predicting_marks_by_facebook_likes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Average Marks Based on Facebook Likes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "It is common for students to have a Facebook group on which they post course relevant discussion and announcements to help each other keep up with various aspects. Among the different type of posts, it is customary for people to announce when assessment marks are available to check online, in lieu of a formal notification from the administration. The premise of this short study is that the amount of likes that this sort of post gets can be used to predict the average mark of the assessment.\n",
    "\n",
    "The reasoning behind this is that students may be less likely to react positively when they check their mark and it turns out to be low, but in case of a high mark, students may feel a need to express their happiness and reward the messenger with a like. Yet, number of likes may be an imperfect measure in many ways:\n",
    "\n",
    "- Low-ish marks for an exam may excite students if their expectation was low; while good-ish marks for an exam may upset them if they had higher expectations. This indicates there may be a need for a possibly-difficult-to-quantify \"expectation\" variable. One possible way to address this is by introducing a difficulty variable for each exam based on historical results.\n",
    "- Number of likes varies depending on the number of students in a class -- this may be addressed by evaluating the percentage of students who liked the post, rather than the raw number.\n",
    "- People may express their happiness through comments. This may be addressed through counting the number of comments, but also some sorts of sentiment analysis to distinguish between happiness and disappointment. In my experience though, people are much more likely to stick with a simple \"like\", rather than a more emotional public display of enthusiasm.\n",
    "\n",
    "This is just a one-day project, so only the 2nd point will be addressed.\n",
    "\n",
    "### Additional information\n",
    "\n",
    "This is done for a UK BSc course, so if you are not familiar with the academic environment there, some aspects may not make sense. For example, 70 is considered quite a good mark (first class), and one can pass if they obtain a mark over 30 and they can compensate with marks from a different module. Furthermore, when I talk about \"closed assessment\" or \"closed exam\" I refer to an exam typically done with no internet access in about 2 hours, and \"open assessment\" typically refers to a few week/months-long project (report/experiment/coding/coursework). Also, a bachelor's degree in UK lasts 3 years.\n",
    "\n",
    "## Collecting data\n",
    "\n",
    "Due to an unstandardised method of announcing that the marks are up, the collection of the data was accomplished via a tedious process using Facebook group search and manually storing relevant data. I had access to 2 groups, so I gathered data from several academic years and connected every exam to its average mark as released by the university department. I will not make the data public because I'm not sure about the privacy policies involved.\n",
    "\n",
    "## Exploring data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['figure.figsize'] = 12, 10\n",
    "plt.rcParams.update({'font.size': 15})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('../data/train.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>likes</th>\n",
       "      <th>year</th>\n",
       "      <th>cohort</th>\n",
       "      <th>closed</th>\n",
       "      <th>number_of_students</th>\n",
       "      <th>mean</th>\n",
       "      <th>median</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>56.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>28.500000</td>\n",
       "      <td>6.750000</td>\n",
       "      <td>2014.500000</td>\n",
       "      <td>2.142857</td>\n",
       "      <td>0.660714</td>\n",
       "      <td>80.571429</td>\n",
       "      <td>61.445536</td>\n",
       "      <td>62.273036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>16.309506</td>\n",
       "      <td>4.806246</td>\n",
       "      <td>0.603023</td>\n",
       "      <td>0.772918</td>\n",
       "      <td>0.477752</td>\n",
       "      <td>36.801609</td>\n",
       "      <td>9.391542</td>\n",
       "      <td>10.718933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2013.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>37.040000</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>14.750000</td>\n",
       "      <td>2.750000</td>\n",
       "      <td>2014.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>42.000000</td>\n",
       "      <td>55.490000</td>\n",
       "      <td>56.875000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>28.500000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>62.050000</td>\n",
       "      <td>63.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>42.250000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>114.000000</td>\n",
       "      <td>68.417500</td>\n",
       "      <td>70.125000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>56.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>131.000000</td>\n",
       "      <td>83.660000</td>\n",
       "      <td>87.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              id      likes         year     cohort     closed  \\\n",
       "count  56.000000  56.000000    56.000000  56.000000  56.000000   \n",
       "mean   28.500000   6.750000  2014.500000   2.142857   0.660714   \n",
       "std    16.309506   4.806246     0.603023   0.772918   0.477752   \n",
       "min     1.000000   0.000000  2013.000000   1.000000   0.000000   \n",
       "25%    14.750000   2.750000  2014.000000   2.000000   0.000000   \n",
