CausalAdmit_Joy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MATH 522 Final Exam - Joy Song - 4/16/2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random as rd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from causalinference import CausalModel\n",
    "from causalgraphicalmodels import CausalGraphicalModel\n",
    "from causalgraphicalmodels.csm import StructuralCausalModel\n",
    "from causalgraphicalmodels.csm import discrete_model, linear_model, logistic_model\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_palette(\"colorblind\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.environ[\"PATH\"] += os.pathsep + 'C:/Program Files (x86)/graphviz-2.38/bin/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem of Interest\n",
    "Given a data set with 500 samples and the following eight variables: \n",
    "\n",
    "**GRE** (GRE scores), **TF** (TOEFL scores), **UR** (university rating), **SOP** (Statement of Purpose strength), **LOR** (Letter of Recommendation strength), **GPA** (undergraduate GPA), **Research** (have research experience or not), **Admit** (chance of admittance),\n",
    "\n",
    "we are interested in the causal relationships between them, especially the causal influence on the variable **Admit** (the chance of admittance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GRE</th>\n",
       "      <th>TF</th>\n",
       "      <th>UR</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>GPA</th>\n",
       "      <th>Research</th>\n",
       "      <th>Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>337</td>\n",
       "      <td>118</td>\n",
       "      <td>4</td>\n",
       "      <td>4.5</td>\n",
       "      <td>4.5</td>\n",
       "      <td>9.65</td>\n",
       "      <td>1</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>324</td>\n",
       "      <td>107</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8.87</td>\n",
       "      <td>1</td>\n",
       "      <td>0.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>316</td>\n",
       "      <td>104</td>\n",
       "      <td>3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>8.00</td>\n",
       "      <td>1</td>\n",
       "      <td>0.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>322</td>\n",
       "      <td>110</td>\n",
       "      <td>3</td>\n",
       "      <td>3.5</td>\n",
       "      <td>2.5</td>\n",
       "      <td>8.67</td>\n",
       "      <td>1</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>314</td>\n",
       "      <td>103</td>\n",
       "      <td>2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.21</td>\n",
       "      <td>0</td>\n",
       "      <td>0.65</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   GRE   TF  UR  SOP  LOR   GPA  Research  Admit\n",
       "0  337  118   4  4.5  4.5  9.65         1   0.92\n",
       "1  324  107   4  4.0  4.5  8.87         1   0.76\n",
       "2  316  104   3  3.0  3.5  8.00         1   0.72\n",
       "3  322  110   3  3.5  2.5  8.67         1   0.80\n",
       "4  314  103   2  2.0  3.0  8.21         0   0.65"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read data, credit to Elliot\n",
    "path = 'graduate_admissions'\n",
    "filename = 'Admission_Predict_Ver1.1.csv'\n",
    "filepath = os.path.join(path, filename)\n",
    "\n",
    "df = pd.read_csv(filepath)\n",
    "df.drop(columns='Serial No.', inplace=True)\n",
    "df.columns = ['GRE', 'TF', 'UR', 'SOP', 'LOR', 'GPA', 'Research', 'Admit']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GRE</th>\n",
       "      <th>TF</th>\n",
       "      <th>UR</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>GPA</th>\n",
       "      <th>Research</th>\n",
       "      <th>Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.00000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>316.472000</td>\n",
       "      <td>107.192000</td>\n",
       "      <td>3.114000</td>\n",
       "      <td>3.374000</td>\n",
