StudentAdmissions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Student Admissions with Neural Networks\n",
    "In this notebook, we predict student admissions to graduate school at UCLA based on three pieces of data:\n",
    "- GRE Scores (Test)\n",
    "- GPA Scores (Grades)\n",
    "- Class rank (1-4)\n",
    "\n",
    "The dataset originally came from here: http://www.ats.ucla.edu/\n",
    "\n",
    "## Loading the data\n",
    "To load the data and format it nicely, we will use two very useful packages called Pandas and Numpy. You can read on the documentation here:\n",
    "- https://pandas.pydata.org/pandas-docs/stable/\n",
    "- https://docs.scipy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380</td>\n",
       "      <td>3.61</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660</td>\n",
       "      <td>3.67</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640</td>\n",
       "      <td>3.19</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520</td>\n",
       "      <td>2.93</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>760</td>\n",
       "      <td>3.00</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>560</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>400</td>\n",
       "      <td>3.08</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>540</td>\n",
       "      <td>3.39</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>700</td>\n",
       "      <td>3.92</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit  gre   gpa  rank\n",
       "0      0  380  3.61     3\n",
       "1      1  660  3.67     3\n",
       "2      1  800  4.00     1\n",
       "3      1  640  3.19     4\n",
       "4      0  520  2.93     4\n",
       "5      1  760  3.00     2\n",
       "6      1  560  2.98     1\n",
       "7      0  400  3.08     2\n",
       "8      1  540  3.39     3\n",
       "9      0  700  3.92     2"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing pandas and numpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Reading the csv file into a pandas DataFrame\n",
    "data = pd.read_csv('data/student_data.csv')\n",
    "\n",
    "# Printing out the first 10 rows of our data\n",
    "data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the data\n",
    "\n",
    "First let's make a plot of our data to see how it looks. In order to have a 2D plot, let's ingore the rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importing matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Function to help us plot\n",
    "def plot_points(data):\n",
    "    X = np.array(data[[\"gre\",\"gpa\"]])\n",
    "    y = np.array(data[\"admit\"])\n",
    "    admitted = X[np.argwhere(y==1)]\n",
    "    rejected = X[np.argwhere(y==0)]\n",
    "    plt.scatter([s[0][0] for s in rejected], [s[0][1] for s in rejected], s = 25, color = 'red', edgecolor = 'k')\n",
    "    plt.scatter([s[0][0] for s in admitted], [s[0][1] for s in admitted], s = 25, color = 'cyan', edgecolor = 'k')\n",
    "    plt.xlabel('Test (GRE)')\n",
    "    plt.ylabel('Grades (GPA)')\n",
    "    \n",
    "# Plotting the points\n",
    "plot_points(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Roughly, it looks like the students with high scores in the grades and test passed, while the ones with low scores didn't, but the data is not as nicely separable as we hoped it would. Maybe it would help to take the rank into account? Let's make 4 plots, each one for each rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Separating the ranks\n",
    "data_rank1 = data[data[\"rank\"]==1]\n",
    "data_rank2 = data[data[\"rank\"]==2]\n",
    "data_rank3 = data[data[\"rank\"]==3]\n",
    "data_rank4 = data[data[\"rank\"]==4]\n",
    "\n",
    "# Plotting the graphs\n",
    "plot_points(data_rank1)\n",
    "plt.title(\"Rank 1\")\n",
    "plt.show()\n",
    "plot_points(data_rank2)\n",
    "plt.title(\"Rank 2\")\n",
    "plt.show()\n",
    "plot_points(data_rank3)\n",
    "plt.title(\"Rank 3\")\n",
    "plt.show()\n",
    "plot_points(data_rank4)\n",
    "plt.title(\"Rank 4\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks more promising, as it seems that the lower the rank, the higher the acceptance rate. Let's use the rank as one of our inputs. In order to do this, we should one-hot encode it.\n",
    "\n",
    "## TODO: One-hot encoding the rank\n",
    "Use the `get_dummies` function in Pandas in order to one-hot encode the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank_1</th>\n",
       "      <th>rank_2</th>\n",
       "      <th>rank_3</th>\n",
       "      <th>rank_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380</td>\n",
       "      <td>3.61</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660</td>\n",
       "      <td>3.67</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640</td>\n",
       "      <td>3.19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520</td>\n",
       "      <td>2.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>760</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>560</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>400</td>\n",
       "      <td>3.08</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>540</td>\n",
       "      <td>3.39</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>700</td>\n",
       "      <td>3.92</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit  gre   gpa  rank_1  rank_2  rank_3  rank_4\n",
       "0      0  380  3.61       0       0       1       0\n",
       "1      1  660  3.67       0       0       1       0\n",
       "2      1  800  4.00       1       0       0       0\n",
       "3      1  640  3.19       0       0       0       1\n",
       "4      0  520  2.93       0       0       0       1\n",
       "5      1  760  3.00       0       1       0       0\n",