       "50%    28.500000   6.000000  2015.000000   2.000000   1.000000   \n",
       "75%    42.250000   9.000000  2015.000000   3.000000   1.000000   \n",
       "max    56.000000  19.000000  2015.000000   3.000000   1.000000   \n",
       "\n",
       "       number_of_students       mean     median  \n",
       "count           56.000000  56.000000  56.000000  \n",
       "mean            80.571429  61.445536  62.273036  \n",
       "std             36.801609   9.391542  10.718933  \n",
       "min             13.000000  37.040000  31.000000  \n",
       "25%             42.000000  55.490000  56.875000  \n",
       "50%             80.000000  62.050000  63.250000  \n",
       "75%            114.000000  68.417500  70.125000  \n",
       "max            131.000000  83.660000  87.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown above, I managed to collect data for 56 exams. It seems that the minimum mean mark was of 37, and the maximum was of 83.66. On average, it looks like exams tend to end up with a mark slightly above 60 (std of 9.39), about 66% percent have been closed exams, and I collected slightly more data from 3rd years (as seen by the mean of the cohort column.) The minimum number of students that an exam had was 13 (I was there!), and the maximum was 131 (I was there too!).\n",
    "\n",
    "Anyway, let's get to what is likely the most interesting question right now: is there a distinguishable structure in the data?\n",
    "\n",
    "Let's plot the mean marks against the number of likes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a quick function to allow reusing\n",
    "def scatter_plot(independent, dependent, title=\"\", xlabel=\"\", ylabel=\"\"):\n",
    "    plt.scatter(independent,dependent)\n",
    "    plt.title(title)\n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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fkTsstroPvZ10oxfneykaZRC/w/6tqYu9hpdrjnzN/RPwnohYk1J6d8s6i3o9Uh4h6sLi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\nIxNwSZIkqUf/CynZxHvoXIdJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cdd619780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot(data['likes'],data['mean'], \n",
    "                      title=\"Relationship between number of likes and mean mark\",\n",
    "                      xlabel=\"Number of students who liked the announcements\",\n",
    "                      ylabel=\"Mean mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, there is very little structure here, but let's see how it looks when we use the percentage of students."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmi4dX0F+I7ip0xaXZhHxf8gn+dtbW4OKDkr7hLLMVXwLuHdE3K65FbwoG/lN2rdedKRI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cdd5ce668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['likes_normalised'] = (100 * data['likes'])/data['number_of_students']\n",
    "\n",
    "scatter_plot(data['likes_normalised'],data['mean'], \n",
    "                      title=\"Relationship between percentage of likes and mean mark\",\n",
    "                      xlabel=\"Percentage of students who liked the announcements\",\n",
    "                      ylabel=\"Mean mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quite a bit better, but let's do it for the median as it seems like a more intuitive measurement here: half the students below the median got less than the mark indicated on the y axis. Also, the median is more resilient to outliers which may be helpful in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jadghwPeAp6aUPtJUhvANKaXXFeOsAq4glyE8rc10LUMoSZKknltuGcJ+9ICf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cdd300ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot(data['likes_normalised'],data['median'], \n",
    "                      title=\"Relationship between percentage of likes and median mark\",\n",
    "                      xlabel=\"Percentage of students who liked the announcements\",\n",
    "                      ylabel=\"Median mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, without starting to remove outliers, this seems to be the best I have. I will stay away from outlier detection, and from the graph there doesn't seem to be any really obvious one (maybe besides that one at 80+ median, but I won't go there).\n",
    "\n",
    "The structure looks like it can be fitted with a polynomial curve, so without further ado, I'll just go ahead and try some polynomial regression.\n",
    "\n",
    "## Fitting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lCCVJklR3Ay1D2Iwe8LOA0yPiMeAyYH3gS8CDwO8BUkoLIuJU4IsR8TS51/sz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cd3947518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Convert series to dataframes to prepare them for fitting\n",
    "X = pd.DataFrame(data['likes_normalised'])\n",
    "y = pd.DataFrame(data['median'])\n",
    "\n",
    "# Add a squared feature\n",
    "X = pd.concat([X,pow(X,2)],axis=1)\n",
    "\n",
    "# Fit data with linear regression\n",
    "model_linear = linear_model.LinearRegression()\n",
    "model_linear.fit(X,y)\n",
    "\n",
    "# Create some new points to graph the curve\n",
    "new_x = np.linspace(X.iloc[:,0].min(),X.iloc[:,0].max())\n",
    "test_x = pd.DataFrame([new_x, pow(new_x,2)]).T\n",
    "\n",
    "# Plot curve\n",
    "plt.plot(test_x.iloc[:,0],model_linear.predict(test_x))\n",
    "# Plot points\n",
    "scatter_plot(X.iloc[:,0],y,\n",
    "                      title=\"Relationship between percentage of likes and median mark\",\n",
    "                      xlabel=\"Percentage of students who liked the announcements\",\n",
    "                      ylabel=\"Median mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks about right to me. I don't think stopping here would be a bad decision, but for the sake of it, I will try to fit it with a cubic polynomial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wvJaW2ZL2fJ5l8zpa09wyWt1f0ZeGyXiv9d/x7TEPP99G0PgenirTe1Sqe/Fj8VQzezyE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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cdd318668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Add a 3rd power and fit the new data\n",