       "      <td>3.48400</td>\n",
       "      <td>8.576440</td>\n",
       "      <td>0.560000</td>\n",
       "      <td>0.72174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>11.295148</td>\n",
       "      <td>6.081868</td>\n",
       "      <td>1.143512</td>\n",
       "      <td>0.991004</td>\n",
       "      <td>0.92545</td>\n",
       "      <td>0.604813</td>\n",
       "      <td>0.496884</td>\n",
       "      <td>0.14114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>290.000000</td>\n",
       "      <td>92.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>6.800000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.34000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>308.000000</td>\n",
       "      <td>103.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>8.127500</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.63000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>317.000000</td>\n",
       "      <td>107.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>3.50000</td>\n",
       "      <td>8.560000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.72000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>325.000000</td>\n",
       "      <td>112.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.00000</td>\n",
       "      <td>9.040000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.82000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>340.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>9.920000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.97000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              GRE          TF          UR         SOP        LOR         GPA  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.00000  500.000000   \n",
       "mean   316.472000  107.192000    3.114000    3.374000    3.48400    8.576440   \n",
       "std     11.295148    6.081868    1.143512    0.991004    0.92545    0.604813   \n",
       "min    290.000000   92.000000    1.000000    1.000000    1.00000    6.800000   \n",
       "25%    308.000000  103.000000    2.000000    2.500000    3.00000    8.127500   \n",
       "50%    317.000000  107.000000    3.000000    3.500000    3.50000    8.560000   \n",
       "75%    325.000000  112.000000    4.000000    4.000000    4.00000    9.040000   \n",
       "max    340.000000  120.000000    5.000000    5.000000    5.00000    9.920000   \n",
       "\n",
       "         Research      Admit  \n",
       "count  500.000000  500.00000  \n",
       "mean     0.560000    0.72174  \n",
       "std      0.496884    0.14114  \n",
       "min      0.000000    0.34000  \n",
       "25%      0.000000    0.63000  \n",
       "50%      1.000000    0.72000  \n",
       "75%      1.000000    0.82000  \n",
       "max      1.000000    0.97000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# describe data\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Causal Graphical Model\n",
    "We start with constructing a causal graphical model which is a Bayesian network where the directed edges indicate the causal relationships between nodes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation\n",
    "In order to make appropriate causal assupmtions, we need to investigate the correlations between these eight variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute correlations, credit to Elliot\n",
    "sns.heatmap(df.corr(), cmap='Blues', annot=True)\n",
    "plt.title('Correlation Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "strongly correlated (>=0.8): **GRE** & **TF**, **GRE** & **GPA**, **GRE** & **Admit**, **TF** & **GPA**, **GPA** & **Admit**;\n",
    "\n",
    "correlated (0.7~0.8): **TF** & **Admit**, **UR** & **SOP**, **UR** & **GPA**, **SOP** & **GPA**;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Assumptions\n",
    "\n",
    "Based on our prior knowledge and intuition about these variables, we exhasut all possible causal assumptions and construct the following ***graduate model***: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     "execution_count": 6,