       "6      1  560  2.98       1       0       0       0\n",
       "7      0  400  3.08       0       1       0       0\n",
       "8      1  540  3.39       0       0       1       0\n",
       "9      0  700  3.92       0       1       0       0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO:  Make dummy variables for rank\n",
    "one_hot_data = pd.concat([data, pd.get_dummies(data['rank'], prefix='rank')], axis=1)\n",
    "\n",
    "# TODO: Drop the previous rank column\n",
    "one_hot_data = one_hot_data.drop('rank', axis=1)\n",
    "\n",
    "# Print the first 10 rows of our data\n",
    "one_hot_data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TODO: Scaling the data\n",
    "The next step is to scale the data. We notice that the range for grades is 1.0-4.0, whereas the range for test scores is roughly 200-800, which is much larger. This means our data is skewed, and that makes it hard for a neural network to handle. Let's fit our two features into a range of 0-1, by dividing the grades by 4.0, and the test score by 800."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank_1</th>\n",
       "      <th>rank_2</th>\n",
       "      <th>rank_3</th>\n",
       "      <th>rank_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.475</td>\n",
       "      <td>0.9025</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.825</td>\n",
       "      <td>0.9175</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.800</td>\n",
       "      <td>0.7975</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.650</td>\n",
       "      <td>0.7325</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0.950</td>\n",
       "      <td>0.7500</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>0.700</td>\n",
       "      <td>0.7450</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.7700</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>0.675</td>\n",
       "      <td>0.8475</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0.875</td>\n",
       "      <td>0.9800</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
       "0      0  0.475  0.9025       0       0       1       0\n",
       "1      1  0.825  0.9175       0       0       1       0\n",
       "2      1  1.000  1.0000       1       0       0       0\n",
       "3      1  0.800  0.7975       0       0       0       1\n",
       "4      0  0.650  0.7325       0       0       0       1\n",
       "5      1  0.950  0.7500       0       1       0       0\n",
       "6      1  0.700  0.7450       1       0       0       0\n",
       "7      0  0.500  0.7700       0       1       0       0\n",
       "8      1  0.675  0.8475       0       0       1       0\n",
       "9      0  0.875  0.9800       0       1       0       0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Making a copy of our data\n",
    "processed_data = one_hot_data[:]\n",
    "\n",
    "# TODO: Scale the columns\n",
    "processed_data['gpa'] = processed_data['gpa']/4\n",
    "processed_data['gre'] = processed_data['gre']/800\n",
    "\n",
    "# Printing the first 10 rows of our procesed data\n",
    "processed_data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting the data into Training and Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to test our algorithm, we'll split the data into a Training and a Testing set. The size of the testing set will be 10% of the total data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training samples is 360\n",
      "Number of testing samples is 40\n",
      "     admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
      "264      1  0.650  0.9750       0       0       1       0\n",
      "145      0  0.475  0.8575       0       0       1       0\n",
      "228      0  0.600  0.8575       0       1       0       0\n",
      "346      0  0.750  0.8375       0       1       0       0\n",
      "353      0  0.875  0.8800       0       1       0       0\n",
      "314      0  0.675  0.8650       0       0       0       1\n",
      "130      1  0.775  0.7925       0       1       0       0\n",
      "315      1  0.375  0.7100       0       1       0       0\n",
      "299      0  0.900  0.8500       0       0       1       0\n",
      "370      1  0.675  0.9425       0       1       0       0\n",
      "    admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
      "15      0  0.600  0.8600       0       0       1       0\n",
      "35      0  0.500  0.7625       0       1       0       0\n",
      "40      0  0.700  0.6050       0       1       0       0\n",
      "42      1  0.750  0.7875       0       1       0       0\n",
      "43      0  0.625  0.8275       0       0       1       0\n",
      "50      0  0.800  0.9650       0       0       1       0\n",
      "65      0  0.750  0.8975       0       1       0       0\n",
      "73      0  0.725  1.0000       0       1       0       0\n",
      "78      0  0.675  0.7800       1       0       0       0\n",
      "88      0  0.875  0.8200       1       0       0       0\n"
     ]
    }
   ],
   "source": [
    "sample = np.random.choice(processed_data.index, size=int(len(processed_data)*0.9), replace=False)\n",
    "train_data, test_data = processed_data.iloc[sample], processed_data.drop(sample)\n",
    "\n",
    "print(\"Number of training samples is\", len(train_data))\n",
    "print(\"Number of testing samples is\", len(test_data))\n",
    "print(train_data[:10])\n",
    "print(test_data[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting the data into features and targets (labels)\n",
    "Now, as a final step before the training, we'll split the data into features (X) and targets (y)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
      "264  0.650  0.9750       0       0       1       0\n",
