",
    "\n",
    "Eventually, we will look to choose the value of $\\lambda$ that minimizes validation error, which we will determine using $k$-fold cross-validation.\n",
    "\n",
    "For this example here, we will solve a simpler but more problem: Find a value that minimizes the of the list returned by a function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Example of hiden function below:\n",
    "\n",
    "### `hidden` takes a single number as a parameter (int or float) and returns a list of 1000 numbers\n",
    "### the input must be between 0 and 50 exclusive\n",
    "\n",
    "def hidden(hp):\n",
    "    if (hp<=0) or (hp >= 50):\n",
    "        print(\"input out of bounds\")\n",
    "    \n",
    "    nums = np.logspace(0,5,num = 1000)\n",
    "    vals = nums** 43.123985172351235134687934\n",
    "    \n",
    "    user_vals = nums** hp\n",
    "    \n",
    "    return vals-user_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00000000e+000, 2.30723993e-001, 7.05271560e-001, 1.61996344e+000,\n",
       "       3.31375824e+000, 6.36678997e+000, 1.17651121e+001, 2.11754143e+001,\n",
       "       3.74021255e+001, 6.51466001e+001, 1.12266087e+002, 1.91858781e+002,\n",
       "       3.25713199e+002, 5.50009289e+002, 9.24733687e+002, 1.54921835e+003,\n",
       "       2.58777014e+003, 4.31192385e+003, 7.17007129e+003, 1.19021624e+004,\n",
       "       1.97285958e+004, 3.26612039e+004, 5.40151345e+004, 8.92512462e+004,\n",
       "       1.47362195e+005, 2.43152787e+005, 4.00991109e+005, 6.60978384e+005,\n",
       "       1.08909625e+006, 1.79389425e+006, 2.95393095e+006, 4.86289616e+006,\n",
       "       8.00380260e+006, 1.31709701e+007, 2.16705811e+007, 3.56504072e+007,\n",
       "       5.86418849e+007, 9.64512784e+007, 1.58624705e+008, 2.60856522e+008,\n",
       "       4.28948461e+008, 7.05317963e+008, 1.15969695e+009, 1.90671893e+009,\n",
       "       3.13482922e+009, 5.15380809e+009, 8.47288977e+009, 1.39291745e+010,\n",
       "       2.28987115e+010, 3.76434747e+010, 6.18817144e+010, 1.01725490e+011,\n",
       "       1.67221763e+011, 2.74885591e+011, 4.51864130e+011, 7.42781250e+011,\n",
       "       1.22098849e+012, 2.00705889e+012, 3.29918651e+012, 5.42315576e+012,\n",
       "       8.91447890e+012, 1.46534101e+013, 2.40868755e+013, 3.95932715e+013,\n",
       "       6.50821040e+013, 1.06979647e+014, 1.75849119e+014, 2.89053862e+014,\n",
       "       4.75134930e+014, 7.81006778e+014, 1.28378517e+015, 2.11022933e+015,\n",
       "       3.46869998e+015, 5.70169046e+015, 9.37217470e+015, 1.54055418e+016,\n",
       "       2.53229012e+016, 4.16245780e+016, 6.84204834e+016, 1.12466287e+017,\n",
       "       1.84866626e+017, 3.03874751e+017, 4.99494452e+017, 8.21044470e+017,\n",
       "       1.34959250e+018, 2.21839360e+018, 3.64648579e+018, 5.99391284e+018,\n",
       "       9.85249680e+018, 1.61950452e+019, 2.66206107e+019, 4.37576359e+019,\n",
       "       7.19266239e+019, 1.18229402e+020, 1.94339599e+020, 3.19445743e+020,\n",
       "       5.25088977e+020, 8.63115057e+020, 1.41874545e+021, 2.33206292e+021,\n",
       "       3.83332856e+021, 6.30103400e+021, 1.03573249e+022, 1.70248531e+022,\n",
       "       2.79846026e+022, 4.59996911e+022, 7.56119929e+022, 1.24287214e+023,\n",
       "       2.04297109e+023, 3.35813373e+023, 5.51993232e+023, 9.07338874e+023,\n",
       "       1.49143827e+024, 2.45155165e+024, 4.02973800e+024, 6.62388181e+024,\n",
       "       1.08880057e+025, 1.78971592e+025, 2.94184552e+025, 4.83565854e+025,\n",
       "       7.94861367e+025, 1.30655336e+026, 2.14764707e+026, 3.53019484e+026,\n",
       "       5.80275772e+026, 9.53828292e+026, 1.56785524e+027, 2.57716203e+027,\n",
       "       4.23621005e+027, 6.96327020e+027, 1.14458753e+028, 1.88141573e+028,\n",
