ML.3141_hw1_YaFo_grade100.ipynb

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    "# 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",
    "### Make sure you restart the notebook and check the filename before submission. Appeals based on wrong filenames and errors due to syntax and execution errors will not be accepted.\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. Perform polynomial regression.\n",
    "1. Experiment with adaptive learning rates."
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    "# I have read and understood the instructions: XXXXXXXXX XXXXXXXXX"
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    "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'"
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   "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."
   ]
  },
  {
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   "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"
   ]
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   "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."
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       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>date</th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
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       "      <th>yr_renovated</th>\n",
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       "      <th>lat</th>\n",
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       "      <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",
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       "      <td>0</td>\n",
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       "      <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",
       "      <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",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5631500400</td>\n",
       "      <td>20150225T000000</td>\n",
       "      <td>180000.0</td>\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",
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       "      <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",
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       "    <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",
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       "      <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",
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       "    <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",
       "      <td>8080</td>\n",
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       "      <td>0</td>\n",
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       "      <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",
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       "           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  "
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       "      <th>bathrooms</th>\n",
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       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
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       "      <th>condition</th>\n",
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       "    <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",
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       "    <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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 5000 entries, 0 to 4999\n",
      "Data columns (total 20 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   id             5000 non-null   int64  \n",
      " 1   date           5000 non-null   object \n",
      " 2   price          5000 non-null   float64\n",
      " 3   bedrooms       5000 non-null   int64  \n",
      " 4   bathrooms      5000 non-null   float64\n",
      " 5   sqft_living    5000 non-null   int64  \n",
      " 6   sqft_lot       5000 non-null   int64  \n",
      " 7   floors         5000 non-null   float64\n",
      " 8   waterfront     5000 non-null   int64  \n",
      " 9   view           5000 non-null   int64  \n",
      " 10  condition      5000 non-null   int64  \n",
      " 11  grade          5000 non-null   int64  \n",
      " 12  sqft_above     5000 non-null   int64  \n",
      " 13  yr_built       5000 non-null   int64  \n",
      " 14  yr_renovated   5000 non-null   int64  \n",
      " 15  zipcode        5000 non-null   int64  \n",
      " 16  lat            5000 non-null   float64\n",
      " 17  long           5000 non-null   float64\n",
      " 18  sqft_living15  5000 non-null   int64  \n",
      " 19  sqft_lot15     5000 non-null   int64  \n",
      "dtypes: float64(5), int64(14), object(1)\n",
      "memory usage: 781.4+ KB\n"
     ]
    }
   ],
   "source": [
    "# adding df.info() for organized listing of feature names & data types\n",
    "df.info()"
   ]
  },
  {
   "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 mean_normalize(data):\n",
    "    \"\"\"\n",
    "    Perform mean normalization on the features and true labels.\n",
    "\n",
    "    Note: Orig used mean normalization standardization (std_dev in denominator) as taught in class\n",
    "    ...then switched to mean normalization method with (x_max - x_min) in denominator per Ben on piazza\n",
    "    \"\"\"\n",
    "    return (data - data.mean(axis=0)) / (data.max(axis=0) - data.min(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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 two values:\n",
    "    - X: The mean normalized inputs.\n",
    "    - y: The mean normalized labels.\n",
    "    \"\"\"\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the normalization function.                             #\n",
    "    ###########################################################################\n",
    "    \n",
    "    X, y = mean_normalize(X), mean_normalize(y)\n",
    "\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-9bb6a28b6b6932fa",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.09120464,  0.0526877 , -0.1336477 , ..., -0.04979677,\n",
       "        -0.08602865,  0.01438542]),\n",
       " array([-0.04546455, -0.00021043, -0.05146311, ..., -0.04380384,\n",
       "        -0.01996705,  0.00107805]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = preprocess(X, y)\n",
    "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": 12,
   "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": {
