hw1 - sol.ipynb

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   "source": [
    "# Exercise 1: Linear Regression\n",
    "\n",
    "### This notebook is executed automatically. Failing to meet any of the submission requirements will results in a 25 point fine or your submission not being graded at all. Kindly reminder: the homework assignments grade is 50% of the final grade. \n",
    "\n",
    "### Do not start the exercise until you fully understand the submission guidelines.\n",
    "\n",
    "## Read the following instructions carefully:\n",
    "\n",
    "1. This jupyter notebook contains all the step by step instructions needed for this exercise.\n",
    "1. Submission includes this notebook only with the exercise number and your ID as the filename. For example: `hw1_123456789_987654321.ipynb` if you submitted in pairs and `hw1_123456789.ipynb` if you submitted the exercise alone.\n",
    "1. Write **efficient vectorized** code whenever possible. Some calculations in this exercise take several minutes when implemented efficiently, and might take much longer otherwise. Unnecessary loops will result in point deduction.\n",
    "1. You are responsible for the correctness of your code and should add as many tests as you see fit. Tests will not be graded nor checked.\n",
    "1. Write your functions in this notebook only. **Do not create Python modules and import them**.\n",
    "1. You are allowed to use functions and methods from the [Python Standard Library](https://docs.python.org/3/library/) and [numpy](https://www.numpy.org/devdocs/reference/) only. **Do not import anything else.**\n",
    "1. Your code must run without errors. Make sure your `numpy` version is at least 1.15.4 and that you are using at least python 3.6. Changes of the configuration we provided are at your own risk. Any code that cannot run will not be graded.\n",
    "1. Write your own code. Cheating will not be tolerated.\n",
    "1. Answers to qualitative questions should be written in **markdown** cells (with $\\LaTeX$ support). Answers that will be written in commented code blocks will not be checked.\n",
    "\n",
    "## In this exercise you will perform the following:\n",
    "1. Load a dataset and perform basic data exploration using a powerful data science library called [pandas](https://pandas.pydata.org/pandas-docs/stable/).\n",
    "1. Preprocess the data for linear regression.\n",
    "1. Compute the cost and perform gradient descent in pure numpy in vectorized form.\n",
    "1. Fit a linear regression model using a single feature.\n",
    "1. Visualize your results using matplotlib.\n",
    "1. Perform multivariate linear regression.\n",
    "1. Pick the best features in the dataset.\n",
    "1. Experiment with adaptive learning rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Circle at 0x1e269e271c0>"
      ]
     },
     "execution_count": 1,
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     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np # used for scientific computing\n",
    "import pandas as pd # used for data analysis and manipulation\n",
    "import matplotlib.pyplot as plt # used for visualization and plotting\n",
    "\n",
    "#circle1 = plt.Circle((0, 0), 2, color='r')\n",
    "# now make a circle with no fill, which is good for hi-lighting key results\n",
    "circle2 = plt.Circle((5, 5), 0.5, color='b', fill=False)\n",
    "#circle3 = plt.Circle((10, 10), 2, color='g', clip_on=False)\n",
    "    \n",
    "ax = plt.gca()\n",
    "ax.cla() # clear things for fresh plot\n",
    "\n",
    "# change default range so that new circles will work\n",
    "ax.set_xlim((0, 10))\n",
    "ax.set_ylim((0, 10))\n",
    "# some data\n",
    "ax.plot(range(11), 'o', color='black')\n",
    "# key data point that we are encircling\n",
    "ax.plot((5), (5), 'o', color='y')\n",
    "    \n",
    "#ax.add_patch(circle1)\n",
    "ax.add_patch(circle2)\n",
    "#ax.add_patch(circle3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### I have read and understood the instructions: *** 316352467 , 208508259 ***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-5ed0076cec86f623",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np # used for scientific computing\n",
    "import pandas as pd # used for data analysis and manipulation\n",
    "import matplotlib.pyplot as plt # used for visualization and plotting\n",
    "\n",
    "np.random.seed(42) \n",
    "\n",
    "# make matplotlib figures appear inline in the notebook\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (14.0, 8.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-9ef8b2769c2c1949",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# Read comma separated data\n",
    "df = pd.read_csv('data.csv') # Make sure this cell runs regardless of your absolute path.\n",
    "# df stands for dataframe, which is the default format for datasets in pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-916f46de8cde2ca7",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part 1: Data Preprocessing (10 Points)\n",
    "\n",
    "For the following exercise, we will use a dataset containing housing prices in King County, USA. The dataset contains 5,000 observations with 18 features and a single target value - the house price. \n",
    "\n",
    "First, we will read and explore the data using pandas and the `.read_csv` method. Pandas is an open source library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-6966afc155aa6616",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### Data Exploration\n",
    "A good practice in any data-oriented project is to first try and understand the data. Fortunately, pandas is built for that purpose. Start by looking at the top of the dataset using the `df.head()` command. This will be the first indication that you read your data properly, and that the headers are correct. Next, you can use `df.describe()` to show statistics on the data and check for trends and irregularities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-5bd0d6844b64ea1a",
     "locked": false,
     "points": 1,
     "schema_version": 1,
     "solution": true
    },
    "scrolled": true
   },
   "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>id</th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5.000000e+03</td>\n",
       "      <td>5.000000e+03</td>\n",
       "      <td>5000.0000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5.000000e+03</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>5000.00000</td>\n",
       "      <td>5000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.630823e+09</td>\n",
       "      <td>5.394699e+05</td>\n",
       "      <td>3.3714</td>\n",
       "      <td>2.062150</td>\n",
       "      <td>2061.036800</td>\n",
       "      <td>1.615893e+04</td>\n",
       "      <td>1.432600</td>\n",
       "      <td>0.009400</td>\n",
       "      <td>0.243000</td>\n",
       "      <td>3.455000</td>\n",
       "      <td>7.595200</td>\n",
       "      <td>1753.151000</td>\n",
       "      <td>1966.660800</td>\n",
       "      <td>95.052800</td>\n",
       "      <td>98078.812600</td>\n",
       "      <td>47.559312</td>\n",
       "      <td>-122.215864</td>\n",
       "      <td>1976.84520</td>\n",
       "      <td>13451.164600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.870890e+09</td>\n",
       "      <td>3.873115e+05</td>\n",
       "      <td>0.9104</td>\n",
       "      <td>0.773592</td>\n",
       "      <td>923.727509</td>\n",
       "      <td>4.600220e+04</td>\n",
       "      <td>0.510793</td>\n",
       "      <td>0.096506</td>\n",
       "      <td>0.774643</td>\n",
       "      <td>0.677692</td>\n",
       "      <td>1.166537</td>\n",
       "      <td>818.390844</td>\n",
       "      <td>28.286855</td>\n",
       "      <td>425.234932</td>\n",
       "      <td>54.126332</td>\n",
       "      <td>0.139521</td>\n",
       "      <td>0.141807</td>\n",
       "      <td>674.73601</td>\n",
       "      <td>26514.749009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000102e+06</td>\n",
       "      <td>7.500000e+04</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>380.000000</td>\n",
       "      <td>6.090000e+02</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>380.000000</td>\n",
       "      <td>1900.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98001.000000</td>\n",