       "       3.09257708e+028, 5.08342353e+028, 8.35587735e+028, 1.37349733e+029,\n",
       "       2.25768621e+029, 3.71107167e+029, 6.10007400e+029, 1.00269965e+030,\n",
       "       1.64818754e+030, 2.70920825e+030, 4.45326101e+030, 7.32004771e+030,\n",
       "       1.20323283e+031, 1.97781395e+031, 3.25103165e+031, 5.34388322e+031,\n",
       "       8.78400795e+031, 1.44387129e+032, 2.37336341e+032, 3.90121608e+032,\n",
       "       6.41262386e+032, 1.05407504e+033, 1.73263583e+033, 2.84802011e+033,\n",
       "       4.68143301e+033, 7.69510544e+033, 1.26488294e+034, 2.07915132e+034,\n",
       "       3.41760495e+034, 5.61768808e+034, 9.23407469e+034, 1.51785101e+035,\n",
       "       2.49496758e+035, 4.10110292e+035, 6.74118785e+035, 1.10808274e+036,\n",
       "       1.82141099e+036, 2.99394429e+036, 4.92129587e+036, 8.08938001e+036,\n",
       "       1.32969183e+037, 2.18568092e+037, 3.59271298e+037, 5.90552190e+037,\n",
       "       9.70720152e+037, 1.59562123e+038, 2.62280238e+038, 4.31123137e+038,\n",
       "       7.08658649e+038, 1.16485764e+039, 1.91473473e+039, 3.14734519e+039,\n",
       "       5.17344860e+039, 8.50385606e+039, 1.39782133e+040, 2.29766878e+040,\n",
       "       3.77679302e+040, 6.20810347e+040, 1.02045700e+041, 1.67737617e+041,\n",
       "       2.75718706e+041, 4.53212619e+041, 7.44968235e+041, 1.22454152e+042,\n",
       "       2.01284011e+042, 3.30860590e+042, 5.43852089e+042, 8.93956863e+042,\n",
       "       1.46944158e+043, 2.41539457e+043, 3.97030479e+043, 6.52618844e+043,\n",
       "       1.07274221e+044, 1.76332000e+044, 2.89845722e+044, 4.76433901e+044,\n",
       "       7.83138216e+044, 1.28728343e+045, 2.11597212e+045, 3.47812914e+045,\n",
       "       5.71717471e+045, 9.39760584e+045, 1.54473145e+046, 2.53915229e+046,\n",
       "       4.17373153e+046, 6.86057114e+046, 1.12770637e+047, 1.85366733e+047,\n",
       "       3.04696564e+047, 5.00844973e+047, 8.23263916e+047, 1.35324005e+048,\n",
       "       2.22438831e+048, 3.65633825e+048, 6.01010593e+048, 9.87911153e+048,\n",
       "       1.62387894e+049, 2.66925099e+049, 4.38758127e+049, 7.21208663e+049,\n",
       "       1.18548673e+050, 1.94864379e+050, 3.20308320e+050, 5.26506796e+050,\n",
       "       8.65445538e+050, 1.42257609e+051, 2.33835942e+051, 3.84367827e+051,\n",
       "       6.31804609e+051, 1.03852882e+052, 1.70708172e+052, 2.80601556e+052,\n",
       "       4.61238803e+052, 7.58161275e+052, 1.24622758e+053, 2.04848657e+053,\n",
       "       3.36719977e+053, 5.53483456e+053, 9.09788422e+053, 1.49546470e+054,\n",
       "       2.45817008e+054, 4.04061704e+054, 6.64176419e+054, 1.09173998e+055,\n",
       "       1.79454757e+055, 2.94978754e+055, 4.84871323e+055, 7.97007229e+055,\n",
       "       1.31008062e+056, 2.15344500e+056, 3.53972518e+056, 5.81842321e+056,\n",
       "       9.56403306e+056, 1.57208792e+057, 2.58411949e+057, 4.24764637e+057,\n",
       "       6.98206866e+057, 1.14767752e+058, 1.88649491e+058, 3.10092598e+058,\n",
       "       5.09714703e+058, 8.37843536e+058, 1.37720530e+059, 2.26378119e+059,\n",
       "       3.72109029e+059, 6.11654211e+059, 1.00540660e+060, 1.65263708e+060,\n",
       "       2.71652218e+060, 4.46528328e+060, 7.33980932e+060, 1.20648115e+061,\n",
       "       1.98315336e+061, 3.25980831e+061, 5.35830986e+061, 8.80772175e+061,\n",
       "       1.44776925e+062, 2.37977068e+062, 3.91174801e+062, 6.42993574e+062,\n",
       "       1.05692068e+063, 1.73731334e+063, 2.85570878e+063, 4.69407127e+063,\n",
       "       7.71587957e+063, 1.26829769e+064, 2.08476431e+064, 3.42683130e+064,\n",
       "       5.63285390e+064, 9.25900351e+064, 1.52194869e+065, 2.50170313e+065,\n",
       "       4.11217448e+065, 6.75938674e+065, 1.11107418e+066, 1.82632817e+066,\n",