    "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": 13,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-cbad8871e083093f",
     "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(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 predictions 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 zero$^{th}$ column of the features (do this for both the training and validation sets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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",
    "###########################################################################\n",
    "\n",
    "def bias_trick(X):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "    - X: inputs  (n features over m instances).\n",
    "    \n",
    "    Output:\n",
    "    - stacks 2 1D arrays (X and np.ones of =size) into 2D column array\n",
    "    - Returns X with a column of ones as the zeroth column, ie the bias 𝜃_0 \n",
    "     \n",
    "    Example:\n",
    "    Input = [0, 10]\n",
    "    Output = [1, 0]\n",
    "             [1, 10]\n",
    "    \"\"\"\n",
    "\n",
    "    return np.column_stack((np.ones(X.shape[0]), X))\n",
    "\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4000, 2) \n",
      " [[ 1.         -0.07464149]\n",
      " [ 1.         -0.02081126]\n",
      " [ 1.          0.15931296]\n",
      " ...\n",
      " [ 1.         -0.08188787]\n",
      " [ 1.         -0.03116323]\n",
      " [ 1.         -0.02598725]]\n"
     ]
    }
   ],
   "source": [
    "X_train, X_val = bias_trick(X_train), bias_trick(X_val)\n",
    "print(X_train.shape, \"\\n\", X_train) # check that bias_trick worked"
   ]
  },
  {
   "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": 16,
   "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",
    "    ###########################################################################\n",
    "   \n",
    "    # using np.mean to avoid extra step of defining m instances\n",
    "    J = np.mean((X @ theta - y) ** 2) / 2 \n",
    "    \n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4c1cfec24e144479",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "𝐽(𝜃) = 0.511\n"
     ]
    }
   ],
   "source": [
    "theta = np.array([-1, 2])\n",
    "J = compute_cost(X_train, y_train, theta)\n",
    "print (f'𝐽(𝜃) = {J:.3f}')"
   ]
  },
  {
   "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": 18,
   "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",
    "    ###########################################################################\n",
    "    \n",
    "    m = X.shape[0] # number of instances or samples (4k for X_train)\n",
    "\n",
    "    for gd in range(num_iters): \n",
    "        J_history.append(compute_cost(X, y, theta)) \n",
    "        theta -= (alpha / m) * X.T @ (X @ theta - y) # update theta after J calc\n",
    "\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-59b95cbea13e7fc1",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Univariate Regression Thetas: [1.94301549e-04 4.08751964e-01] \n",
      " ========================================\n",
      "MSE on univariate training set, 𝐽(𝜃)_min: 0.00080\n",
      "\n",
      "MSE on validation/testing set: 0.00071\n"
     ]
    }
   ],
   "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)\n",
    "print (f'Univariate Regression Thetas: {theta} \\n', \"=\"*40)\n",
    "J_val = compute_cost(X_val, y_val, theta)\n",
    "print(f'MSE on univariate training set, 𝐽(𝜃)_min: {J_history[-1]:.5f}\\n')\n",
    "print(f'MSE on validation/testing set: {J_val:.5f}')"
   ]
  },
  {
   "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": 20,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-a565f1f721f6377f",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "data": {
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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)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from https://towardsdatascience.com/normal-equation-in-python-the-closed-form-solution-for-linear-regression-13df33f9ad71\n",
    "\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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",
    "    \n",
    "    pinv_theta = []\n",
    "    ###########################################################################\n",
    "    # TODO: Implement the pseudoinverse algorithm.                            #\n",
    "    ###########################################################################\n",
    "    \n",
    "    pinv_theta = np.linalg.inv(X.T @ X) @ X.T @ y # from Normal Equation above (credit: Andrew Ng)\n",
    "    \n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return pinv_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-ee89ac06af3087ae",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pseudo-Inverse Theta: [1.94301549e-04 4.08751964e-01], \n",
      " 𝐽(𝜃_pinv): 0.0008\n"
     ]
    }
   ],
   "source": [
    "theta_pinv = pinv(X_train ,y_train)\n",
    "J_pinv = compute_cost(X_train, y_train, theta_pinv)\n",
    "print(f'Pseudo-Inverse Theta: {theta_pinv}, \\n 𝐽(𝜃_pinv): {J_pinv:.4f}')"
   ]
  },
  {
   "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": 23,
   "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": 24,
   "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",
    "    **{should be - threshold: loss improvement stop condition}\n",
    "\n",
    "    Returns two values:\n",
    "    - theta: The learned parameters of your model.\n",
    "    - J_history: the loss value for every iteration.\n",
    "    **- iters: output num of iters until stopping condition reached** {added}\n",
    "    \"\"\"\n",
    "    # last input should really be threshold (1e-8) instead of num_iters, no? \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",
    "    ###########################################################################\n",
    "    # TODO: Implement the gradient descent optimization algorithm.            #\n",
    "    ###########################################################################\n",
    "    \n",
    "    m = X.shape[0] # m instances - needed for GD formula (unless use .mean)\n",
    "    threshold = 1e-8\n",
    "    loss_chg = 1\n",
    "    iters = 1\n",
    "    \n",
    "    while loss_chg >= threshold:\n",
    "        J_history.append(compute_cost(X, y, theta))    \n",
    "        theta -= (alpha / m) * X.T @ (X @ theta - y)\n",
    "        \n",
    "        if iters > 1: \n",
    "            loss_chg = abs(J_history[iters - 1] - J_history[iters - 2]) # account for diff indexes\n",
    "        iters += 1 \n",