       "      <td>47.155900</td>\n",
       "      <td>-122.514000</td>\n",
       "      <td>620.00000</td>\n",
       "      <td>660.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.154075e+09</td>\n",
       "      <td>3.179062e+05</td>\n",
       "      <td>3.0000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>1410.000000</td>\n",
       "      <td>5.400000e+03</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1190.000000</td>\n",
       "      <td>1949.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98033.000000</td>\n",
       "      <td>47.463675</td>\n",
       "      <td>-122.329000</td>\n",
       "      <td>1490.00000</td>\n",
       "      <td>5391.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.022900e+09</td>\n",
       "      <td>4.490000e+05</td>\n",
       "      <td>3.0000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1890.000000</td>\n",
       "      <td>7.875000e+03</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1530.000000</td>\n",
       "      <td>1968.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98070.000000</td>\n",
       "      <td>47.572850</td>\n",
       "      <td>-122.235000</td>\n",
       "      <td>1820.00000</td>\n",
       "      <td>7800.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.345078e+09</td>\n",
       "      <td>6.500000e+05</td>\n",
       "      <td>4.0000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2500.000000</td>\n",
       "      <td>1.123400e+04</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>2130.000000</td>\n",
       "      <td>1990.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98118.000000</td>\n",
       "      <td>47.679200</td>\n",
       "      <td>-122.129000</td>\n",
       "      <td>2340.00000</td>\n",
       "      <td>10469.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.842300e+09</td>\n",
       "      <td>7.060000e+06</td>\n",
       "      <td>9.0000</td>\n",
       "      <td>6.750000</td>\n",
       "      <td>10040.000000</td>\n",
       "      <td>1.651359e+06</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>7680.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>98199.000000</td>\n",
       "      <td>47.777600</td>\n",
       "      <td>-121.315000</td>\n",
       "      <td>5790.00000</td>\n",
       "      <td>434728.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 id         price   bedrooms    bathrooms   sqft_living  \\\n",
       "count  5.000000e+03  5.000000e+03  5000.0000  5000.000000   5000.000000   \n",
       "mean   4.630823e+09  5.394699e+05     3.3714     2.062150   2061.036800   \n",
       "std    2.870890e+09  3.873115e+05     0.9104     0.773592    923.727509   \n",
       "min    1.000102e+06  7.500000e+04     0.0000     0.000000    380.000000   \n",
       "25%    2.154075e+09  3.179062e+05     3.0000     1.500000   1410.000000   \n",
       "50%    4.022900e+09  4.490000e+05     3.0000     2.000000   1890.000000   \n",
       "75%    7.345078e+09  6.500000e+05     4.0000     2.500000   2500.000000   \n",
       "max    9.842300e+09  7.060000e+06     9.0000     6.750000  10040.000000   \n",
       "\n",
       "           sqft_lot       floors   waterfront         view    condition  \\\n",
       "count  5.000000e+03  5000.000000  5000.000000  5000.000000  5000.000000   \n",
       "mean   1.615893e+04     1.432600     0.009400     0.243000     3.455000   \n",
       "std    4.600220e+04     0.510793     0.096506     0.774643     0.677692   \n",
       "min    6.090000e+02     1.000000     0.000000     0.000000     1.000000   \n",
       "25%    5.400000e+03     1.000000     0.000000     0.000000     3.000000   \n",
       "50%    7.875000e+03     1.000000     0.000000     0.000000     3.000000   \n",
       "75%    1.123400e+04     2.000000     0.000000     0.000000     4.000000   \n",
       "max    1.651359e+06     3.500000     1.000000     4.000000     5.000000   \n",
       "\n",
       "             grade   sqft_above     yr_built  yr_renovated       zipcode  \\\n",
       "count  5000.000000  5000.000000  5000.000000   5000.000000   5000.000000   \n",
       "mean      7.595200  1753.151000  1966.660800     95.052800  98078.812600   \n",
       "std       1.166537   818.390844    28.286855    425.234932     54.126332   \n",
       "min       3.000000   380.000000  1900.000000      0.000000  98001.000000   \n",
       "25%       7.000000  1190.000000  1949.000000      0.000000  98033.000000   \n",
       "50%       7.000000  1530.000000  1968.000000      0.000000  98070.000000   \n",
       "75%       8.000000  2130.000000  1990.000000      0.000000  98118.000000   \n",
       "max      13.000000  7680.000000  2015.000000   2015.000000  98199.000000   \n",
       "\n",
       "               lat         long  sqft_living15     sqft_lot15  \n",
       "count  5000.000000  5000.000000     5000.00000    5000.000000  \n",
       "mean     47.559312  -122.215864     1976.84520   13451.164600  \n",
       "std       0.139521     0.141807      674.73601   26514.749009  \n",
       "min      47.155900  -122.514000      620.00000     660.000000  \n",
       "25%      47.463675  -122.329000     1490.00000    5391.500000  \n",
       "50%      47.572850  -122.235000     1820.00000    7800.000000  \n",
       "75%      47.679200  -122.129000     2340.00000   10469.250000  \n",
       "max      47.777600  -121.315000     5790.00000  434728.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-9b9bd1b387905904",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "We will start with one variable linear regression by extracting the target column and the `sqft_living` variable from the dataset. We use pandas and select both columns as separate variables and transform them into a numpy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-c7cd243e8b5fe5aa",
     "locked": false,
     "points": 1,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "X = df['sqft_living'].values\n",
    "y = df['price'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-508e7e1a13f9bbe4",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Preprocessing\n",
    "\n",
    "As the number of features grows, calculating gradients gets computationally expensive. We can speed this up by normalizing the input data to ensure all values are within the same range. This is especially important for datasets with high standard deviations or differences in the ranges of the attributes. Use [mean normalization](https://en.wikipedia.org/wiki/Feature_scaling) for the fearures (`X`) and the true labels (`y`).\n",
    "\n",
    "Implement the cost function `preprocess`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def preprocess(X, y):\n",
    "    \"\"\"\n",
    "    Perform mean normalization on the features and true labels.\n",
    "\n",
    "    Input:\n",
    "    - X: Inputs (n features over m instances).\n",
    "    - y: True labels.\n",
    "\n",
    "    Returns a two vales:\n",
    "    - X: The mean normalized inputs.\n",
    "    - y: The mean normalized labels.\n",
    "    \"\"\"\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the normalization function.                             #\n",
    "    ###########################################################################\n",
    "    #calculate for y (1-demention)\n",
    "    avgy = sum(y)/len(y)\n",
    "    maxy = max(y)\n",
    "    miny = min(y)\n",
    "    y = np.array([(i-avgy)/(maxy-miny) for i in y])\n",
    "    #calculate for X matrix (n*m demention) \n",
    "    if X.ndim == 1:\n",
    "        avgx = sum(X)/len(X)\n",
    "        maxx = max(X)\n",
    "        minx = min(X)\n",
    "        X = np.array([(x - avgx)/(maxx-minx) for x in X])\n",
    "    else:\n",
    "        colums = X.shape[1]\n",
    "        for i in range(colums):\n",
    "            X[:,i]=(X[:,i]-(X.mean(axis=0))[i])/(X[:,i].max()-X[:,i].min())\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-9bb6a28b6b6932fa",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "X, y = preprocess(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will split the data into two datasets: \n",
    "1. The training dataset will contain 80% of the data and will always be used for model training.\n",