       "       3.00202690e+066, 4.93458168e+066, 8.11121855e+066, 1.33328154e+067,\n",
       "       2.19158150e+067, 3.60241206e+067, 5.92146477e+067, 9.73340762e+067,\n",
       "       1.59992886e+068, 2.62988304e+068, 4.32287021e+068, 7.10571784e+068,\n",
       "       1.16800236e+069, 1.91990386e+069, 3.15584193e+069, 5.18741513e+069,\n",
       "       8.52681354e+069, 1.40159496e+070, 2.30387170e+070, 3.78698906e+070,\n",
       "       6.22486321e+070, 1.02321188e+071, 1.68190451e+071, 2.76463052e+071,\n",
       "       4.54436137e+071, 7.46979392e+071, 1.22784736e+072, 2.01827409e+072,\n",
       "       3.31753800e+072, 5.45320303e+072, 8.96370239e+072, 1.47340857e+073,\n",
       "       2.42191531e+073, 3.98102325e+073, 6.54380690e+073, 1.07563825e+074,\n",
       "       1.76808035e+074, 2.90628205e+074, 4.77720108e+074, 7.85252420e+074,\n",
       "       1.29075865e+075, 2.12168451e+075, 3.48751889e+075, 5.73260911e+075,\n",
       "       9.42297614e+075, 1.54890169e+076, 2.54600712e+076, 4.18499917e+076,\n",
       "       6.87909232e+076, 1.13075079e+077, 1.85867159e+077, 3.05519140e+077,\n",
       "       5.02197081e+077, 8.25486445e+077, 1.35689333e+078, 2.23039339e+078,\n",
       "       3.66620910e+078, 6.02633115e+078, 9.90578173e+078, 1.62826286e+079,\n",
       "       2.67645704e+079, 4.39942622e+079, 7.23155678e+079, 1.18868713e+080,\n",
       "       1.95390446e+080, 3.21173042e+080, 5.27928183e+080, 8.67781943e+080,\n",
       "       1.42641655e+081, 2.34467219e+081, 3.85405487e+081, 6.33510263e+081,\n",
       "       1.04133249e+082, 1.71169026e+082, 2.81359083e+082, 4.62483988e+082,\n",
       "       7.60208049e+082, 1.24959197e+083, 2.05401678e+083, 3.37629005e+083,\n",
       "       5.54977671e+083, 9.12244537e+083, 1.49950194e+084, 2.46480630e+084,\n",
       "       4.05152531e+084, 6.65969466e+084, 1.09468730e+085, 1.79939223e+085,\n",
       "       2.95775095e+085, 4.86180308e+085, 7.99158874e+085, 1.31361739e+086,\n",
       "       2.15925856e+086, 3.54928122e+086, 5.83413095e+086, 9.58985265e+086,\n",
       "       1.57633201e+087, 2.59109572e+087, 4.25911355e+087, 7.00091784e+087,\n",
       "       1.15077586e+088, 1.89158780e+088, 3.10929741e+088, 5.11090757e+088,\n",
       "       8.40105424e+088, 1.38092328e+089, 2.26989262e+089, 3.73113595e+089,\n",
       "       6.13305466e+089, 1.00812085e+090, 1.65709863e+090, 2.72385585e+090,\n",
       "       4.47733801e+090, 7.35962428e+090, 1.20973823e+091, 1.98850719e+091,\n",
       "       3.26860867e+091, 5.37277545e+091, 8.83149956e+091, 1.45167773e+092,\n",
       "       2.38619524e+092, 3.92230839e+092, 6.44729435e+092, 1.05977400e+093,\n",
       "       1.74200349e+093, 2.86341821e+093, 4.70674364e+093, 7.73670979e+093,\n",
       "       1.27172166e+094, 2.09039246e+094, 3.43608257e+094, 5.64806066e+094,\n",
       "       9.28399963e+094, 1.52605742e+095, 2.50845687e+095, 4.12327593e+095,\n",
       "       6.77763475e+095, 1.11407370e+096, 1.83125863e+096, 3.01013134e+096,\n",
       "       4.94790334e+096, 8.13311604e+096, 1.33688094e+097, 2.19749802e+097,\n",
       "       3.61213733e+097, 5.93745068e+097, 9.75968447e+097, 1.60424812e+098,\n",
       "       2.63698282e+098, 4.33454047e+098, 7.12490082e+098, 1.17115556e+099,\n",
       "       1.92508694e+099, 3.16436162e+099, 5.20141936e+099, 8.54983299e+099,\n",
       "       1.40537878e+100, 2.31009136e+100, 3.79721263e+100, 6.24166820e+100,\n",
       "       1.02597420e+101, 1.68644507e+101, 2.77209406e+101, 4.55662957e+101,\n",
       "       7.48995979e+101, 1.23116213e+102, 2.02372273e+102, 3.32649420e+102,\n",
       "       5.46792480e+102, 8.98790129e+102, 1.47738626e+103, 2.42845364e+103,\n",
       "       3.99177064e+103, 6.56147292e+103, 1.07854210e+104, 1.77285356e+104,\n",