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   ],
   "source": [
    "# graduate model: a causal graphical model where each node is observed\n",
    "grad = CausalGraphicalModel(\n",
    "    nodes=[\"GRE\",\"TF\",\"UR\",\"SOP\",\"LOR\",\"GPA\",\"Research\",\"Admit\"],\n",
    "    edges=[\n",
    "        (\"GRE\",\"Admit\"),\n",
    "        (\"TF\",\"Admit\"),\n",
    "        (\"UR\",\"Admit\"),\n",
    "        (\"SOP\",\"Admit\"),\n",
    "        (\"LOR\",\"Admit\"),\n",
    "        (\"GPA\",\"Admit\"),\n",
    "        (\"Research\",\"Admit\"),\n",
    "        (\"UR\",\"GPA\"),                # better universities might be more strict\n",
    "        (\"UR\",\"LOR\"),                # some of the letters are written by the professors at the university\n",
    "        (\"UR\",\"Research\"),           # better universities might require research experience \n",
    "        (\"GPA\",\"LOR\"),               # some professors take GPA into consideration while writing letters\n",
    "        (\"Research\",\"LOR\"),          # some letters are from the professors the students did research with\n",
    "        (\"Research\",\"SOP\")           # research experience might polish the statement of purpose\n",
    "    ]\n",
    ")\n",
    "\n",
    "grad.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model, however, does not explain the strong correlations between the three variables **GRE**, **TF** and **GPA**. Given the fact that they do not apply any causal influence on each other, this correlation is interpreted as due to some hidden common \"parent\" of the three variables, for example, the ability on exams.\n",
    "\n",
    "Therefore, combining the correlation information with this causal model, we propose the following ***latent graduate model*** where the four variables **GRE**, **TF**, **GPA** and **UR** are assumued to have an *unobserved* parent: **AB** ( the ability on exams):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "<text text-anchor=\"middle\" x=\"200.247\" y=\"-230.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">UR</text>\r\n",
       "</g>\r\n",
       "<!-- UR&#45;&gt;Research -->\r\n",
       "<g id=\"edge10\" class=\"edge\"><title>UR&#45;&gt;Research</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M214.818,-218.834C224.5,-209.421 237.433,-196.847 248.575,-186.015\"/>\r\n",
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       "</g>\r\n",
       "<!-- UR&#45;&gt;LOR -->\r\n",
       "<g id=\"edge9\" class=\"edge\"><title>UR&#45;&gt;LOR</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M197.956,-215.871C194.717,-191.67 188.769,-147.211 184.913,-118.393\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"188.343,-117.637 183.547,-108.189 181.405,-118.565 188.343,-117.637\"/>\r\n",
       "</g>\r\n",
       "<!-- UR&#45;&gt;GPA -->\r\n",
       "<g id=\"edge8\" class=\"edge\"><title>UR&#45;&gt;GPA</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M187.879,-217.811C180.439,-208.673 170.81,-196.849 162.402,-186.524\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"165.014,-184.188 155.986,-178.644 159.586,-188.608 165.014,-184.188\"/>\r\n",
       "</g>\r\n",
       "<!-- UR&#45;&gt;Admit -->\r\n",
       "<g id=\"edge7\" class=\"edge\"><title>UR&#45;&gt;Admit</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M226.54,-229.683C255.703,-224.505 301.732,-211.569 325.247,-180 354,-141.4 361.121,-111.239 333.247,-72 308.795,-37.5771 260.262,-25.325 224.589,-21.0642\"/>\r\n",
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       "</g>\r\n",
       "<!-- AB -->\r\n",
       "<g id=\"node8\" class=\"node\"><title>AB</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"114.247\" cy=\"-306\" rx=\"27\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"114.247\" y=\"-302.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">AB</text>\r\n",