    "2. The validation dataset will contain the remaining 20% of the data and will be used for model evaluation. For example, we will pick the best alpha and the best features using the validation dataset, while still training the model using the training dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# training and validation split\n",
    "np.random.seed(42)\n",
    "indices = np.random.permutation(X.shape[0])\n",
    "idx_train, idx_val = indices[:int(0.8*X.shape[0])], indices[int(0.8*X.shape[0]):]\n",
    "X_train, X_val = X[idx_train], X[idx_val]\n",
    "y_train, y_val = y[idx_train], y[idx_val]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-0c168d036748663e",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Data Visualization\n",
    "Another useful tool is data visualization. Since this problem has only two parameters, it is possible to create a two-dimensional scatter plot to visualize the data. Note that many real-world datasets are highly dimensional and cannot be visualized naively. We will be using `matplotlib` for all data visualization purposes since it offers a wide range of visualization tools and is easy to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-cbad8871e083093f",
     "locked": true,
     "schema_version": 1,
     "solution": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train, y_train, 'ro', ms=1, mec='k') # the parameters control the size, shape and color of the scatter plot\n",
    "plt.ylabel('Price in USD')\n",
    "plt.xlabel('sq.ft')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-c50f0a0e569142ed",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Bias Trick\n",
    "\n",
    "Make sure that `X` takes into consideration the bias $\\theta_0$ in the linear model. Hint, recall that the predications of our linear model are of the form:\n",
    "\n",
    "$$\n",
    "\\hat{y} = h_\\theta(x) = \\theta^T x = \\theta_0 + \\theta_1 x_1\n",
    "$$\n",
    "\n",
    "Add columns of ones as the zeroth column of the features (do this for both the training and validation sets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-44853962dc1651df",
     "locked": false,
     "points": 2,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "X_train = np.column_stack((np.ones(len(X_train)),X_train))\n",
    "X_val = np.column_stack((np.ones(len(X_val)),X_val))\n",
    "###########################################################################\n",
    "pass\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-c7d7fd68c1b24943",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part 2: Single Variable Linear Regression (40 Points)\n",
    "Simple linear regression is a linear regression model with a single explanatory varaible and a single target value. \n",
    "\n",
    "$$\n",
    "\\hat{y} = h_\\theta(x) = \\theta^T x = \\theta_0 + \\theta_1 x_1\n",
    "$$\n",
    "\n",
    "## Gradient Descent \n",
    "\n",
    "Our task is to find the best possible linear line that explains all the points in our dataset. We start by guessing initial values for the linear regression parameters $\\theta$ and updating the values using gradient descent. \n",
    "\n",
    "The objective of linear regression is to minimize the cost function $J$:\n",
    "\n",
    "$$\n",
    "J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^{n}(h_\\theta(x^{(i)})-y^{(i)})^2\n",
    "$$\n",
    "\n",
    "where the hypothesis (model) $h_\\theta(x)$ is given by a **linear** model:\n",
    "\n",
    "$$\n",
    "h_\\theta(x) = \\theta^T x = \\theta_0 + \\theta_1 x_1\n",
    "$$\n",
    "\n",
    "$\\theta_j$ are parameters of your model. and by changing those values accordingly you will be able to lower the cost function $J(\\theta)$. One way to accopmlish this is to use gradient descent:\n",
    "\n",
    "$$\n",
    "\\theta_j = \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}\n",
    "$$\n",
    "\n",
    "In linear regresion, we know that with each step of gradient descent, the parameters $\\theta_j$ get closer to the optimal values that will achieve the lowest cost $J(\\theta)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-0f83af93c0436542",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Implement the cost function `compute_cost`. (10 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(X, y, theta):\n",
    "    \"\"\"\n",
    "    Computes the average squared difference between an obserbation's actual and\n",
    "    predicted values for linear regression.  \n",
    "\n",
    "    Input:\n",
    "    - X: inputs  (n features over m instances).\n",
    "    - y: true labels (1 value over m instances).\n",
    "    - theta: the parameters (weights) of the model being learned.\n",
    "\n",
    "    Returns a single value:\n",
    "    - J: the cost associated with the current set of parameters (single number).\n",
    "    \"\"\"\n",
    "    \n",
    "    J = 0  # Use J for the cost.\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the MSE cost function.                                  #\n",
    "    sum = 0\n",
    "    m = len(X)-1\n",
    "    hypothes = np.subtract(np.dot(X,theta),y)\n",
    "    sum = hypothes.T.dot(hypothes)\n",
    "    sum = np.sum(sum) \n",
    "    J = (0.5)*(1/m)*sum\n",
    "    ###########################################################################\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4c1cfec24e144479",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta = np.array([-1, 2])\n",
    "J = compute_cost(X_train, y_train, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-afdc527b73d275bb",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Implement the gradient descent function `gradient_descent`. (10 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta, alpha, num_iters):\n",
    "    \"\"\"\n",
    "    Learn the parameters of the model using gradient descent using \n",
    "    the *training set*. Gradient descent is an optimization algorithm \n",
    "    used to minimize some (loss) function by iteratively moving in \n",
    "    the direction of steepest descent as defined by the negative of \n",
    "    the gradient. We use gradient descent to update the parameters\n",
    "    (weights) of our model.\n",
    "\n",
    "    Input:\n",
    "    - X: Inputs  (n features over m instances).\n",
    "    - y: True labels (1 value over m instances).\n",
    "    - theta: The parameters (weights) of the model being learned.\n",
    "    - alpha: The learning rate of your model.\n",
    "    - num_iters: The number of updates performed.\n",
    "\n",
    "    Returns two values:\n",
    "    - theta: The learned parameters of your model.\n",
    "    - J_history: the loss value for every iteration.\n",
    "    \"\"\"\n",
    "    \n",
    "    J_history = [] # Use a python list to save cost in every iteration\n",
    "    theta = theta.copy() # avoid changing the original thetas\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the gradient descent optimization algorithm.            #\n",
    "    if X.ndim == 2:\n",
    "        m = len(X)-1\n",
    "        sum0 = 0\n",
    "        sum1 = 0\n",
    "        for j in range(0,num_iters):\n",
    "            J_history.insert(j, compute_cost(X, y, theta))\n",
    "            sum0 = np.dot(X,theta)-y\n",
    "            temp0 = theta[0] - alpha*(1/m)*np.sum(sum0)   \n",
    "            sum1 = np.dot((np.dot(X,theta)-y),X[:,1])\n",
    "            temp1 = theta[1] - alpha*(1/m)*np.sum(sum1)\n",
    "            theta[0] = temp0\n",
    "            theta[1] = temp1\n",
    "    else:\n",
    "        m = len(X)-1\n",
    "        sum0 = 0\n",
    "        sumTemp = 0\n",
    "        for j in range(1,num_iters):\n",
    "            J_history.insert(j, compute_cost(X, y, theta))\n",
    "            sum0 = np.dot(X,theta)-y\n",
    "            temp0 = theta[0] - alpha*(1/m)*np.sum(sum0) \n",
    "            for i in range(1,X.ndim):\n",
    "                sumTemp = np.dot((np.dot(X,theta)-y),X[:,i])\n",
    "                temp1 = theta[i] - alpha*(1/m)*np.sum(sumTemp)\n",
    "                theta[i] = temp1\n",
    "            theta[0] = temp0\n",
    "    ###########################################################################\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-59b95cbea13e7fc1",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.random(size=2)\n",
    "iterations = 40000\n",
    "alpha = 0.1\n",