       "       2.91412801e+104, 4.79009787e+104, 7.87372331e+104, 1.29424326e+105,\n",
       "       2.12741233e+105, 3.49693399e+105, 5.74808518e+105, 9.44841493e+105,\n",
       "       1.55308319e+106, 2.55288047e+106, 4.19629723e+106, 6.89766350e+106,\n",
       "       1.13380343e+107, 1.86368936e+107, 3.06343936e+107, 5.03552840e+107,\n",
       "       8.27714973e+107, 1.36055647e+108, 2.23641468e+108, 3.67610660e+108,\n",
       "       6.04260016e+108, 9.93252392e+108, 1.63265860e+109, 2.68368255e+109,\n",
       "       4.41130316e+109, 7.25107949e+109, 1.19189618e+110, 1.95917933e+110,\n",
       "       3.22040099e+110, 5.29353407e+110, 8.70124655e+110, 1.43026739e+111,\n",
       "       2.35100200e+111, 3.86445949e+111, 6.35220523e+111, 1.04414372e+112,\n",
       "       1.71631123e+112, 2.82118656e+112, 4.63732536e+112, 7.62260348e+112,\n",
       "       1.25296544e+113, 2.05956191e+113, 3.38540486e+113, 5.56475919e+113,\n",
       "       9.14707283e+113, 1.50355008e+114, 2.47146042e+114, 4.06246303e+114,\n",
       "       6.67767354e+114, 1.09764258e+115, 1.80424997e+115, 2.96573586e+115,\n",
       "       4.87492827e+115, 8.01316327e+115, 1.31716370e+116, 2.16508781e+116,\n",
       "       3.55886305e+116, 5.84988109e+116, 9.61574195e+116, 1.58058757e+117,\n",
       "       2.59809079e+117, 4.27061169e+117, 7.01981790e+117, 1.15388256e+118,\n",
       "       1.89669443e+118, 3.11769144e+118, 5.12470526e+118, 8.42373419e+118,\n",
       "       1.38465129e+119, 2.27602054e+119, 3.74120873e+119, 6.14961179e+119,\n",
       "       1.01084243e+120, 1.66157223e+120, 2.73120932e+120, 4.48942528e+120,\n",
       "       7.37949273e+120, 1.21300411e+121, 1.99387548e+121, 3.27743279e+121,\n",
       "       5.38728009e+121, 8.85534156e+121, 1.45559676e+122, 2.39263714e+122,\n",
       "       3.93289727e+122, 6.46469982e+122, 1.06263502e+123, 1.74670630e+123,\n",
       "       2.87114845e+123, 4.71945023e+123, 7.75759623e+123, 1.27515487e+124,\n",
       "       2.09603580e+124, 3.44535880e+124, 5.66330848e+124, 9.30906322e+124,\n",
       "       1.53017725e+125, 2.51522883e+125, 4.13440736e+125, 6.79593203e+125,\n",
       "       1.11708132e+126, 1.83620240e+126, 3.01825766e+126, 4.96126098e+126,\n",
       "       8.15507265e+126, 1.34049005e+127, 2.20343051e+127, 3.62188886e+127,\n",
       "       5.95347975e+127, 9.78603225e+127, 1.60857904e+128, 2.64410176e+128,\n",
       "       4.34624223e+128, 7.14413560e+128, 1.17431728e+129, 1.93028401e+129,\n",
       "       3.17290431e+129, 5.21546140e+129, 8.57291460e+129, 1.40917282e+130,\n",
       "       2.31632781e+130, 3.80746379e+130, 6.25851855e+130, 1.02874398e+131,\n",
       "       1.69099790e+131, 2.77957776e+131, 4.56893090e+131, 7.51018010e+131,\n",
       "       1.23448584e+132, 2.02918608e+132, 3.33547459e+132, 5.48268631e+132,\n",
       "       9.01216553e+132, 1.48137469e+133, 2.43500963e+133, 4.00254704e+133,\n",
       "       6.57918664e+133, 1.08145379e+134, 1.77763965e+134, 2.92199515e+134,\n",
       "       4.80302949e+134, 7.89497964e+134, 1.29773727e+135, 2.13315561e+135,\n",
       "       3.50637450e+135, 5.76360303e+135, 9.47392239e+135, 1.55727598e+136,\n",
       "       2.55977236e+136, 4.20762578e+136, 6.91628481e+136, 1.13686431e+137,\n",
       "       1.86872068e+137, 3.07170959e+137, 5.04912260e+137, 8.29949519e+137,\n",
       "       1.36422951e+138, 2.24245223e+138, 3.68603082e+138, 6.05891310e+138,\n",
       "       9.95933832e+138, 1.63706622e+139, 2.69092757e+139, 4.42321215e+139,\n",
       "       7.27065491e+139, 1.19511389e+140, 1.96446844e+140, 3.22909496e+140,\n",
       "       5.30782479e+140, 8.72473691e+140, 1.43412862e+141, 2.35734889e+141,\n",