    "\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return theta, J_history, iters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding output for efficient gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The resulting # of iterations until 1e-8 loss improvement threshold was met was: 2986 \n",
      "\n",
      "Univariate Regression Thetas using Efficient GD: [1.57852216e-04 4.42833488e-01] \n",
      " \n",
      " ======================================== \n",
      "\n",
      "MSE on univariate training set w Effic GD, 𝐽(𝜃)_min: 0.00081\n",
      "\n",
      "MSE on validation/testing set: 0.00072\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.random(size = 2)\n",
    "iterations = 40000\n",
    "alpha = 0.1\n",
    "theta, J_history, iters = efficient_gradient_descent(X_train, y_train, theta, alpha, iterations)\n",
    "print (f'The resulting # of iterations until 1e-8 loss improvement threshold was met was: {iters:.0f} \\n')\n",
    "print (f'Univariate Regression Thetas using Efficient GD: {theta} \\n \\n', \"=\"*40, '\\n')\n",
    "J_val = compute_cost(X_val, y_val, theta)\n",
    "print(f'MSE on univariate training set w Effic GD, 𝐽(𝜃)_min: {J_history[-1]:.5f}\\n')\n",
    "print (f'MSE on validation/testing set: {J_val:.5f}')"
   ]
  },
  {
   "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": 26,
   "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",
    "    ###########################################################################\n",
    "    # TODO: Implement the function.                                           #\n",
    "    ###########################################################################\n",
    "    \n",
    "    for key in alphas:\n",
    "        print(f'Loss for alpha = {key} is com-pu-tiiiing...please hold') # status updates\n",
    "        np.random.seed(42)\n",
    "        theta = np.random.random(X_train.shape[1]) # corresponding n random thetas to start\n",
    "\n",
    "        theta, J_hist = gradient_descent(X_train, y_train, theta, key, iterations)\n",
    "\n",
    "        alpha_dict[key] = compute_cost(X_val, y_val, theta) # training thetas compute cost in validation data\n",
    "\n",
    "\n",
    "    ###########################################################################\n",
    "    #                             END OF YOUR CODE                            #\n",
    "    ###########################################################################\n",
    "    return alpha_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss for alpha = 1e-05 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 3e-05 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.0001 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.0003 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.001 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.003 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.01 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.03 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.1 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 0.3 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 1 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 2 is com-pu-tiiiing...please hold\n",
      "Loss for alpha = 3 is com-pu-tiiiing...please hold\n",
      "==================== \n",
      " Alpha Dictionary: {1e-05: 0.03315313543381558, 3e-05: 0.008192951588224312, 0.0001: 0.0019743816823580705, 0.0003: 0.0017952179251561678, 0.001: 0.0013675183294403243, 0.003: 0.0008713832962435313, 0.01: 0.0007110832423673495, 0.03: 0.0007084293856373828, 0.1: 0.0007084282449873675, 0.3: 0.0007084282449873647, 1: 0.0007084282449873637, 2: 0.08536244961128663, 3: nan}\n"
     ]
    }
   ],
   "source": [
    "import warnings \n",
    "warnings.filterwarnings('ignore') # only added to suppress ugly output for alpha = 3\n",
    "\n",
    "alpha_dict = find_best_alpha(X_train, y_train, X_val, y_val, 40000)\n",
    "print(\"=\"*20, f\"\\n Alpha Dictionary: {alpha_dict}\")"
   ]
  },
  {
   "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": 28,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4f81cf375ac46b73",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best learning rate (𝛼) = 1\n"
     ]
    }
   ],
   "source": [
    "best_alpha = None\n",
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "###########################################################################\n",
    "\n",
    "best_alpha = sorted(alpha_dict, key=alpha_dict.get)[:1][0]\n",
    "\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################\n",
    "\n",
    "print(f'Best learning rate (𝛼) = {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": 30,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-448638e817503ca3",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 3 alphas / learning rates = [1, 0.3, 0.1]\n"
     ]
    }
   ],
   "source": [
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "###########################################################################\n",
    "\n",
    "best_three_alphas = sorted(alpha_dict, key=alpha_dict.get)[0:3]\n",
    "print(f'Top 3 alphas / learning rates = {best_three_alphas}')\n",
    "\n",
    "###########################################################################\n",
    "#                             END OF YOUR CODE                            #\n",
    "###########################################################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Best 3 Alphas - Visualization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "iterations = 10000\n",
    "for key in best_three_alphas:\n",
    "    np.random.seed(42)\n",
    "    theta = np.random.random(size=2)\n",
    "    theta, J_history = gradient_descent(X_train, y_train, theta, key, iterations)\n",
    "    plt.plot(np.arange(iterations), J_history, label=key)\n",
    "\n",
    "# use same scales & labels as previous loss function graphs for apples-to-apples comp\n",
    "plt.xscale('log')\n",
    "plt.xlabel('Iterations', fontsize=12)\n",
    "plt.ylabel('Loss', fontsize=12)\n",
    "plt.title('Training loss as a function of 10K iterations for best 3 alphas', fontsize=20)\n",
    "plt.legend([f'Best alpha: {best_alpha}', f'2nd best alpha: {best_three_alphas[1]}', \n",
    "            f'3rd best alpha: {best_three_alphas[2]}'], loc='center', fontsize=12)\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-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": 32,