    "theta, J_history = gradient_descent(X_train ,y_train, theta, alpha, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-86125cd57f0fdb89",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "You can evaluate the learning process by monitoring the loss as training progress. In the following graph, we visualize the loss as a function of the iterations. This is possible since we are saving the loss value at every iteration in the `J_history` array. This visualization might help you find problems with your code. Notice that since the network converges quickly, we are using logarithmic scale for the number of iterations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-a565f1f721f6377f",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(iterations), J_history)\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-3bdd058ecc5db0eb",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Implement the pseudo-inverse function `pinv`. **Do not use `np.linalg.pinv`**, instead use only direct matrix multiplication as you saw in class (you can calculate the inverse of a matrix using `np.linalg.inv`). (10 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pinv(X, y):\n",
    "    \"\"\"\n",
    "    Calculate the optimal values of the parameters using the pseudoinverse\n",
    "    approach as you saw in class using the *training set*.\n",
    "\n",
    "    Input:\n",
    "    - X: Inputs  (n features over m instances).\n",
    "    - y: True labels (1 value over m instances).\n",
    "\n",
    "    Returns two values:\n",
    "    - theta: The optimal parameters of your model.\n",
    "\n",
    "    ########## DO NOT USE np.linalg.pinv ##############\n",
    "    \"\"\"\n",
    "    pinv_theta = []\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the pseudoinverse algorithm.                            #\n",
    "    pinv_theta = np.dot(np.dot(np.linalg.inv(np.dot(np.transpose(X),X)),np.transpose(X)),y)\n",
    "    ###########################################################################\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return pinv_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-ee89ac06af3087ae",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta_pinv = pinv(X_train ,y_train)\n",
    "J_pinv = compute_cost(X_train, y_train, theta_pinv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add the loss value for the theta calculated using the psuedo-inverse to our graph. This is another sanity check as the loss of our model should converge to the psuedo-inverse loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-639b53fc41479335",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(iterations), J_history)\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations')\n",
    "plt.hlines(y = J_pinv, xmin = 0, xmax = len(J_history), color='r',\n",
    "           linewidth = 1, linestyle = 'dashed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-5043aa5363cbe5c9",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "We can use a better approach for the implementation of `gradient_descent`. Instead of performing 40,000 iterations, we wish to stop when the improvement of the loss value is smaller than `1e-8` from one iteration to the next. Implement the function `efficient_gradient_descent`. (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def efficient_gradient_descent(X, y, theta, alpha, num_iters):\n",
    "    \"\"\"\n",
    "    Learn the parameters of your model using the *training set*, but stop \n",
    "    the learning process once the improvement of the loss value is smaller \n",
    "    than 1e-8. This function is very similar to the gradient descent \n",
    "    function you already implemented.\n",
    "\n",
    "    Input:\n",
    "    - X: Inputs  (n features over m instances).\n",
    "    - y: True labels (1 value over m instances).\n",
    "    - theta: The parameters (weights) of the model being learned.\n",
    "    - alpha: The learning rate of your model.\n",
    "    - num_iters: The number of updates performed.\n",
    "\n",
    "    Returns two values:\n",
    "    - theta: The learned parameters of your model.\n",
    "    - J_history: the loss value for every iteration.\n",
    "    \"\"\"\n",
    "    \n",
    "    J_history = [] # Use a python list to save cost in every iteration\n",
    "    theta = theta.copy() # avoid changing the original thetas\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the gradient descent optimization algorithm.            #\n",
    "    m = len(X)-1\n",
    "    sum0 = 0\n",
    "    sum1 = 0\n",
    "    costPrev = 1\n",
    "    cost = 0\n",
    "    for j in range(0,num_iters):\n",
    "        cost = compute_cost(X, y, theta)\n",
    "        if(costPrev-cost < 0.000000001):\n",
    "            break\n",
    "        J_history.insert(j, cost)\n",
    "        sum0 = np.dot(X,theta)-y\n",
    "        temp0 = theta[0] - alpha*(1/m)*np.sum(sum0)   \n",
    "        sum1 = np.dot((np.dot(X,theta)-y),X[:,1])\n",
    "        temp1 = theta[1] - alpha*(1/m)*np.sum(sum1)\n",
    "        theta[0] = temp0\n",
    "        theta[1] = temp1\n",
    "        costPrev = cost\n",
    "    ###########################################################################\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-6e2524d07523d950",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "The learning rate is another factor that determines the performance of our model in terms of speed and accuracy. Complete the function `find_best_alpha`. Make sure you use the training dataset to learn the parameters (thetas) and use those parameters with the validation dataset to compute the cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_best_alpha(X_train, y_train, X_val, y_val, iterations):\n",
    "    \"\"\"\n",
    "    Iterate over provided values of alpha and train a model using the \n",
    "    *training* dataset. maintain a python dictionary with alpha as the \n",
    "    key and the loss on the *validation* set as the value.\n",
    "\n",
    "    Input:\n",
    "    - X_train, y_train, X_val, y_val: the training and validation data\n",
    "    - iterations: maximum number of iterations\n",
    "\n",
    "    Returns:\n",
    "    - alpha_dict: A python dictionary - {key (alpha) : value (validation loss)}\n",
    "    \"\"\"\n",
    "    \n",
    "    alphas = [0.00001, 0.00003, 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 2, 3]\n",
    "    alpha_dict = {}\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the function.                                           #\n",
    "    #chose a random theta\n",
    "    thetaTemp = [1,1]\n",
    "    for alpha in alphas:\n",
    "        theta, J_history= efficient_gradient_descent(X_train, y_train, thetaTemp, alpha, iterations)\n",
    "        temp = {alpha:compute_cost(X_val, y_val, theta)}\n",
    "        alpha_dict.update(temp)\n",
    "    ###########################################################################\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return alpha_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-a8b088fe7a10910a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (4000,18) and (2,) not aligned: 18 (dim 1) != 2 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-40-41baf2b550ed>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0malpha_dict\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfind_best_alpha\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m40000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-39-70b2b8bbddbe>\u001b[0m in \u001b[0;36mfind_best_alpha\u001b[1;34m(X_train, y_train, X_val, y_val, iterations)\u001b[0m\n\u001b[0;32m     20\u001b[0m     \u001b[0mthetaTemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     21\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;32min\u001b[0m \u001b[0malphas\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 22\u001b[1;33m         \u001b[0mtheta\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ_history\u001b[0m\u001b[1;33m=\u001b[0m \u001b[0mefficient_gradient_descent\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mthetaTemp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0miterations\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     23\u001b[0m         \u001b[0mtemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m{\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mcompute_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     