       "</g>\r\n",
       "<!-- AB&#45;&gt;GRE -->\r\n",
       "<g id=\"edge1\" class=\"edge\"><title>AB&#45;&gt;GRE</title>\r\n",
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       "</g>\r\n",
       "<!-- AB&#45;&gt;GPA -->\r\n",
       "<g id=\"edge3\" class=\"edge\"><title>AB&#45;&gt;GPA</title>\r\n",
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       "</g>\r\n",
       "<!-- AB&#45;&gt;TF -->\r\n",
       "<g id=\"edge2\" class=\"edge\"><title>AB&#45;&gt;TF</title>\r\n",
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       "<!-- AB&#45;&gt;UR -->\r\n",
       "<g id=\"edge4\" class=\"edge\"><title>AB&#45;&gt;UR</title>\r\n",
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       "</svg>\r\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x5424fb5748>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# latent graduate model: a causal graphical model contaning unobserved nodes\n",
    "grad_latent = CausalGraphicalModel(\n",
    "    nodes=[\"AB\",\"GRE\",\"TF\",\"UR\",\"SOP\",\"LOR\",\"GPA\",\"Research\",\"Admit\"],\n",
    "    edges=[\n",
    "        (\"AB\",\"GRE\"),\n",
    "        (\"AB\",\"TF\"),\n",
    "        (\"AB\",\"GPA\"),\n",
    "        (\"AB\",\"UR\"),\n",
    "        (\"GRE\",\"Admit\"),\n",
    "        (\"TF\",\"Admit\"),\n",
    "        (\"UR\",\"Admit\"),\n",
    "        (\"SOP\",\"Admit\"),\n",
    "        (\"LOR\",\"Admit\"),\n",
    "        (\"GPA\",\"Admit\"),\n",
    "        (\"Research\",\"Admit\"),\n",
    "        (\"UR\",\"GPA\"),                # better universities might be more strict\n",
    "        (\"UR\",\"LOR\"),                # some of the letters are written by the professors at the university\n",
    "        (\"UR\",\"Research\"),           # better universities might require research experience \n",
    "        (\"GPA\",\"LOR\"),               # some professors take GPA into consideration while writing letters\n",
    "        (\"Research\",\"LOR\"),          # some letters are from the professors the students did research with\n",
    "        (\"Research\",\"SOP\")           # research experience might polish the statement of purpose\n",
    "    ]\n",
    ")\n",
    "\n",
    "grad_latent.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Structural Causal Model\n",
    "\n",
    "In order to do inference on this model, we need to designate certain structural relationships between the variables. In other words, we hope to find the set of CPDs associated with this Bayesian network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Continuous Model\n",
    "\n",
    "The continuous model assumes that all the variabls are continuous except **Research** (dummy variable)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structural Assumptions\n",
    "\n",
    "For the nodes without parents (**GRE**, **TF**, **UR**) in the ***graduate model***, we shouldn't assume that they are independently distributed due to the fact that they are strongly correlated. We utilize the ***latent graduate model*** where the three nodes have a common parent **AB**. Although the variable **AB** is unobserved, but we are able to assume that people's abilities on exams are normally distributed. We choose standard normal distribution believing that linear regression would pick the appropriate parameters:\n",
    "\n",
    "$\\mathbf{AB} \\sim \\mathcal{N}(0,1)$\n",
    "\n",
    "Given a student's ability on exams, this student's performances on GRE, TF, and college entrance exams are assumed to be normally distributed, this means that we obtain the following three CPDs:\n",
    "\n",
    "$\\mathbf{GRE} | \\mathbf{AB} \\sim \\mathcal{N}(\\mu_{gre},\\sigma^2_{gre}),\\quad \\mathbf{TF}|\\mathbf{AB}\\sim \\mathcal{N}(\\mu_{tf},\\sigma^2_{tf}),\\quad \\mathbf{UR}|\\mathbf{AB} \\sim \\mathcal{N}(\\mu_{ur},\\sigma^2_{ur})$\n",
    "\n",
    "For the variable **GPA**, we also assume that it's normally distributed given the university rating and student's ability on exams:\n",