   "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 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "theta = np.random.random(size = X_train.shape[1])\n",
    "theta, J_hist = gradient_descent(X_train, y_train, theta, best_alpha, 40000)\n",
    "\n",
    "plt.figure(figsize = (8, 6));\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": 33,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-15626dda8db26550",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "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",
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       "    }\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>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",
       "    </tr>\n",
       "    <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",
       "      <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>5631500400</td>\n",
       "      <td>20150225T000000</td>\n",
       "      <td>180000.0</td>\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>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",
       "      <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": [
       "           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": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read comma separated data\n",
    "df = pd.read_csv('data.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 20)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "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": 35,
   "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": 36,
   "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": 37,
   "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": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 17)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "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": 39,
   "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": 40,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-2985911f4b7af3e1",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 18)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###########################################################################\n",
    "#                            START OF YOUR CODE                           #\n",
    "###########################################################################\n",
    "\n",
    "X_train, X_val = bias_trick(X_train), bias_trick(X_val)\n",
    "X_train.shape # check to make sure bias_trick worked for n-dim X input matrix (4000,18)\n",
    "\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": 41,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-81ab741781b2f6ec",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multivariate regression MSE 𝐽(𝜃) w/random thetas: 0.94691\n"
     ]
    }
   ],
   "source": [
    "theta = np.ones(X_train.shape[1])\n",
    "J = compute_cost(X_train, y_train, theta)\n",
    "print (f'Multivariate regression MSE 𝐽(𝜃) w/random thetas: {J:.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-6f25fb05bd6c648a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Thetas for multivariate regression: [ 2.13594754e-04 -5.81882342e-02  2.25011708e-02  2.43443642e-01\n",
      "  1.45099553e-03  3.28001377e-04  1.14192068e-01  2.75149885e-02\n",
      "  1.16945498e-02  1.30819392e-01  3.19911338e-02 -4.77569048e-02\n",
      "  4.38559155e-03 -1.68765887e-02  5.11881918e-02 -3.06079420e-02\n",
      "  2.50028220e-02 -2.71593683e-02] \n",
      " \n",
      " ======================================== \n",
      "\n",
      "MSE on multivariate training set, 𝐽(𝜃)_min: 0.00047\n",
      "\n",
      "MSE on validation/testing set: 0.00042\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.random(X_train.shape[1])\n",
    "iterations = 40000\n",
    "theta, J_history = gradient_descent(X_train, y_train, theta, best_alpha, iterations)\n",
    "\n",
    "print (f'Thetas for multivariate regression: {theta} \\n \\n', \"=\"*40, '\\n')\n",
    "J_val = compute_cost(X_val, y_val, theta)\n",
    "print(f'MSE on multivariate training set, 𝐽(𝜃)_min: {J_history[-1]:.5f}\\n')\n",
    "print(f'MSE on validation/testing set: {J_val:.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-827d1de1293be51f",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pseudo-Inverse X-Var Theta: [ 2.13594754e-04 -5.81882342e-02  2.25011708e-02  2.43443642e-01\n",
      "  1.45098776e-03  3.28001330e-04  1.14192068e-01  2.75149885e-02\n",
      "  1.16945498e-02  1.30819392e-01  3.19911340e-02 -4.77569048e-02\n",
      "  4.38559153e-03 -1.68765887e-02  5.11881918e-02 -3.06079419e-02\n",
      "  2.50028219e-02 -2.71593661e-02], \n",
      " ======================================== \n",
      " 𝐽(𝜃_pinv)_min: 0.0005\n"
     ]
    }
   ],
   "source": [
    "theta_pinv = pinv(X_train ,y_train)\n",
    "J_pinv = compute_cost(X_train, y_train, theta_pinv)\n",
    "print(f'Pseudo-Inverse X-Var Theta: {theta_pinv}, \\n', '='*40, f'\\n 𝐽(𝜃_pinv)_min: {J_pinv:.4f}')"
   ]
  },
  {
   "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": 44,
   "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 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,7))\n",
    "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: Polynomial Regression (10 points)\n",
    "\n",
    "Linear Regression allows us to explore linear relationships but if we need a model that describes non-linear dependencies we can also use Polynomial Regression. In order to perform polynomial regression, we create additional features using a function of the original features and use standard linear regression on the new features. For example, consider the following single variable $(x)$ cubic regression:\n",
    "\n",
    "$$ x_0 = 1, \\space x_1 = x, \\space x_2 = x^2, \\space x_3 = x^3$$\n",
    "\n",
    "And after using standard linear regression:\n",
    "\n",
    "$$ f(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 +  \\theta_3 x^3$$\n",
    "\n",
    "As required. \n",
    "\n",
    "For this exercise, use polynomial regression by using all **quadratic** feature combinations: \n",
    "\n",
    "$$ 1, x, y, z, x^2, y^2, z^2, xy, xz, yz, ...$$\n",
    "\n",
    "and evaluate the MSE cost on the training and testing datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": 45,
     "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": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resulting quadratic feature combo dataset has 170 features, pre-bias\n"
     ]
    },
    {
     "data": {