24\u001b[0m         \u001b[0malpha_dict\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtemp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-20-d6175f93988a>\u001b[0m in \u001b[0;36mefficient_gradient_descent\u001b[1;34m(X, y, theta, alpha, num_iters)\u001b[0m\n\u001b[0;32m     28\u001b[0m     \u001b[0mcost\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnum_iters\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 30\u001b[1;33m         \u001b[0mcost\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcompute_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     31\u001b[0m         \u001b[1;32mif\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcostPrev\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mcost\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m0.000000001\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     32\u001b[0m             \u001b[1;32mbreak\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-12-a39a7718e3ca>\u001b[0m in \u001b[0;36mcompute_cost\u001b[1;34m(X, y, theta)\u001b[0m\n\u001b[0;32m     18\u001b[0m     \u001b[0msum\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m     \u001b[0mm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 20\u001b[1;33m     \u001b[0mhypothes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubtract\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     21\u001b[0m     \u001b[0msum\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mhypothes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mhypothes\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m     \u001b[0msum\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mdot\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: shapes (4000,18) and (2,) not aligned: 18 (dim 1) != 2 (dim 0)"
     ]
    }
   ],
   "source": [
    "alpha_dict = find_best_alpha(X_train, y_train, X_val, y_val, 40000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-5bd93130c022d3e1",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Obtain the best learning rate from the dictionary `alpha_dict`. This can be done in a single line using built-in functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4f81cf375ac46b73",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "best_alpha = None\n",
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "best_alpha = min(alpha_dict, key=alpha_dict.get)\n",
    "###########################################################################\n",
    "pass\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################\n",
    "print(best_alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-d16367ecb7183996",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Pick the best three alpha values you just calculated and provide **one** graph with three lines indicating the training loss as a function of iterations (Use 10,000 iterations). Note you are required to provide general code for this purpose (no hard-coding). Make sure the visualization is clear and informative. (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-448638e817503ca3",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "###########################################################################\n",
    "#pick best 3 alphas\n",
    "alphas = sorted(alpha_dict,key=alpha_dict.get)[:3]\n",
    "#pick random theta\n",
    "thetaTemp = [1,1]\n",
    "#draw\n",
    "for i in range(0,3):\n",
    "    _, J_history= gradient_descent(X_train, y_train, thetaTemp, alphas[i], 10000)\n",
    "    plt.plot(np.arange(10000), J_history, label = \"plot of alpha: \" + '{}'.format(alphas[i]))\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "pass\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-b73893d236bff1d5",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "This is yet another sanity check. This function plots the regression lines of your model and the model based on the pseudoinverse calculation. Both models should exhibit the same trend through the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-c7ee7d8763464371",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(X_train[:,1], y_train, 'ro', ms=1, mec='k')\n",
    "plt.ylabel('Price in USD')\n",
    "plt.xlabel('sq.ft')\n",
    "plt.plot(X_train[:, 1], np.dot(X_train, theta), 'o')\n",
    "plt.plot(X_train[:, 1], np.dot(X_train, theta_pinv), '-')\n",
    "\n",
    "plt.legend(['Training data', 'Linear regression', 'Best theta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-e77c602466fab37d",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part 2: Multivariate Linear Regression (30 points)\n",
    "\n",
    "In most cases, you will deal with databases that have more than one feature. It can be as little as two features and up to thousands of features. In those cases, we use a multiple linear regression model. The regression equation is almost the same as the simple linear regression equation:\n",
    "\n",
    "$$\n",
    "\\hat{y} = h_\\theta(\\vec{x}) = \\theta^T \\vec{x} = \\theta_0 + \\theta_1 x_1 + ... + \\theta_n x_n\n",
    "$$\n",
    "\n",
    "\n",
    "If you wrote vectorized code, this part should be straightforward. If your code is not vectorized, you should go back and edit your functions such that they support both multivariate and single variable regression. **Your code should not check the dimensionality of the input before running**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-15626dda8db26550",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
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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>date</th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7129300520</td>\n",
       "      <td>20141013T000000</td>\n",
       "      <td>221900.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6414100192</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>538000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>20150225T000000</td>\n",
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       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2487200875</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>604000.0</td>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1954400510</td>\n",
       "      <td>20150218T000000</td>\n",
       "      <td>510000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           id             date     price  bedrooms  bathrooms  sqft_living  \\\n",
       "0  7129300520  20141013T000000  221900.0         3       1.00         1180   \n",
       "1  6414100192  20141209T000000  538000.0         3       2.25         2570   \n",
       "2  5631500400  20150225T000000  180000.0         2       1.00          770   \n",
       "3  2487200875  20141209T000000  604000.0         4       3.00         1960   \n",
       "4  1954400510  20150218T000000  510000.0         3       2.00         1680   \n",
       "\n",
       "   sqft_lot  floors  waterfront  view  condition  grade  sqft_above  yr_built  \\\n",
       "0      5650     1.0           0     0          3      7        1180      1955   \n",
       "1      7242     2.0           0     0          3      7        2170      1951   \n",
       "2     10000     1.0           0     0          3      6         770      1933   \n",
       "3      5000     1.0           0     0          5      7        1050      1965   \n",
       "4      8080     1.0           0     0          3      8        1680      1987   \n",
       "\n",
       "   yr_renovated  zipcode      lat     long  sqft_living15  sqft_lot15  \n",
       "0             0    98178  47.5112 -122.257           1340        5650  \n",
       "1          1991    98125  47.7210 -122.319           1690        7639  \n",
       "2             0    98028  47.7379 -122.233           2720        8062  \n",
       "3             0    98136  47.5208 -122.393           1360        5000  \n",
       "4             0    98074  47.6168 -122.045           1800        7503  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read comma separated data\n",
    "df = pd.read_csv('data.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-2dc0f4dc3491520c",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Preprocessing\n",
    "\n",