    "\n",
    "$\\mathbf{GPA}|\\mathbf{AB},\\mathbf{UR} \\sim \\mathcal{N}(\\mu_{gpa},\\sigma^2_{gpa})$\n",
    "\n",
    "For the binary variable **Research**, assume that it follows Bernoulli distribution when the university rating is given:\n",
    "\n",
    "$P(\\mathbf{Research} = 1|\\mathbf{UR}) = p_{re}, \\quad P(\\mathbf{Research} = 0|\\mathbf{UR}) = 1 - p_{re}$\n",
    "\n",
    "The variable **SOP** has only one parent which is the binary variable **Research**. The assumption is that having research experiences will polish a student's SOP to some extent, hence the normally distributed **SOP** will have a slightly higher mean value when conditioned on **Research** = 1. Denote the affect of research experience on SOP strength as $\\delta(\\mathbf{Research})$ then we have\n",
    "\n",
    "$\\mathbf{SOP} \\sim \\mathcal{N}(\\mu_{sop}+\\delta(\\mathbf{Research}),\\sigma^2_{sop})$\n",
    "\n",
    "The variable **LOR** has three parents: **UR**, **GPA** and **Research**, it's normally distributed as a linear combination of **UR** and **GPA**, and it's also affected by **Research**. Denote the affect of research experience on LOR strength as $\\Delta(\\mathbf{Research})$ then we have\n",
    "\n",
    "$\\mathbf{LOR}|\\mathbf{UR},\\mathbf{GPA} \\sim \\mathcal{N}(\\mu_{lor}+\\Delta(\\mathbf{Research}),\\sigma^2_{lor})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters Learning\n",
    "\n",
    "Develop fitting models for each variable that are able to take any values of parents as input.\n",
    "\n",
    "One problem about our idea of the continuous model is, all the variables except **Research** are modeled as continuous variables under no constraint, while some variables (**UR**, **SOP** and **LOR**) in the dataset only take on finite number of values, and all of the variables stay in a certain range:\n",
    "\n",
    "**GRE**: integers from 260 to 340\n",
    "\n",
    "**TF**: integers from 0 to 120\n",
    "\n",
    "**UR**: five fixed values: 1, 2, 3, 4, 5\n",
    "\n",
    "**GPA**: real values from 6.00 to 10.00\n",
    "\n",
    "**SOP**: nine fixed values: 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "\n",
    "**LOR**: nine fixed values: 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "\n",
    "**Admit**: real values from 0.00 to 1.00\n",
    "\n",
    "To address this problem, after predicting **UR**, **SOP** and **LOR**, we will convert the continuous values into categorical values based on their quantiles. For the other continuous variables, we will force those out-of-range values to be the maximum or minimum values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given any AB, fit a GRE distribution and predict\n",
    "# force GRE values to be integers in [260,340]\n",
    "def fit_gre_cont(AB,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_gre = smf.ols('GRE ~ AB', data = dataset).fit()\n",
    "    pred = LR_gre.predict(pd.DataFrame({'AB':AB})['AB'])\n",
    "    pred = round(pred)\n",
    "    pred[pred < 260] = 260\n",
    "    pred[pred > 340] = 340\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given any AB, fit a TF distribution and predict\n",
    "# force TL values to be integers in [0,120]\n",
    "def fit_tf_cont(AB,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_tl = smf.ols('TF ~ AB', data = dataset).fit()\n",
    "    pred = LR_tl.predict(pd.DataFrame({'AB':AB})['AB'])\n",
    "    pred = round(pred)\n",
    "    pred[pred < 0] = 0\n",
    "    pred[pred > 120] = 120\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given any AB, fit a UR distribution and predict\n",
    "# convert continuous UR values into integers from 1 to 5\n",
    "def fit_ur_cont(AB,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_ur = smf.ols('UR ~ AB', data = dataset).fit()\n",
    "    pred = LR_ur.predict(pd.DataFrame({'AB':AB})['AB'])\n",
    "    pred = pd.qcut(pred,5,labels=False)+1\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given any AB, fit a GPA distribution and predict given any UR\n",