       "       3.87489220e+141, 6.36935399e+141, 1.04696255e+142, 1.72094468e+142,\n",
       "       2.82880279e+142, 4.64984454e+142, 7.64318189e+142, 1.25634801e+143,\n",
       "       2.06512202e+143, 3.39454429e+143, 5.57978212e+143, 9.17176678e+143,\n",
       "       1.50760915e+144, 2.47813252e+144, 4.07343028e+144, 6.69570096e+144,\n",
       "       1.10060583e+145, 1.80912082e+145, 2.97374232e+145, 4.88808890e+145,\n",
       "       8.03479605e+145, 1.32071959e+146, 2.17093280e+146, 3.56847076e+146,\n",
       "       5.86567375e+146, 9.64170114e+146, 1.58485461e+147, 2.60510474e+147,\n",
       "       4.28214087e+147, 7.03876899e+147, 1.15699764e+148, 1.90181485e+148,\n",
       "       3.12610814e+148, 5.13854020e+148, 8.44647537e+148, 1.38838938e+149,\n",
       "       2.28216501e+149, 3.75130871e+149, 6.16621363e+149, 1.01357135e+150,\n",
       "       1.66605790e+150, 2.73858264e+150, 4.50154518e+150, 7.39941481e+150,\n",
       "       1.21627880e+151, 1.99925826e+151, 3.28628073e+151, 5.40182389e+151,\n",
       "       8.87924793e+151, 1.45952636e+152, 2.39909644e+152, 3.94351473e+152,\n",
       "       6.48215228e+152, 1.06550377e+153, 1.75142181e+153, 2.87889957e+153,\n",
       "       4.73219112e+153, 7.77853907e+153, 1.27859735e+154, 2.10169437e+154,\n",
       "       3.45466009e+154, 5.67859746e+154, 9.33419449e+154, 1.53430820e+155,\n",
       "       2.52201909e+155, 4.14556883e+155, 6.81427870e+155, 1.12009705e+156,\n",
       "       1.84115951e+156, 3.02640591e+156, 4.97465467e+156, 8.17708854e+156,\n",
       "       1.34410892e+157, 2.20937901e+157, 3.63166671e+157, 5.96955210e+157,\n",
       "       9.81245116e+157, 1.61292164e+158, 2.65123993e+158, 4.35797559e+158,\n",
       "       7.16342230e+158, 1.17748753e+159, 1.93549511e+159, 3.18147005e+159,\n",
       "       5.22954135e+159, 8.59605851e+159, 1.41297710e+160, 2.32258109e+160,\n",
       "       3.81774263e+160, 6.27541439e+160, 1.03152123e+161, 1.69556301e+161,\n",
       "       2.78708167e+161, 4.58126544e+161, 7.53045500e+161, 1.23781853e+162,\n",
       "       2.03466419e+162, 3.34447922e+162, 5.49748767e+162, 9.03649527e+162,\n",
       "       1.48537390e+163, 2.44158332e+163, 4.01335254e+163, 6.59694817e+163,\n",
       "       1.08437335e+164, 1.78243867e+164, 2.92988353e+164, 4.81599601e+164,\n",
       "       7.91629337e+164, 1.30124071e+165, 2.13891440e+165, 3.51584050e+165,\n",
       "       5.77916277e+165, 9.49949872e+165, 1.56148009e+166, 2.56668287e+166,\n",
       "       4.21898492e+166, 6.93495640e+166, 1.13993345e+167, 1.87376559e+167,\n",
       "       3.08000215e+167, 5.06275349e+167, 8.32190096e+167, 1.36791246e+168,\n",
       "       2.24850608e+168, 3.69598183e+168, 6.07527008e+168, 9.98622510e+168,\n",
       "       1.64148573e+169, 2.69819215e+169, 4.43515330e+169, 7.29028317e+169,\n",
       "       1.19834028e+170, 1.96977182e+170, 3.23781240e+170, 5.32215409e+170,\n",
       "       8.74829070e+170, 1.43800027e+171, 2.36371292e+171, 3.88535307e+171,\n",
       "       6.38654905e+171, 1.04978899e+172, 1.72559064e+172, 2.83643958e+172,\n",
       "       4.66239752e+172, 7.66381584e+172, 1.25973972e+173, 2.07069714e+173,\n",
       "       3.40370839e+173, 5.59484561e+173, 9.19652739e+173, 1.51167917e+174,\n",
       "       2.48482262e+174, 4.08442714e+174, 6.71377705e+174, 1.10357709e+175,\n",
       "       1.81400483e+175, 2.98177040e+175, 4.90128505e+175, 8.05648723e+175,\n",
       "       1.32428508e+176, 2.17679357e+176, 3.57810440e+176, 5.88150905e+176,\n",
       "       9.66773041e+176, 1.58913317e+177, 2.61213762e+177, 4.29370118e+177,\n",
       "       7.05777124e+177, 1.16012114e+178, 1.90694910e+178, 3.13454755e+178,\n",
       "       5.15241249e+178, 8.46927794e+178, 1.39213755e+179, 2.28832607e+179,\n",