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       "<style scoped>\n",
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       "<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>...</th>\n",
       "      <th>(lat, lat)</th>\n",
       "      <th>(lat, long)</th>\n",
       "      <th>(lat, sqft_living15)</th>\n",
       "      <th>(lat, sqft_lot15)</th>\n",
       "      <th>(long, long)</th>\n",
       "      <th>(long, sqft_living15)</th>\n",
       "      <th>(long, sqft_lot15)</th>\n",
       "      <th>(sqft_living15, sqft_living15)</th>\n",
       "      <th>(sqft_living15, sqft_lot15)</th>\n",
       "      <th>(sqft_lot15, sqft_lot15)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>-5808.576778</td>\n",
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       "      <td>14946.774049</td>\n",
       "      <td>-163824.38</td>\n",
       "      <td>-690752.050</td>\n",
       "      <td>1795600</td>\n",
       "      <td>7571000</td>\n",
       "      <td>31922500</td>\n",
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       "    <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>...</td>\n",
       "      <td>2277.293841</td>\n",
       "      <td>-5837.184999</td>\n",
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       "      <td>-206719.11</td>\n",
       "      <td>-934394.841</td>\n",
       "      <td>2856100</td>\n",
       "      <td>12909910</td>\n",
       "      <td>58354321</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>...</td>\n",
       "      <td>2278.907096</td>\n",
       "      <td>-5835.146731</td>\n",
       "      <td>129847.088</td>\n",
       "      <td>384862.9498</td>\n",
       "      <td>14940.906289</td>\n",
       "      <td>-332473.76</td>\n",
       "      <td>-985442.446</td>\n",
       "      <td>7398400</td>\n",
       "      <td>21928640</td>\n",
       "      <td>64995844</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>...</td>\n",
       "      <td>2258.226433</td>\n",
       "      <td>-5816.213274</td>\n",
       "      <td>64628.288</td>\n",
       "      <td>237604.0000</td>\n",
       "      <td>14980.046449</td>\n",
       "      <td>-166454.48</td>\n",
       "      <td>-611965.000</td>\n",
       "      <td>1849600</td>\n",
       "      <td>6800000</td>\n",
       "      <td>25000000</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>...</td>\n",
       "      <td>2267.359642</td>\n",
       "      <td>-5811.392356</td>\n",
       "      <td>85710.240</td>\n",
       "      <td>357268.8504</td>\n",
       "      <td>14894.982025</td>\n",
       "      <td>-219681.00</td>\n",
       "      <td>-915703.635</td>\n",
       "      <td>3240000</td>\n",
       "      <td>13505400</td>\n",
       "      <td>56295009</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 170 columns</p>\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  ...   (lat, lat)  (lat, long)  \\\n",
       "0          3      7        1180  ...  2257.314125 -5808.576778   \n",
       "1          3      7        2170  ...  2277.293841 -5837.184999   \n",
       "2          3      6         770  ...  2278.907096 -5835.146731   \n",
       "3          5      7        1050  ...  2258.226433 -5816.213274   \n",
       "4          3      8        1680  ...  2267.359642 -5811.392356   \n",
       "\n",
       "   (lat, sqft_living15)  (lat, sqft_lot15)  (long, long)  \\\n",
       "0             63665.008        268438.2800  14946.774049   \n",
       "1             80648.490        364540.7190  14961.937761   \n",
       "2            129847.088        384862.9498  14940.906289   \n",
       "3             64628.288        237604.0000  14980.046449   \n",
       "4             85710.240        357268.8504  14894.982025   \n",
       "\n",
       "   (long, sqft_living15)  (long, sqft_lot15)  (sqft_living15, sqft_living15)  \\\n",
       "0             -163824.38         -690752.050                         1795600   \n",
       "1             -206719.11         -934394.841                         2856100   \n",
       "2             -332473.76         -985442.446                         7398400   \n",
       "3             -166454.48         -611965.000                         1849600   \n",
       "4             -219681.00         -915703.635                         3240000   \n",
       "\n",
       "   (sqft_living15, sqft_lot15)  (sqft_lot15, sqft_lot15)  \n",
       "0                      7571000                  31922500  \n",
       "1                     12909910                  58354321  \n",
       "2                     21928640                  64995844  \n",
       "3                      6800000                  25000000  \n",
       "4                     13505400                  56295009  \n",
       "\n",
       "[5 rows x 170 columns]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Your code here ###\n",
    "\n",
    "def quadratic_combinations(df):\n",
    "    rng = range(len(df.columns))\n",
    "    return pd.concat([df.iloc[:, i:].mul(df.iloc[:, i], axis=0) for i in rng],\n",
    "                     axis=1, keys=df.columns)\n",
    "\n",
    "df_quadratic = pd.concat([all_features, quadratic_combinations(all_features)], axis=1)\n",
    "\n",
    "print(f'Resulting quadratic feature combo dataset has {df_quadratic.shape[1]} features, pre-bias')\n",
    "df_quadratic.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>...</th>\n",
       "      <th>(lat, lat)</th>\n",
       "      <th>(lat, long)</th>\n",
       "      <th>(lat, sqft_living15)</th>\n",
       "      <th>(lat, sqft_lot15)</th>\n",
       "      <th>(long, long)</th>\n",
       "      <th>(long, sqft_living15)</th>\n",
       "      <th>(long, sqft_lot15)</th>\n",
       "      <th>(sqft_living15, sqft_living15)</th>\n",
       "      <th>(sqft_living15, sqft_lot15)</th>\n",
       "      <th>(sqft_lot15, sqft_lot15)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\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",
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       "      <td>5000.000000</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>5.000000e+03</td>\n",
       "      <td>5.000000e+03</td>\n",
       "      <td>5.000000e+03</td>\n",
       "      <td>5.000000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\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>...</td>\n",
       "      <td>2261.907601</td>\n",
       "      <td>-5812.504998</td>\n",
       "      <td>94024.314354</td>\n",
       "      <td>6.394521e+05</td>\n",