      "145  0.475  0.8575       0       0       1       0\n",
      "228  0.600  0.8575       0       1       0       0\n",
      "346  0.750  0.8375       0       1       0       0\n",
      "353  0.875  0.8800       0       1       0       0\n",
      "314  0.675  0.8650       0       0       0       1\n",
      "130  0.775  0.7925       0       1       0       0\n",
      "315  0.375  0.7100       0       1       0       0\n",
      "299  0.900  0.8500       0       0       1       0\n",
      "370  0.675  0.9425       0       1       0       0\n",
      "264    1\n",
      "145    0\n",
      "228    0\n",
      "346    0\n",
      "353    0\n",
      "314    0\n",
      "130    1\n",
      "315    1\n",
      "299    0\n",
      "370    1\n",
      "Name: admit, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "features = train_data.drop('admit', axis=1)\n",
    "targets = train_data['admit']\n",
    "features_test = test_data.drop('admit', axis=1)\n",
    "targets_test = test_data['admit']\n",
    "\n",
    "print(features[:10])\n",
    "print(targets[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the 2-layer Neural Network\n",
    "The following function trains the 2-layer neural network. First, we'll write some helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Activation (sigmoid) function\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "def sigmoid_prime(x):\n",
    "    return sigmoid(x) * (1-sigmoid(x))\n",
    "def error_formula(y, output):\n",
    "    return - y*np.log(output) - (1 - y) * np.log(1-output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO: Backpropagate the error\n",
    "Now it's your turn to shine. Write the error term. Remember that this is given by the equation $$ (y-\\hat{y}) \\sigma'(x) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Write the error term formula\n",
    "def error_term_formula(x, y, output):\n",
    "    return (y - output) * sigmoid_prime(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0\n",
      "Train loss:  0.27065920109859926\n",
      "=========\n",
      "Epoch: 100\n",
      "Train loss:  0.2143477848333157\n",
      "=========\n",
      "Epoch: 200\n",
      "Train loss:  0.2118080166538295\n",
      "=========\n",
      "Epoch: 300\n",
      "Train loss:  0.2105495643490621\n",
      "=========\n",
      "Epoch: 400\n",
      "Train loss:  0.20988368249589698\n",
      "=========\n",
      "Epoch: 500\n",
      "Train loss:  0.2094905133735335\n",
      "=========\n",
      "Epoch: 600\n",
      "Train loss:  0.20922599045765186\n",
      "=========\n",
      "Epoch: 700\n",
      "Train loss:  0.20902438033915038\n",
      "=========\n",
      "Epoch: 800\n",
      "Train loss:  0.2088550038141913\n",
      "=========\n",
      "Epoch: 900\n",
      "Train loss:  0.2087031992901194\n",
      "=========\n",
      "Finished training!\n"
     ]
    }
   ],
   "source": [
    "# Neural Network hyperparameters\n",
    "epochs = 1000\n",
    "learnrate = 0.5\n",
    "\n",
    "# Training function\n",
    "def train_nn(features, targets, epochs, learnrate):\n",
    "    \n",
    "    # Use to same seed to make debugging easier\n",
    "    np.random.seed(42)\n",
    "\n",
    "    n_records, n_features = features.shape\n",
    "    last_loss = None\n",
    "\n",
    "    # Initialize weights\n",
    "    weights = np.random.normal(scale=1 / n_features**.5, size=n_features)\n",
    "\n",
    "    for e in range(epochs):\n",
    "        del_w = np.zeros(weights.shape)\n",
    "        for x, y in zip(features.values, targets):\n",
    "            # Loop through all records, x is the input, y is the target\n",
    "\n",
    "            # Activation of the output unit\n",
    "            #   Notice we multiply the inputs and the weights here \n",
    "            #   rather than storing h as a separate variable \n",
    "            output = sigmoid(np.dot(x, weights))\n",
    "\n",
    "            # The error, the target minus the network output\n",
    "            error = error_formula(y, output)\n",
    "\n",
    "            # The error term\n",
    "            error_term = error_term_formula(x, y, output)\n",
    "\n",
    "            # The gradient descent step, the error times the gradient times the inputs\n",
    "            del_w += error_term * x\n",
    "\n",
    "        # Update the weights here. The learning rate times the \n",
    "        # change in weights, divided by the number of records to average\n",
    "        weights += learnrate * del_w / n_records\n",
    "\n",
    "        # Printing out the mean square error on the training set\n",
    "        if e % (epochs / 10) == 0:\n",
    "            out = sigmoid(np.dot(features, weights))\n",
    "            loss = np.mean((out - targets) ** 2)\n",
    "            print(\"Epoch:\", e)\n",
    "            if last_loss and last_loss < loss:\n",
    "                print(\"Train loss: \", loss, \"  WARNING - Loss Increasing\")\n",
    "            else:\n",
    "                print(\"Train loss: \", loss)\n",
    "            last_loss = loss\n",
    "            print(\"=========\")\n",
    "    print(\"Finished training!\")\n",
    "    return weights\n",
    "    \n",
    "weights = train_nn(features, targets, epochs, learnrate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating the Accuracy on the Test Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction accuracy: 0.750\n"
     ]
    }
   ],
   "source": [
    "# Calculate accuracy on test data\n",
    "test_out = sigmoid(np.dot(features_test, weights))\n",
    "predictions = test_out > 0.5\n",
    "accuracy = np.mean(predictions == targets_test)\n",
    "print(\"Prediction accuracy: {:.3f}\".format(accuracy))"
   ]
  }
 ],
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