    "Like in the single variable case, we need to create a numpy array from the dataframe. Before doing so, we should notice that some of the features are clearly irrelevant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-a87b4027bd3bda4b",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "X = df.drop(columns=['price', 'id', 'date']).values\n",
    "y = df['price'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-1aa12f54513b1efa",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Use the **same** `preprocess` function you implemented previously. Notice that proper vectorized implementation should work regardless of the dimensionality of the input. You might want to check that your code in the previous parts still works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-f40a9df530db9399",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "# preprocessing\n",
    "X, y = preprocess(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# training and validation split\n",
    "np.random.seed(42)\n",
    "indices = np.random.permutation(X.shape[0])\n",
    "idx_train, idx_val = indices[:int(0.8*X.shape[0])], indices[int(0.8*X.shape[0]):]\n",
    "X_train, X_val = X[idx_train,:], X[idx_val,:]\n",
    "y_train, y_val = y[idx_train], y[idx_val]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using 3D visualization, we can still observe trends in the data. Visualizing additional dimensions requires advanced techniques we will learn later in the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-0c68216a26a9b5af",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import mpl_toolkits.mplot3d.axes3d as p3\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = p3.Axes3D(fig)\n",
    "xx = X_train[:, 1][:1000]\n",
    "yy = X_train[:, 2][:1000]\n",
    "zz = y_train[:1000]\n",
    "ax.scatter(xx, yy, zz, marker='o')\n",
    "ax.set_xlabel('bathrooms')\n",
    "ax.set_ylabel('sqft_living')\n",
    "ax.set_zlabel('price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-70fcd47d69caea00",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Use the bias trick again (add a column of ones as the zeroth column in the both the training and validation datasets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-2985911f4b7af3e1",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "###########################################################################\n",
    "X_train = np.column_stack((np.ones(len(X_train)),X_train))\n",
    "X_val = np.column_stack((np.ones(len(X_val)),X_val))\n",
    "pass\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-2b89288ff61c80ac",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "Make sure the functions `compute_cost` (10 points), `gradient_descent` (15 points), and `pinv` (5 points) work on the multi-dimensional dataset. If you make any changes, make sure your code still works on the single variable regression model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-81ab741781b2f6ec",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "shape = X_train.shape[1]\n",
    "theta = np.ones(shape)\n",
    "J = compute_cost(X_train, y_train, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-6f25fb05bd6c648a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "shape = X_train.shape[1]\n",
    "theta = np.random.random(shape)\n",
    "iterations = 40000\n",
    "theta, J_history = gradient_descent(X_train ,y_train, theta, best_alpha, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-827d1de1293be51f",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "theta_pinv = pinv(X_train ,y_train)\n",
    "J_pinv = compute_cost(X_train, y_train, theta_pinv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use visualization to make sure the code works well. Notice we use logarithmic scale for the number of iterations, since gradient descent converges after ~500 iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4fa207b72d2445c2",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "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": [
    "plt.plot(np.arange(iterations), J_history)\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations - multivariate linear regression')\n",
    "plt.hlines(y = J_pinv, xmin = 0, xmax = len(J_history), color='r',\n",
    "           linewidth = 1, linestyle = 'dashed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-cad652570cee3629",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part 3: Find best features for regression (10 points)\n",
    "\n",
    "Adding additional features to our regression model makes it more complicated but does not necessarily improves performance.\n",
    "Use forward and backward selection and find 4 features that best minimizes the loss. First, we will reload the dataset as a dataframe in order to access the feature names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
       "      <td>8080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living  sqft_lot  floors  waterfront  view  \\\n",
       "0         3       1.00         1180      5650     1.0           0     0   \n",
       "1         3       2.25         2570      7242     2.0           0     0   \n",
       "2         2       1.00          770     10000     1.0           0     0   \n",
       "3         4       3.00         1960      5000     1.0           0     0   \n",
       "4         3       2.00         1680      8080     1.0           0     0   \n",
       "\n",
       "   condition  grade  sqft_above  yr_built  yr_renovated  zipcode      lat  \\\n",
       "0          3      7        1180      1955             0    98178  47.5112   \n",
       "1          3      7        2170      1951          1991    98125  47.7210   \n",
       "2          3      6         770      1933             0    98028  47.7379   \n",
       "3          5      7        1050      1965             0    98136  47.5208   \n",
       "4          3      8        1680      1987             0    98074  47.6168   \n",
       "\n",
       "      long  sqft_living15  sqft_lot15  \n",
       "0 -122.257           1340        5650  \n",
       "1 -122.319           1690        7639  \n",
       "2 -122.233           2720        8062  \n",
       "3 -122.393           1360        5000  \n",
       "4 -122.045           1800        7503  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns_to_drop = ['price', 'id', 'date']\n",
    "all_features = df.drop(columns=columns_to_drop)\n",
    "all_features.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Feature Selection\n",
    "\n",
    "Complete the function `forward_selection`. Train the model using a single feature at a time, and choose the best feature using the validation dataset. Next, check which feature performs best when added to the feature you previously chose. Repeat this process until you reach 4 features + bias. You are free to use any arguments you need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def forward_selection():\n",
    "    \"\"\"\n",
    "    Train the model using the training set using a single feature. \n",
    "    Choose the best feature according to the validation set. Next, \n",
    "    check which feature performs best when added to the feature\n",
    "    you previously chose. Repeat this process until you reach 4 \n",
    "    features and the bias. Don't forget the bias trick.\n",
    "\n",
    "    Returns:\n",
    "    - The names of the best features using forward selection.\n",
    "    \"\"\"\n",
    "    np.random.seed(42)\n",
    "    best_features = None\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the function.                                           #\n",
    "    ###########################################################################\n",
    "    # for instructors: we have some RuntimeWarning here but the method works it take about 1 minute\n",
    "    best_features = []\n",
    "    cost_dict = {}\n",
    "    iterations = 10000\n",
    "    alpha = 0.1\n",
    "    length= len(all_features.columns)\n",
    "    #bias trick already preformed in cell 29\n",
    "    thetaTemp = np.random.random(2)\n",
    "    for i in range(1,length+1):\n",
    "        #every iteration create 2-D model with the current feature\n",
    "        feature_X_train_Curr = np.column_stack((np.ones(len(X_train[:,i])),X_train[:,i]))\n",
    "        feature_X_Val_Curr = np.column_stack((np.ones(len(X_val[:,i])),X_val[:,i]))\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr,y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    \n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(3)\n",