       "      <td>14936.737518</td>\n",
       "      <td>-241572.745948</td>\n",
       "      <td>-1.642866e+06</td>\n",
       "      <td>4.363095e+06</td>\n",
       "      <td>3.043571e+07</td>\n",
       "      <td>8.838251e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\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>...</td>\n",
       "      <td>13.261841</td>\n",
       "      <td>19.146642</td>\n",
       "      <td>32122.188990</td>\n",
       "      <td>1.259665e+06</td>\n",
       "      <td>34.642851</td>\n",
       "      <td>82350.372694</td>\n",
       "      <td>3.235174e+06</td>\n",
       "      <td>3.245702e+06</td>\n",
       "      <td>6.998693e+07</td>\n",
       "      <td>6.413257e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\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>...</td>\n",
       "      <td>2223.678905</td>\n",
       "      <td>-5847.213798</td>\n",
       "      <td>29467.732000</td>\n",
       "      <td>3.150464e+04</td>\n",
       "      <td>14717.329225</td>\n",
       "      <td>-707138.490000</td>\n",
       "      <td>-5.300378e+07</td>\n",
       "      <td>3.844000e+05</td>\n",
       "      <td>8.052000e+05</td>\n",
       "      <td>4.356000e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\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>...</td>\n",
       "      <td>2252.800445</td>\n",
       "      <td>-5829.657941</td>\n",
       "      <td>70637.167250</td>\n",
       "      <td>2.564985e+05</td>\n",
       "      <td>14915.492641</td>\n",
       "      <td>-286084.890000</td>\n",
       "      <td>-1.278168e+06</td>\n",
       "      <td>2.220100e+06</td>\n",
       "      <td>8.956315e+06</td>\n",
       "      <td>2.906827e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\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>...</td>\n",
       "      <td>2263.176057</td>\n",
       "      <td>-5814.647213</td>\n",
       "      <td>86700.395500</td>\n",
       "      <td>3.707634e+05</td>\n",
       "      <td>14941.395225</td>\n",
       "      <td>-222748.890000</td>\n",
       "      <td>-9.540648e+05</td>\n",
       "      <td>3.312400e+06</td>\n",
       "      <td>1.401188e+07</td>\n",
       "      <td>6.084000e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\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>...</td>\n",
       "      <td>2273.306113</td>\n",
       "      <td>-5798.739070</td>\n",
       "      <td>111361.788750</td>\n",
       "      <td>4.979418e+05</td>\n",
       "      <td>14964.384241</td>\n",
       "      <td>-181688.365000</td>\n",
       "      <td>-6.593326e+05</td>\n",
       "      <td>5.475600e+06</td>\n",
       "      <td>2.328856e+07</td>\n",
       "      <td>1.096052e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\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>...</td>\n",
       "      <td>2282.699062</td>\n",
       "      <td>-5736.326611</td>\n",
       "      <td>275201.595000</td>\n",
       "      <td>2.076787e+07</td>\n",
       "      <td>15009.680196</td>\n",
       "      <td>-75873.120000</td>\n",
       "      <td>-8.074902e+04</td>\n",
       "      <td>3.352410e+07</td>\n",
       "      <td>1.106480e+09</td>\n",
       "      <td>1.889884e+11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 170 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        bedrooms    bathrooms   sqft_living      sqft_lot       floors  \\\n",
       "count  5000.0000  5000.000000   5000.000000  5.000000e+03  5000.000000   \n",
       "mean      3.3714     2.062150   2061.036800  1.615893e+04     1.432600   \n",
       "std       0.9104     0.773592    923.727509  4.600220e+04     0.510793   \n",
       "min       0.0000     0.000000    380.000000  6.090000e+02     1.000000   \n",
       "25%       3.0000     1.500000   1410.000000  5.400000e+03     1.000000   \n",
       "50%       3.0000     2.000000   1890.000000  7.875000e+03     1.000000   \n",
       "75%       4.0000     2.500000   2500.000000  1.123400e+04     2.000000   \n",
       "max       9.0000     6.750000  10040.000000  1.651359e+06     3.500000   \n",
       "\n",
       "        waterfront         view    condition        grade   sqft_above  ...  \\\n",
       "count  5000.000000  5000.000000  5000.000000  5000.000000  5000.000000  ...   \n",
       "mean      0.009400     0.243000     3.455000     7.595200  1753.151000  ...   \n",
       "std       0.096506     0.774643     0.677692     1.166537   818.390844  ...   \n",
       "min       0.000000     0.000000     1.000000     3.000000   380.000000  ...   \n",
       "25%       0.000000     0.000000     3.000000     7.000000  1190.000000  ...   \n",
       "50%       0.000000     0.000000     3.000000     7.000000  1530.000000  ...   \n",
       "75%       0.000000     0.000000     4.000000     8.000000  2130.000000  ...   \n",
       "max       1.000000     4.000000     5.000000    13.000000  7680.000000  ...   \n",
       "\n",
       "        (lat, lat)  (lat, long)  (lat, sqft_living15)  (lat, sqft_lot15)  \\\n",
       "count  5000.000000  5000.000000           5000.000000       5.000000e+03   \n",
       "mean   2261.907601 -5812.504998          94024.314354       6.394521e+05   \n",
       "std      13.261841    19.146642          32122.188990       1.259665e+06   \n",
       "min    2223.678905 -5847.213798          29467.732000       3.150464e+04   \n",
       "25%    2252.800445 -5829.657941          70637.167250       2.564985e+05   \n",
       "50%    2263.176057 -5814.647213          86700.395500       3.707634e+05   \n",
       "75%    2273.306113 -5798.739070         111361.788750       4.979418e+05   \n",
       "max    2282.699062 -5736.326611         275201.595000       2.076787e+07   \n",
       "\n",
       "       (long, long)  (long, sqft_living15)  (long, sqft_lot15)  \\\n",
       "count   5000.000000            5000.000000        5.000000e+03   \n",
       "mean   14936.737518         -241572.745948       -1.642866e+06   \n",
       "std       34.642851           82350.372694        3.235174e+06   \n",
       "min    14717.329225         -707138.490000       -5.300378e+07   \n",
       "25%    14915.492641         -286084.890000       -1.278168e+06   \n",
       "50%    14941.395225         -222748.890000       -9.540648e+05   \n",
       "75%    14964.384241         -181688.365000       -6.593326e+05   \n",
       "max    15009.680196          -75873.120000       -8.074902e+04   \n",
       "\n",