    "X_ = pd.concat([X,pow(X.iloc[:,0],3)],axis=1)\n",
    "model_linear.fit(X_,y)\n",
    "\n",
    "test_x_ = pd.concat([test_x, pow(test_x.iloc[:,0],3)],axis=1)\n",
    "plt.plot(test_x_.iloc[:,0],model_linear.predict(test_x_))\n",
    "# Plot points\n",
    "scatter_plot(X_[[0]],y,\n",
    "                      title=\"Relationship between percentage of likes and median mark\",\n",
    "                      xlabel=\"Percentage of students who liked the announcements\",\n",
    "                      ylabel=\"Median mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks pretty, but it likely overfits. So let's try to add L2 regularization and find the regularization parameter through 10-fold cross validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regularization parameter that provided the best results was 10016.299663688093.\n"
     ]
    },
    {
     "data": {
      "image/png": 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cpqbR7PqKfjS8jPdaX4cvj4X4/nYhDcfwRKmOUYkexbfFc8zsuRDCV82MLy2kALxMhBBe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\nA7gkSZLUIgO4JEmS1CIDuCRJktSi/w80SReJeAle7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9cd39718d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "\n",
    "list_reg_params = np.linspace(0.00001, X_.max().max() * 100, 2000)\n",
    "model_ridge = linear_model.RidgeCV(alphas=list_reg_params, cv=10)\n",
    "model_ridge.fit(X_,y)\n",
    "\n",
    "reg_param = model_ridge.alpha_\n",
    "print(\"The regularization parameter that provided the best results was {}.\".format(reg_param))\n",
    "plt.plot(test_x_.iloc[:,0],model_ridge.predict(test_x_))\n",
    "scatter_plot(X_[[0]],y,\n",
    "                      title=\"Relationship between percentage of likes and median mark\",\n",
    "                      xlabel=\"Percentage of students who liked the announcements\",\n",
    "                      ylabel=\"Median mark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regularization parameter introduced only a very subtle difference. It's also a very big number as I haven't normalised the data. Now let's see which of the 2 polynomial curves fit the data better.\n",
    "\n",
    "## Evaluating the models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_ridge_reg = linear_model.Ridge(alpha=reg_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average error for quadratic polynomial: 7.05 (+/- 3.87)\n",
      "Average error  for cubic polynomial: 6.86 (+/- 4.75)\n"
     ]
    }
   ],
   "source": [
    "from sklearn import cross_validation\n",
    "\n",
    "scores_quadratic = abs(cross_validation.cross_val_score(\n",
    "        model_linear, X, y, cv=10, scoring=\"mean_absolute_error\"))\n",
    "scores_cubic = abs(cross_validation.cross_val_score(\n",
    "        model_ridge_reg, X_, y, cv=10, scoring=\"mean_absolute_error\"))\n",
    "\n",
    "print(\"Average error for quadratic polynomial: {:.2f} (+/- {:.2f})\" .format(\n",
    "        scores_quadratic.mean(), scores_quadratic.std() * 2))\n",
    "print(\"Average error  for cubic polynomial: {:.2f} (+/- {:.2f})\" .format(\n",
    "        scores_cubic.mean(), scores_cubic.std() * 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not too bad. An error of less than 7 marks is better than I expected. Now for a comparison test, let's just predict that the median of a module is the mean of the medians of all the other modules (but using K-fold CV)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average error  for naive predictor: 8.18 (+/- 6.37)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.cross_validation import KFold\n",
    "\n",
    "kf = KFold(X.shape[0], n_folds=10)\n",
    "scores_naive = []\n",
    "for train, test in kf:\n",
    "    train_mean = data['median'][train].mean()\n",
    "    scores_naive.append(mean_absolute_error(data['median'][test], [train_mean] * len(test)))\n",
    "    \n",
    "print(\"Average error  for naive predictor: {:.2f} (+/- {:.2f})\" .format(\n",
    "        np.mean(scores_naive), np.std(scores_naive) * 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D'aww, the regression predictor is not much better than the naive one. At least it's not worse! As a last test, let's see what are the chances that the the regression results are better just by chance. For this, a paired one-tailed t-test will be performed, with the null hypothesis that the 2 algorithms perform the same, and the alternative hypothesis that the regression one performs better. The p-value I will choose is 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value: 0.0387\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import ttest_rel\n",
    "\n",
    "results = ttest_rel(scores_naive, scores_cubic)\n",
    "print(\"P-value: {:.4f}\" .format(results.pvalue/2)) # Dividing by 2 because it's one-tailed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Everything was not in vain! It seems that the algorithm is likely to perform better than the naive approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "And this is it. The algorithm appears to predict grades with an average error of approximately 7 marks, and performs better than a naive predictor. Not bad I'd say considering we only have the number of likes on Facebook!\n",
    "\n",
    "I did not put aside a separate testing set because the data was not very big to begin with, and I don't think that a small test set would necessarily give a good indication of the algorithm performance. However, I will nonetheless test it on this year's exams once the results and the statistics are up!"
   ]
  }
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