       "       3.76143595e+179, 6.18286028e+179, 1.01630765e+180, 1.67055568e+180,\n",
       "       2.74597587e+180, 4.51369780e+180, 7.41939068e+180, 1.21956233e+181,\n",
       "       2.00465556e+181, 3.29515255e+181, 5.41640695e+181, 8.90321884e+181,\n",
       "       1.46346658e+182, 2.40557317e+182, 3.95416086e+182, 6.49965186e+182,\n",
       "       1.06838026e+183, 1.75615004e+183, 2.88667160e+183, 4.74496640e+183,\n",
       "       7.79953845e+183, 1.28204912e+184, 2.10736822e+184, 3.46398648e+184,\n",
       "       5.69392772e+184, 9.35939359e+184, 1.53845031e+185, 2.52882767e+185,\n",
       "       4.15676044e+185, 6.83267491e+185, 1.12312093e+186, 1.84613001e+186,\n",
       "       3.03457617e+186, 4.98808453e+186, 8.19916386e+186, 1.34773755e+187,\n",
       "       2.21534357e+187, 3.64147096e+187, 5.98566783e+187, 9.83894140e+187,\n",
       "       1.61727598e+188, 2.65839736e+188, 4.36974062e+188, 7.18276108e+188,\n",
       "       1.18066634e+189, 1.94072028e+189, 3.19005893e+189, 5.24365931e+189,\n",
       "       8.61926491e+189, 1.41679166e+190, 2.32885126e+190, 3.82804922e+190,\n",
       "       6.29235585e+190, 1.03430598e+191, 1.70014044e+191, 2.79460582e+191,\n",
       "       4.59363328e+191, 7.55078463e+191, 1.24116021e+192, 2.04015708e+192,\n",
       "       3.35350816e+192, 5.51232899e+192, 9.06089069e+192, 1.48938389e+193,\n",
       "       2.44817475e+193, 4.02418721e+193, 6.61475766e+193, 1.08730078e+194,\n",
       "       1.78725064e+194, 2.93779321e+194, 4.82899754e+194, 7.93766463e+194,\n",
       "       1.30475361e+195, 2.14468873e+195, 3.52533206e+195, 5.79476452e+195,\n",
       "       9.52514409e+195, 1.56569554e+196, 2.57361203e+196, 4.23037473e+196,\n",
       "       6.95367839e+196, 1.14301087e+197, 1.87882411e+197, 3.08831709e+197,\n",
       "       5.07642118e+197, 8.34436723e+197, 1.37160535e+198, 2.25457627e+198,\n",
       "       3.70595971e+198, 6.09167121e+198, 1.00131845e+199, 1.64591718e+199,\n",
       "       2.70547634e+199, 4.44712669e+199, 7.30996442e+199, 1.20157539e+200,\n",
       "       1.97508953e+200, 3.24655338e+200, 5.33652207e+200, 8.77190807e+200,\n",
       "       1.44188237e+201, 2.37009413e+201, 3.89584219e+201, 6.40379053e+201,\n",
       "       1.05262306e+202, 1.73024914e+202, 2.84409699e+202, 4.67498438e+202,\n",
       "       7.68450550e+202, 1.26314058e+203, 2.07628731e+203, 3.41289723e+203,\n",
       "       5.60994977e+203, 9.22135484e+203, 1.51576019e+204, 2.49153078e+204,\n",
       "       4.09545369e+204, 6.73190193e+204, 1.10655637e+205, 1.81890201e+205,\n",
       "       2.98982016e+205, 4.91451683e+205, 8.07823697e+205, 1.32786019e+206,\n",
       "       2.18267016e+206, 3.58776405e+206, 5.89738710e+206, 9.69382995e+206,\n",
       "       1.59342328e+207, 2.61918949e+207, 4.30529269e+207, 7.07682479e+207,\n",
       "       1.16325306e+208, 1.91209720e+208, 3.14300975e+208, 5.16632223e+208,\n",
       "       8.49214208e+208, 1.39589584e+209, 2.29450377e+209, 3.77159053e+209,\n",
       "       6.19955187e+209, 1.01905133e+210, 1.67506561e+210, 2.75338906e+210,\n",
       "       4.52588323e+210, 7.43942048e+210, 1.22285473e+211, 2.01006744e+211,\n",
       "       3.30404833e+211, 5.43102938e+211, 8.92725446e+211, 1.46741744e+212,\n",
       "       2.41206739e+212, 3.96483574e+212, 6.51719868e+212, 1.07126452e+213,\n",
       "       1.76089104e+213, 2.89446462e+213, 4.75777617e+213, 7.82059451e+213,\n",
       "       1.28551021e+214, 2.11305739e+214, 3.47333805e+214, 5.70929936e+214,\n",
       "       9.38466073e+214, 1.54260359e+215, 2.53565463e+215, 4.16798226e+215])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hidden(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Run the above cell and test out the functionality of `hidden`. Remember it takes a single number, between 0 and 50, as an argument\n",