       "       (sqft_living15, sqft_living15)  (sqft_living15, sqft_lot15)  \\\n",
       "count                    5.000000e+03                 5.000000e+03   \n",
       "mean                     4.363095e+06                 3.043571e+07   \n",
       "std                      3.245702e+06                 6.998693e+07   \n",
       "min                      3.844000e+05                 8.052000e+05   \n",
       "25%                      2.220100e+06                 8.956315e+06   \n",
       "50%                      3.312400e+06                 1.401188e+07   \n",
       "75%                      5.475600e+06                 2.328856e+07   \n",
       "max                      3.352410e+07                 1.106480e+09   \n",
       "\n",
       "       (sqft_lot15, sqft_lot15)  \n",
       "count              5.000000e+03  \n",
       "mean               8.838251e+08  \n",
       "std                6.413257e+09  \n",
       "min                4.356000e+05  \n",
       "25%                2.906827e+07  \n",
       "50%                6.084000e+07  \n",
       "75%                1.096052e+08  \n",
       "max                1.889884e+11  \n",
       "\n",
       "[8 rows x 170 columns]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_quadratic.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_quadratic.values\n",
    "y = df['price'].values\n",
    "X, y = preprocess(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4000, 171)\n"
     ]
    }
   ],
   "source": [
    "# training and validation split for quadratic (polynomial) regression\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",
    "\n",
    "# add bias \n",
    "X_train, X_val = bias_trick(X_train), bias_trick(X_val)\n",
    "print(X_train.shape) # check that bias_trick worked (should be (4000,171))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial Regression Thetas: \n",
      " [ 2.97528315e-04  5.05546964e-01  5.18099246e-01  2.74834896e-01\n",
      " -2.53119108e-01] (first 5) \n",
      " [0.56134691 0.41811721 0.15352102 0.10042883 0.11703341] (last 5) \n",
      " ======================================== \n",
      "\n",
      "MSE on quadratic training set, 𝐽(𝜃_poly)_min: 0.00029\n",
      "\n",
      "MSE on validation/testing set: 0.00041\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "iterations = 40000\n",
    "theta = np.random.random(X_train.shape[1])\n",
    "theta, J_history = gradient_descent(X_train, y_train, theta, best_alpha, iterations)\n",
    "\n",
    "print (f'Polynomial Regression Thetas: \\n {theta[:5]} (first 5) \\n {theta[166:]} (last 5) \\n', '='*40, '\\n')\n",
    "J_val = compute_cost(X_val, y_val, theta)\n",
    "print(f'MSE on quadratic training set, 𝐽(𝜃_poly)_min: {J_history[-1]:.5f}\\n')\n",
    "print(f'MSE on validation/testing set: {J_val:.5f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Commentary on Quadratic Dataset and theta_pinv:\n",
    "Note we could not calculate a theta_pinv with the expanded 171-feature quadratic dataset, so we wanted to comment briefly on why that could be. Note there are 5 features in the data that are either Booleans masked as floats (eg waterfront) and/or have minimum values in the data that are 0. If the original data contain either a 0 or 1 (in either of the instances of the product), then the resulting product of those two features will be:\n",
    "\n",
    "- the same as one or both features if the data of one or both features = 1, rendering the new $x_{i}\\cdot x_{j}$ column (or those cells / instances) redundant, useless, and potentially even harmful to the accuracy and efficiency of the model. And if one or both of $x_{i}$ or $x_{j} = 0$ then the resulting product will also =0, and just duplicate the feature with value 0. \n",
    "\n",
    "\n",
    "This was the case for the **following 5 features**: \n",
    "1) Waterfront (really a 1 or 0 Boolean disguised as a float)\n",
    "\n",
    "2) View (had 0's)\n",
    "\n",
    "3) Bedrooms (had 0's)\n",
    "\n",
    "4) Bathrooms (had 0's) \n",
    "\n",
    "5) Year Renovated (which had a 0 unless there was a specific renovation date, as most places aren't renovated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot resulting loss function from polynomial regression \n",
    "plt.figure(figsize = (10,7))\n",
    "plt.plot(np.arange(iterations), J_history)\n",
    "plt.xscale('log')\n",
    "plt.ylim(-0.05,1) # adding this for better viz, but it's specific to output 😬 \n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations for Polynomial Regression')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Give an explanations to the results and compare them to regular linear regression. Do they make sense?"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use this Markdown cell for your answer\n",
    "\n",
    "#### The MSE's for the training & validation sets, comparing the two mean-normalization methods we tried, were: \n",
    "\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "\n",
    "#### The takeaways / conclusions from the above are as follows: \n",
    "- As we learned in class, as a function of $\\Delta$, or degrees of polynomial, we will always continue to get lower and lower MSE's in the training data as we increase $\\Delta$, as by definition we're fitting our best-fit model ($\\hat{h}$) to conform to more & more of the data, and since all polynomials of lower degrees are subsets of polynomials with higher degrees (with coefficients of 0). \n",
    "\n",
    "\n",
    "- On the other hand, this is not the case for our validation or test data, as there exists a threshold or turning point where the validation loss or MSE actually starts to reverse, and increasing $\\Delta$ begins to have the reverse effect, so the graph is more like a wide U-shape or smiley face. In our two normalization methods we see this trend also, as the improvement in MSE completely flattened going from multivariate (17 features) to quadratic (170 features), and had we added more degrees or increased $\\Delta$, the validation MSE would've started to increase. \n",
    "\n",
    "\n",
    "- One last comment is that the mean normalization method with $X_{max} - X_{min}$ in the denominator, compared to mean normalization/standardization with $X_{std}$ in the denominator (both methods use $X - X_{mean}$ in the numerator) performed significantly better in this exercise across the board, with much lower MSE's and also materially better run-time and efficiency. And interesting topic to debate offline..."