    "# force GPA values to stay in [6,10]\n",
    "def fit_gpa_cont(AB,UR,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_gpa = smf.ols('GPA ~ AB + UR', data = dataset).fit()\n",
    "    pred = LR_gpa.predict(pd.DataFrame({'AB':AB,'UR':UR})[['AB','UR']])\n",
    "    pred[pred < 6] = 6\n",
    "    pred[pred > 10] = 10\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit a Research distribution and predict given any UR\n",
    "# use logistic regression for the binary Research\n",
    "def fit_re_cont(UR,n_samples):\n",
    "    LR_re = smf.logit('Research ~ UR', data = df).fit()\n",
    "    pred = LR_re.predict(pd.DataFrame({'UR':UR})['UR'])\n",
    "    pred = [ 0 if x < 0.5 else 1 for x in pred]\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# given any BS, fit a SOP distribution and predict given any Research\n",
    "# convert continuous SOP values into 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "def fit_sop_cont(Research,BS,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['BS'] = BS[0:len(df)]\n",
    "    LR_sop = smf.ols('SOP ~ C(Research) + BS', data = dataset).fit()\n",
    "    pred = LR_sop.predict(pd.DataFrame({'Research':Research,'BS':BS})[['Research','BS']])\n",
    "    pred = (pd.qcut(pred,9,labels=False)+2)/2\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit a LOR distribution and predict given any UR, GPA, Research\n",
    "# convert continuous LOR values into 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "def fit_lor_cont(Research,UR,GPA,n_samples):\n",
    "    LR_lor = smf.ols('LOR ~ C(Research) + UR + GPA', data = df).fit()\n",
    "    pred = LR_lor.predict(pd.DataFrame({'Research':Research,'UR':UR,'GPA':GPA})[['Research','UR','GPA']])\n",
    "    pred = (pd.qcut(pred,9,labels=False)+2)/2\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit a Admit distribution and predict given any Research,GRE,TF,UR,GPA,SOP,LOR\n",
    "# force Admit values to stay in [0,1]\n",
    "def fit_ad_cont(Research,GRE,TF,UR,GPA,SOP,LOR,n_samples):\n",
    "    LR_ad = smf.ols('Admit ~ C(Research) + GRE + TF + UR + GPA + SOP + LOR', data = df).fit()\n",
    "    pred = LR_ad.predict(pd.DataFrame({'Research':Research,'GRE':GRE,'TF':TF,'UR':UR,'GPA':GPA,\n",
    "                                      'SOP':SOP,'LOR':LOR})[['Research','GRE','TF','UR','GPA','SOP','LOR']])\n",
    "    pred[pred < 0] = 0\n",
    "    pred[pred > 1] = 1\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuous Model Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_cont = StructuralCausalModel({\n",
    "    \"BS\": lambda n_samples: np.random.normal(size = n_samples),  # base normal distribution for sop\n",
    "    \"AB\": lambda n_samples: np.random.normal(size = n_samples),\n",
    "    \"GRE\": lambda AB, n_samples: fit_gre_cont(AB,n_samples),\n",
    "    \"TF\": lambda AB, n_samples: fit_tf_cont(AB,n_samples),\n",
    "    \"UR\": lambda AB, n_samples: fit_ur_cont(AB,n_samples),\n",
    "    \"GPA\": lambda AB, UR, n_samples: fit_gpa_cont(AB,UR,n_samples),\n",
    "    \"Research\": lambda UR, n_samples: fit_re_cont(UR,n_samples),\n",
    "    \"SOP\": lambda Research, BS, n_samples: fit_sop_cont(Research,BS,n_samples),\n",
    "    \"LOR\": lambda Research, UR, GPA, n_samples: fit_lor_cont(Research,UR,GPA,n_samples),\n",
    "    \"Admit\": lambda Research, GRE, TF, UR, GPA, SOP, LOR, n_samples: fit_ad_cont(Research,GRE,TF,UR,GPA,SOP,LOR,n_samples)\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.587163\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UR</th>\n",
       "      <th>Research</th>\n",
       "      <th>GPA</th>\n",
       "      <th>LOR</th>\n",
       "      <th>TF</th>\n",
       "      <th>GRE</th>\n",
       "      <th>SOP</th>\n",
       "      <th>Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>9.300996</td>\n",