    "    for i in range(1,length+1):\n",
    "        #every iteration create 3-D model with the current feature and the first best feature\n",
    "        temp1 = np.column_stack((np.array(all_features[best_features[0]].values)[0:4000],X_train[:,i]))\n",
    "        feature_X_train_Curr = np.column_stack((np.ones(len(X_train[:,i])),temp1))\n",
    "        temp2 = np.column_stack((np.array(all_features[best_features[0]].values)[4000:5000],X_val[:,i]))\n",
    "        feature_X_Val_Curr = np.column_stack((np.ones(len(X_val[:,i])),temp2))\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr,y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    \n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(4)\n",
    "    for i in range(1,length+1):\n",
    "        #every iteration create 4-D model with the current feature and the first and second best features\n",
    "        temp1 = np.column_stack((np.array(all_features[best_features[0]].values)[0:4000],X_train[:,i]))\n",
    "        temp1_1 = np.column_stack((np.array(all_features[best_features[1]].values)[0:4000],temp1))\n",
    "        feature_X_train_Curr = np.column_stack((np.ones(len(X_train[:,i])),temp1_1))\n",
    "        temp2 = np.column_stack((np.array(all_features[best_features[0]].values)[4000:5000],X_val[:,i]))\n",
    "        temp2_1 = np.column_stack((np.array(all_features[best_features[1]].values)[4000:5000],temp2))\n",
    "        feature_X_Val_Curr = np.column_stack((np.ones(len(X_val[:,i])),temp2_1))\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr,y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    del cost_dict[best_features[1]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)  \n",
    "\n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(5)\n",
    "    for i in range(1,length+1):\n",
    "        #every iteration create 5-D model with the current feature and the first, second and third best features\n",
    "        temp1 = np.column_stack((np.array(all_features[best_features[0]].values)[0:4000],X_train[:,i]))\n",
    "        temp1_1 = np.column_stack((np.array(all_features[best_features[1]].values)[0:4000],temp1))\n",
    "        temp1_2 = np.column_stack((np.array(all_features[best_features[2]].values)[0:4000],temp1_1))\n",
    "        feature_X_train_Curr = np.column_stack((np.ones(len(X_train[:,i])),temp1_2))\n",
    "        temp2 = np.column_stack((np.array(all_features[best_features[0]].values)[4000:5000],X_val[:,i]))\n",
    "        temp2_1 = np.column_stack((np.array(all_features[best_features[1]].values)[4000:5000],temp2))\n",
    "        temp2_2 = np.column_stack((np.array(all_features[best_features[2]].values)[4000:5000],temp2_1))\n",
    "        feature_X_Val_Curr = np.column_stack((np.ones(len(X_val[:,i])),temp2_2))\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr,y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    del cost_dict[best_features[1]]\n",
    "    del cost_dict[best_features[2]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return best_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\97250\\anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:87: RuntimeWarning: overflow encountered in reduce\n",
      "  return ufunc.reduce(obj, axis, dtype, out, **passkwargs)\n",
      "<ipython-input-14-ab7e1db389c9>:33: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  temp0 = theta[0] - alpha*(1/m)*np.sum(sum0)\n",
      "<ipython-input-14-ab7e1db389c9>:35: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  temp1 = theta[1] - alpha*(1/m)*np.sum(sum1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['sqft_living', 'bedrooms', 'yr_built', 'bathrooms']"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forward_selection()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backward Feature Selection\n",
    "\n",
    "Complete the function `backward_selection`. Train the model with all but one of the features at a time and remove the worst feature (the feature that its absence yields the best loss value using the validation dataset). Next, remove an additional feature along with the feature you previously removed. Repeat this process until you reach 4 features + bias. You are free to use any arguments you need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "this is a help function to find the index of a colum by name ataFrame\n",
    "\"\"\"\n",
    "def indexOfColum(name):\n",
    "    arr = list(all_features.columns)\n",
    "    for i in range(0,len(arr)):\n",
    "        if(arr[i] == name):\n",
    "            return i;\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_selection():\n",
    "    \"\"\"\n",
    "    Train the model using the training set using all but one of the \n",
    "    features at a time. Remove the worst feature according to the \n",
    "    validation set. Next, remove an additional feature along with the \n",
    "    feature you previously removed. Repeat this process until you \n",
    "    reach 4 features and the bias. Don't forget the bias trick.\n",
    "\n",
    "    Returns:\n",
    "    - The names of the best features using backward selection.\n",
    "    \"\"\"\n",
    "    np.random.seed(42)\n",
    "    best_features = None\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the function.                                           #\n",
    "    ###########################################################################\n",
    "    \n",
    "    best_features = []\n",
    "    cost_dict = {}\n",
    "    iterations = 10000\n",
    "    alpha = 0.1\n",
    "    length= len(all_features.columns)\n",
    "    #bias trick\n",
    "    thetaTemp = np.random.random(X_train.shape[1]-1)\n",
    "    for i in range(1,length+1):\n",
    "    #every iteration create model without the current feature\n",
    "        feature_X_train_Curr = np.delete(X_train, i, 1)\n",
    "        feature_X_Val_Curr = np.delete(X_val, i, 1)\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr, y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    \n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(X_train.shape[1]-2)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[0])\n",
    "    feature_X_train_Curr = np.delete(X_train, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr = np.delete(X_val, indexOfFirstFeature, 1)\n",
    "    for i in range(1,length):\n",
    "    #every iteration create model without the current feature and the previous\n",
    "        feature_X_train_Curr1 = np.delete(feature_X_train_Curr, i, 1)\n",
    "        feature_X_Val_Curr1 = np.delete(feature_X_Val_Curr, i, 1)\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr1, y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr1, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    \n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(X_train.shape[1]-3)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[0])\n",
    "    feature_X_train_Curr = np.delete(X_train, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr = np.delete(X_val, indexOfFirstFeature, 1)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[1])\n",
    "    feature_X_train_Curr1 = np.delete(feature_X_train_Curr, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr1 = np.delete(feature_X_Val_Curr, indexOfFirstFeature, 1)\n",
    "    for i in range(1,length-1):\n",
    "    #every iteration create model without the current feature and the 2 previous features\n",
    "        feature_X_train_Curr2 = np.delete(feature_X_train_Curr1, i, 1)\n",
    "        feature_X_Val_Curr2 = np.delete(feature_X_Val_Curr1, i, 1)\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr2, y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr2, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    del cost_dict[best_features[1]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    \n",
    "    cost_dict = {}\n",
    "    thetaTemp = np.random.random(X_train.shape[1]-4)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[0])\n",
    "    feature_X_train_Curr = np.delete(X_train, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr = np.delete(X_val, indexOfFirstFeature, 1)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[1])\n",
    "    feature_X_train_Curr1 = np.delete(feature_X_train_Curr, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr1 = np.delete(feature_X_Val_Curr, indexOfFirstFeature, 1)\n",