    "\n",
    "#### Question 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Code a function called \"minimize\"\n",
    "### ACCEPT one input: a function.\n",
    "\n",
    "### That function will be similar to `hidden` created above and available for your exploration.\n",
    "### Like 'hidden', the passed function will take a single argument, a number between 0 and 50 exclusive \n",
    "### and then, the function will return a numpy array of 1000 numbers.\n",
    "\n",
    "### RETURN the value that makes the mean of the array returned by 'passed_func' as close to 0 as possible\n",
    "\n",
    "### Note, you will almost certainly NOT be able to find the number that makes the mean exactly 0\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "def minimize(passed_func,*args):\n",
    "    \"\"\"\n",
    "    Find the numeric value that minimizes the output of 'passed_func'\n",
    "    \n",
    "    Positional Argument:\n",
    "        passed_func -- a function that takes a single number (between 0 and 50 exclusive)\n",
    "            as input, and returns a list of 1000 floats.\n",
    "        \n",
    "    Example:\n",
    "        passed_func = hidden\n",
    "        min_hidden = minimize(passed_func)\n",
    "        print(round(min_hidden,4))\n",
    "        #--> 43.1204 (answers will vary, must be close to 43.123985172351)\n",
    "    \n",
    "    \"\"\"\n",
    "    # Create values to test        \n",
    "    test_vals = list(np.linspace(.1,49.9, 1000))    \n",
    "    # Find mean of returned array from function    \n",
    "    ret_vals = [abs(np.mean(passed_func(x))) for x in test_vals]    \n",
    "    # Find smallest mean    \n",
    "    min_mean = min(ret_vals)    \n",
    "    # Return the test value that creates the smallest mean    \n",
    "    return test_vals[ret_vals.index(min_mean)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0642517968059461e+213"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(np.linspace(.1,49.9, 1000)) \n",
    "np.mean(hidden(0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 7",
     "locked": true,
     "points": "20",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
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   "source": [
    "The above simulates hyper parameter tuning.  \n",
    "\n",
    "In the case of ridge regression, you would be searching lambda parameters to minimize validation error.  \n",
    "\n",
    "The `hidden` function would be analogous to the model building; the returned list analogous to residuals; and the mean of that list analogous to validation error.  \n",
    "\n",
    "See below for an example of using the functions built above that automatically performs hyper-parameter tuning using mean-absolute-deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9414414414414414"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def lambda_search_func(lambda_param):\n",
    "    \n",
    "    # Define X and y\n",
    "    # with preprocessing\n",
    "    df = preprocess_for_regularization(data.head(50),'SalePrice', ['GrLivArea','YearBuilt'])\n",
    "    \n",
    "    y_true = df['SalePrice'].values\n",
    "    X = df[['GrLivArea','YearBuilt']].values\n",
    "    \n",
    "    # Calculate Weights then use for predictions\n",
    "    weights = ridge_regression_weights(X, y_true, lambda_param )\n",
    "    y_pred = weights[0] + np.matmul(X,weights[1:])\n",
    "    \n",
    "    # Calculate Residuals\n",
    "    resid = y_true - y_pred\n",
    "    \n",
    "    # take absolute value to tune on mean-absolute-deviation\n",
    "    # Alternatively, could use:\n",
    "    # return resid **2-S\n",
    "    # for tuning on mean-squared-error\n",
    "    \n",