       "      <td>5.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>318.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.862639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8.911357</td>\n",
       "      <td>3.5</td>\n",
       "      <td>107.0</td>\n",
       "      <td>317.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.779059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>9.294356</td>\n",
       "      <td>4.5</td>\n",
       "      <td>108.0</td>\n",
       "      <td>317.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>0.849186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>8.534287</td>\n",
       "      <td>3.0</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>0.717397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.752073</td>\n",
       "      <td>1.0</td>\n",
       "      <td>106.0</td>\n",
       "      <td>314.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.544427</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UR  Research       GPA  LOR     TF    GRE  SOP     Admit\n",
       "0   5         1  9.300996  5.0  108.0  318.0  5.0  0.862639\n",
       "1   4         1  8.911357  3.5  107.0  317.0  4.0  0.779059\n",
       "2   5         1  9.294356  4.5  108.0  317.0  3.5  0.849186\n",
       "3   3         1  8.534287  3.0  107.0  316.0  3.5  0.717397\n",
       "4   1         0  7.752073  1.0  106.0  314.0  1.0  0.544427"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs_cont = grad_cont.sample(500).drop(columns = ['AB','BS'])\n",
    "gs_cont.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(gs_cont.corr(), cmap='Blues', annot=True)\n",
    "plt.title('Correlation in the Continuous Model')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete Model\n",
    "\n",
    "With the following features of our data, the continuous model first treat them as continuous variables, then convert them into the corresponding format, which could result in large errors:\n",
    "\n",
    "**GRE**: integers from 260 to 340\n",
    "\n",
    "**TF**: integers from 0 to 120\n",
    "\n",
    "**UR**: five fixed values: 1, 2, 3, 4, 5\n",
    "\n",
    "**GPA**: real values from 6.00 to 10.00\n",
    "\n",
    "**Research**: binary variable\n",
    "\n",
    "**SOP**: nine fixed values: 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "\n",
    "**LOR**: nine fixed values: 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5\n",
    "\n",
    "**Admit**: real values from 0.00 to 1.00\n",
    "\n",
    "Therefore, we condiser a discrete model which directly treats **UR**, **SOP** and **LOR** as categorical variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_latent.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structural Assumptions\n",
    "\n",
    "For continuous variables, we still assume that **GRE** and **TF** are normally distributed given **AB**\n",
    "\n",
    "$\\mathbf{AB} \\sim \\mathcal{N}(0,1), \\quad \\mathbf{GRE} | \\mathbf{AB} \\sim \\mathcal{N}(\\mu_{gre},\\sigma^2_{gre}),\\quad \\mathbf{TF}|\\mathbf{AB}\\sim \\mathcal{N}(\\mu_{tf},\\sigma^2_{tf})$\n",
    "\n",
    "**UR** is regarded as a categorical variable taking values 1,2,3,4,5:\n",
    "\n",
    "$P(\\mathbf{UR} = k | \\mathbf{AB}) = p_{ur}(k),\\quad \\sum_{k=1}^5p_{ur}(k) = 1$\n",
    "\n",
    "The variable **GPA** is still assumed to be normally distributed given **UR** and **AB**\n",
    "\n",
    "$\\mathbf{GPA}|\\mathbf{AB},\\mathbf{UR} \\sim \\mathcal{N}(\\mu_{gpa},\\sigma^2_{gpa})$\n",
    "\n",
    "This time for the binary variable **Research**, since the parent **UR** is treated as a categorical variable, we are able to entirely specify it's discrete distribution:\n",
    "\n",
    "$P(\\mathbf{Research} = 1|\\mathbf{UR} = k) = p_{re}(k), \\quad P(\\mathbf{Research} = 0|\\mathbf{UR} = k) = 1 - p_{re}(k), \\quad k = 1,2,3,4,5$\n",
    "\n",
    "For the variable **SOP**, since it has a binary parent **Research**, when treated as a categorical variable, we are able to entirely specify its discrete distribution:\n",