    "    indexOfFirstFeature = indexOfColum(best_features[2])\n",
    "    feature_X_train_Curr2 = np.delete(feature_X_train_Curr1, indexOfFirstFeature, 1)\n",
    "    feature_X_Val_Curr2 = np.delete(feature_X_Val_Curr1, indexOfFirstFeature, 1)\n",
    "    for i in range(1,length-2):\n",
    "    #every iteration create model without the current feature and the 3 previous features\n",
    "        feature_X_train_Curr3 = np.delete(feature_X_train_Curr2, i, 1)\n",
    "        feature_X_Val_Curr3 = np.delete(feature_X_Val_Curr2, i, 1)\n",
    "        thetaCurr,_ = gradient_descent(feature_X_train_Curr3, y_train, thetaTemp, alpha, iterations)\n",
    "        costCurr = compute_cost(feature_X_Val_Curr3, y_val, thetaCurr)\n",
    "        temp = {all_features.columns[i-1]:costCurr}\n",
    "        #add the name of the feature and the cost to cost_dict\n",
    "        cost_dict.update(temp)\n",
    "    #find the first feature\n",
    "    del cost_dict[best_features[0]]\n",
    "    del cost_dict[best_features[1]]\n",
    "    del cost_dict[best_features[2]]\n",
    "    best_first_feture = min(cost_dict, key=cost_dict.get)\n",
    "    #append the name of the best feature to best_features\n",
    "    best_features.append(best_first_feture)\n",
    "    pass\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return best_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['bedrooms', 'waterfront', 'bathrooms', 'sqft_living']"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backward_selection()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Give an explanations to the results. Do they make sense?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ANSWER:\n",
    "the result of Forward Feature Selection : ['sqft_living', 'bedrooms', 'yr_built', 'bathrooms']\n",
    "the result of Backward Feature Selection : ['bedrooms', 'waterfront', 'bathrooms', 'sqft_living']\n",
    "In terms of result, we have 3 equal futures that are: 'bedrooms', 'bathrooms','sqft_living'. and only one is different. so the results do make sense. we can see that there is a high level of accuracy for using each of the functions and 75% match.\n",
    "In terms of runtime, it makes sense that the forward selection is better than the backward selection because in the backward selection we always create a large dimensions model for each column so the calculation of the hypotheses is longer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use this Markdown cell for your answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Adaptive Learning Rate (10 points)\n",
    "\n",
    "So far, we kept the learning rate alpha constant during training. However, changing alpha during training might improve convergence in terms of the global minimum found and running time. Implement the adaptive learning rate method based on the gradient descent algorithm above. \n",
    "\n",
    "**Your task is to find proper hyper-parameter values for the adaptive technique and compare this technique to the constant learning rate. Use clear visualizations of the validation loss and the learning rate as a function of the iteration**. \n",
    "\n",
    "Time based decay: this method reduces the learning rate every iteration according to the following formula:\n",
    "\n",
    "$$\\alpha = \\frac{\\alpha_0}{1 + D \\cdot t}$$\n",
    "\n",
    "Where $\\alpha_0$ is the original learning rate, $D$ is a decay factor and $t$ is the current iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Your code here ###\n",
    "def gradient_descent_adaptive_learning_rate(X, y, theta, alpha, num_iters, d):\n",
    "    \"\"\"\n",
    "    Learn the parameters of the model using adaptive learning rate gradient descent using \n",
    "    the training set.\n",
    "\n",
    "    Input:\n",
    "    - X: Inputs  (n features over m instances).\n",
    "    - y: True labels (1 value over m instances).\n",
    "    - theta: The parameters (weights) of the model being learned.\n",
    "    - alpha: The learning rate of your model.\n",
    "    - num_iters: The number of updates performed.\n",
    "    - d: decay factor\n",
    "\n",
    "    Returns two values:\n",
    "    - theta: The learned parameters of your model.\n",
    "    - J_history: the loss value for every iteration.\n",
    "    \"\"\"\n",
    "    J_history = [] # Use a python list to save cost in every iteration\n",
    "    theta = theta.copy() # avoid changing the original thetas\n",
    "    if X.ndim == 2:\n",
    "        m = len(X)-1\n",
    "        sum0 = 0\n",
    "        sum1 = 0\n",
    "        costPrev = 1\n",
    "        cost = 0\n",
    "        alpha1 = best_alpha\n",
    "        for j in range(0,num_iters):\n",
    "            cost = compute_cost(X, y, theta)\n",
    "            if(costPrev-cost < 0.000000001):\n",
    "                break\n",
    "            J_history.insert(j, cost)\n",
    "            sum0 = np.dot(X,theta)-y\n",
    "            alpha = alpha1 / (1 + (d*j))\n",
    "            temp0 = theta[0] - alpha*(1/m)*np.sum(sum0)   \n",
    "            sum1 = np.dot((np.dot(X,theta)-y),X[:,1])\n",
    "            temp1 = theta[1] - alpha*(1/m)*np.sum(sum1)\n",
    "            theta[0] = temp0\n",
    "            theta[1] = temp1\n",
    "            cost = costPrev\n",
    "    else:\n",
    "        m = len(X)-1\n",
    "        sum0 = 0\n",
    "        sumTemp = 0\n",
    "        for j in range(1,num_iters):\n",
    "            J_history.insert(j, compute_cost(X, y, theta))\n",
    "            sum0 = np.dot(X,theta)-y\n",
    "            alpha = alpha / (1 + (d*j))\n",
    "            temp0 = theta[0] - alpha*(1/m)*np.sum(sum0) \n",
    "            for i in range(1,X.ndim):\n",
    "                sumTemp = np.dot((np.dot(X,theta)-y),X[:,i])\n",
    "                temp1 = theta[i] - alpha*(1/m)*np.sum(sumTemp)\n",
    "                theta[i] = temp1\n",
    "            theta[0] = temp0\n",
    "    pass\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01\n"
     ]
    }
   ],
   "source": [
    "D = [0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.0005,0.1,0.01,0.001,0.0001]\n",
    "best_D = 0\n",
    "# the code is generic but we decided randomly to work with three variable linear regression\n",
    "X = df[['sqft_living','bedrooms','bathrooms']].values\n",
    "y = df['price'].values\n",
    "X,y = preprocess(X,y)\n",
    "# training and validation split\n",
    "np.random.seed(42)\n",
    "indices = np.random.permutation(X.shape[0])\n",
    "idx_train, idx_val = indices[:int(0.8*X.shape[0])], indices[int(0.8*X.shape[0]):]\n",
    "X_train, X_val = X[idx_train], X[idx_val]\n",
    "y_train, y_val = y[idx_train], y[idx_val]\n",
    "X_train = np.column_stack((np.ones(len(X_train)),X_train))\n",
    "X_val = np.column_stack((np.ones(len(X_val)),X_val))\n",
    "current_minimum = 1000\n",
    "theta1 = np.random.random(X_train.shape[1])\n",
    "for d in D:\n",
    "    iterations = 10000\n",
    "    theta, J_history = gradient_descent_adaptive_learning_rate(X_train, y_train, theta1, best_alpha, iterations, d)\n",
    "    temp = compute_cost(X_val, y_val, theta)\n",
    "    if temp < current_minimum:\n",
    "        current_minimum = temp\n",
    "        best_D = d\n",
    "print(best_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "#comparation of the gradient descent adaptive learning rate method to the constant learning rate#\n",
    "D = [0,0.01]\n",
    "np.random.seed(42)\n",
    "theta = np.random.random(size=4)\n",
    "iterations = 10000\n",
    "alpha = 0.1\n",
    "for i in range(0,2):\n",
    "    theta, J_history = gradient_descent_adaptive_learning_rate(X_train ,y_train, theta, alpha, iterations, D[i])\n",
    "    plt.plot(np.arange(10000), J_history, label = \"plot of D: \" + '{}'.format(D[i]))\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### explanation:\n",
    "the graph shows a run of D = 0 for the constant learning rate (if we set D to be 0 we run constant learning rate GD) and also a run of D = 0.01 which is the best D we found for the adaptive learning rate.\n",
    "we can see a small difference between the adaptive learning rate and constant learning rate. the adaptive learning rate is better than the constant learning rate and convergent faster"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}