    "    return abs(resid)\n",
    "\n",
    "minimize(lambda_search_func)    # --> about 1.4957957957957957"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
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   "source": [
    "Implementing a k-folds cross-validation strategy will come in later assignments.\n",
    "\n",
    "#### Question 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Why is cross-validation useful?\n",
    "### 'a') to minimize the liklihood of overfitting\n",
    "### 'b') Cross-validation allows us to fit on all our data\n",
    "### 'c') cross-validation standardizes outputs\n",
    "### 'd') cross-validation is not useful\n",
    "### assing the character associated with your choice as a string to ans1\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "ans1 = 'a'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 8",
     "locked": true,
     "points": "2",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "<a id = \"sklearn\"></a>\n",
    "\n",
    "### Ridge Regression in `sklearn`  \n",
    "\n",
    "Below gives the syntax for implementing ridge regression in sklearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "nbgrader": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LeastSquares Intercept: -2024976.3625856352 Coefs: [  95.16733349 1045.86241944] \n",
      "\n",
      "Ridge alpha = 100000 Intercept: -1876820.7548806793 Coefs: [ 96.01060155 970.05661101] \n",
      "\n",
      "Ridge, alpha = 0 Intercept: -2024976.3625856352 Coefs: [  95.16733349 1045.86241944] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge, LinearRegression\n",
    "\n",
    "### Note, the \"alpha\" parameter defines regularization strength.\n",
    "### Lambda is a reserved word in `Python` -- Thus \"alpha\" instead\n",
    "\n",
    "### An alpha of 0 is equivalent to least-squares regression\n",
    "lr = LinearRegression()\n",
    "reg = Ridge(alpha = 100000)\n",
    "reg0 = Ridge(alpha = 0)\n",
    "\n",
    "# Notice how the consistent sklearn syntax may be used to easily fit many kinds of models\n",
    "for m, name in zip([lr, reg, reg0], [\"LeastSquares\",\"Ridge alpha = 100000\",\"Ridge, alpha = 0\"]):\n",
    "    \n",
    "    m.fit(data[['GrLivArea','YearBuilt']], data['SalePrice'])\n",
    "    print(name, \"Intercept:\", m.intercept_, \"Coefs:\",m.coef_,\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "Note, in the above example, an alpha of 100,000 is set for the ridge regularization. The reason an alpha value this high is required is because standardization / mean centering of our inputs did not occur, and instead of working with inputs on the order of [-4,4] we are on the interval of [0,2000].  \n",
    "\n",
    "#### Question 9:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### Above, the coefficent around 95/96 corresponds with:\n",
    "### 'a') Living Area\n",
    "### 'b') Year Built\n",
    "### 'c') Sale Price\n",
    "### Assign character associated with your choice as string to ans1\n",
    "### YOUR ANSWER BELOW\n",
    "\n",
    "ans1 = 'a'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 9",
     "locked": true,
     "points": "5",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "locked": true,
     "solution": false
    }
   },
   "source": [
    "#### Queston 10:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### GRADED\n",
    "### True or False:\n",
    "### A larger \"alpha\" corresponds to a greater amount of regularization\n",
    "### assign boolean choice to ans1\n",
    "\n",
    "ans1 = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "nbgrader": {
     "grade": true,
     "grade_id": "Question 10",
     "locked": true,
     "points": "5",
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
   ]
  }
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