   ]
  },
  {
   "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": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Your code here ###\n",
    "\n",
    "def adaptive_alpha(X, y, theta, alpha_zero, decay, iterations):\n",
    "    J_history = []\n",
    "    theta = theta.copy()\n",
    "    m = X.shape[0] # m instances\n",
    "    alpha = alpha_zero # starting alpha \n",
    "    \n",
    "    for iters in range (iterations):\n",
    "        # use alpha_zero for 1st iter, then update\n",
    "        (alpha := alpha_zero) if (iters == 0) else (alpha := alpha / (1 + decay * iters))\n",
    "        \n",
    "        J_history.append(compute_cost(X, y, theta))\n",
    "        theta -= (alpha / m) * X.T @ (X @ theta - y)\n",
    "    \n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataset Comments:\n",
    "**NOTE:** using original univariate dataset as per Piazza comment from Yarden R on 13-Mar, below:\n",
    "- \"Use the same one you used to find the best alpha in the constant learning rate method.\"\n",
    "\n",
    "**NOTE:** this requires re-defining X_train, X_val etc to the original univariate data\n",
    "- We provide a condensed duplication below to quickly re-define datasets, so don't have to go back to top\n",
    "\n",
    "## Re-define data to univariate version used to find best_alpha:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data.csv')\n",
    "X = df['sqft_living'].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, X_val = bias_trick(X_train), bias_trick(X_val) # add bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "iterations = 40000\n",
    "decay_dict = {} # create dict for evaluating MSE on validation data for each decay factor\n",
    "\n",
    "for decay in [0, 0.00001, 0.00003, 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 2, 3]:\n",
    "    np.random.seed(42)\n",
    "    theta = np.ones(X_train.shape[1])\n",
    "    theta, J_history = adaptive_alpha (X_train, y_train, theta, best_alpha, decay, iterations)\n",
    "    decay_dict[decay] = compute_cost(X_val, y_val, theta)\n",
    "    plt.plot(np.arange(iterations), J_history, label = decay)\n",
    "\n",
    "theta_pinv = pinv(X_train, y_train)    \n",
    "J_pinv_adapt = compute_cost(X_train, y_train, theta_pinv)\n",
    "    \n",
    "plt.xscale('log')\n",
    "plt.ylim(0,0.003) # for enhanced visualization/magnification, at risk of being output-specifc\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss as a function of iterations - adaptive learning with various decays: Training Dataset', \n",
    "             fontsize=16, y=1.03)\n",
    "plt.hlines(y = J_pinv_adapt, xmin = 0, xmax = len(J_history), color='r',\n",
    "           linewidth = 1, linestyle = 'dashed')\n",
    "plt.legend(title = \"Decay Factors\", bbox_to_anchor=(1.04,1), borderaxespad=0)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decay Dictionary: {0: 0.0007084282449873637, 1e-05: 0.0007114715973533488, 3e-05: 0.0007397165816081741, 0.0001: 0.0008805686716559811, 0.0003: 0.001142081171416907, 0.001: 0.0014845926680638337, 0.003: 0.0017566555090923574, 0.01: 0.001971351446440168, 0.03: 0.002097861595438005, 0.1: 0.002182051221721328, 0.3: 0.0022265322895093412, 1: 0.002253383562942629, 2: 0.0022619976602874996, 3: 0.0022654009506461793}\n"
     ]
    }
   ],
   "source": [
    "print(f'Decay Dictionary: {decay_dict}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization for Validation Dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "plt.bar(range(len(decay_dict)), list(decay_dict.values()), align='center')\n",
    "plt.title(\"MSE on Validation Data for Various Decay Factors\", fontsize=16)\n",
    "plt.xticks(range(len(decay_dict)), list(decay_dict.keys()))\n",
    "plt.ylabel(\"Validation Loss / MSE\", fontsize=12)\n",
    "plt.xlabel(\"Decay Factor\", fontsize=12)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Not So) Brief Commentary: \n",
    "1) Large decay values 'shrink' our learning rate too quickly and never converge toward the pseudo-inverse value (the horizontal dashed red line), at least not inside our scope of # of iterations. The loss reduction really flattens the larger the decay factor becomes. \n",
    "\n",
    "2) The smaller the decay factor gets, the faster the model 'learns' and converges towards the pseudo-inverse loss value. Can illustrate this in the extreme with a decay factor of 0, which means the alpha / learning rate doesn't decay at all and converges to the pseudo-inverse value, as it did earlier in the exercise. Can also clearly see that each progressively lower decay value from 3 down to 0.0001 gets \"better\", flattening at a lower loss minimum, though none of these decay factors converge all the way to our theoretical $J_{pinv}$. \n",
    "\n",
    "3) This relationship can also be observed in our second plot, which looks at the MSE on the validation dataset for each decay factor, and it can be clearly seen that it gets progressively higher as we move to the right and increase the value of the decay factor. Note we **added this decay_dict** in the code above as we need to **evaluate the validation data using the thetas we generated from our training dataset model, or $\\hat{h}$**, in a fashion similar to what we did for finding best_alpha above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Create Assignment",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}