    "\n",
    "$s_1 = 1, \\quad s_2 = 1.5, \\quad s_3 = 2, \\quad s_4 = 2.5, \\quad s_5 = 3, \\quad s_6 = 3.5, \\quad s_7 = 4, \\quad s_8 = 4.5, \\quad s_9 = 5$\n",
    "\n",
    "$P(\\mathbf{SOP}=s_i|\\mathbf{Research}=j) = p_{i,j}, \\quad \\forall i = 1,2,\\dots,9, \\forall j = 0,1 \\quad \\Rightarrow \\quad \\sum_{i=1}^9p_{i,j} = 1, \\quad \\forall j = 0,1$\n",
    "\n",
    "For the categorical variable **LOR**, it has both discrete parents (**Research**, **UR**) and continuous parents (**GPA**), hence we have:\n",
    "\n",
    "$(\\mathbf{LOR} = s_i|\\mathbf{Research} = j, \\mathbf{UR} = k,\\mathbf{GPA}) \\sim \\mathcal{N}(\\mu_{lor}(s_i,j,k),\\sigma^2_{lor})$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same as fit_gre_cont\n",
    "def fit_gre_disc(AB,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_gre = smf.ols('GRE ~ AB', data = dataset).fit()\n",
    "    pred = LR_gre.predict(pd.DataFrame({'AB':AB})['AB'])\n",
    "    pred = round(pred)\n",
    "    pred[pred < 260] = 260\n",
    "    pred[pred > 340] = 340\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same as fit_tf_cont\n",
    "def fit_tf_disc(AB,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_tl = smf.ols('TF ~ AB', data = dataset).fit()\n",
    "    pred = LR_tl.predict(pd.DataFrame({'AB':AB})['AB'])\n",
    "    pred = round(pred)\n",
    "    pred[pred < 0] = 0\n",
    "    pred[pred > 120] = 120\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given any AB, fit a UR distribution and predict\n",
    "# use multinomial logistic regression\n",
    "def fit_ur_disc_1(AB,n_samples):\n",
    "    LR_ur = LogisticRegression(random_state=0).fit(sm.add_constant(AB[0:len(df)]), np.array(df['UR']))\n",
    "    AB = sm.add_constant(AB)\n",
    "    pred = LR_ur.predict(AB)\n",
    "    return pred\n",
    "\n",
    "# It turns out that using multinomial logistic regression is problematic\n",
    "# most of the predictions are the same\n",
    "# so this is an alternative model for UR which does not depend on AB\n",
    "def fit_ur_disc_2(n_samples):\n",
    "    ur_prob = [sum(df['UR'] == i)/len(df) for i in range(1,6)]\n",
    "    return np.random.choice([1,2,3,4,5],n_samples,p=ur_prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same as fit_gpa_cont except that UR now is treated as a categorical variable\n",
    "def fit_gpa_disc(AB,UR,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['AB'] = AB[0:len(df)]\n",
    "    LR_gpa = smf.ols('GPA ~ AB + C(UR)', data = dataset).fit()\n",
    "    pred = LR_gpa.predict(pd.DataFrame({'AB':AB,'UR':UR})[['AB','UR']])\n",
    "    pred[pred < 6] = 6\n",
    "    pred[pred > 10] = 10\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# credit to Joseph\n",
    "# specify the discrete distribution for Research given UR\n",
    "df_ur = [df[df['UR'] == i] for i in range(1,6)]\n",
    "re_prob = [[sum(seg['Research'] == i)/len(seg) for i in np.arange(2)] for seg in df_ur]\n",
    "\n",
    "def fit_re_disc(UR,n_samples):\n",
    "    pred = np.zeros(n_samples)\n",
    "    for i in np.arange(n_samples):\n",
    "        pred[i] = np.random.binomial(1, re_prob[UR[i]-1][1], 1)[0]\n",
    "    return pred.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# credit to Joseph\n",
    "# specify the discrete distribution for SOP given Research\n",
    "df_re = [df[df['Research'] == i] for i in np.arange(2)]\n",
    "sop_prob = [[sum(seg['SOP'] == i)/len(seg) for i in np.arange(1,5.5,.5)] for seg in df_re]\n",
    "\n",
    "def fit_sop_disc(Research,n_samples):\n",
    "    pred = np.zeros(n_samples)\n",
    "    for i in np.arange(n_samples):\n",
    "        element = [1,2,3,4,5,6,7,8,9]  # need to be treated as categorical data, cannot use original values\n",
    "        pred[i] = np.random.choice(element,1,p=sop_prob[int(Research[i])])[0]\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same as fit_lor_cont except that now UR is treated as a categorical variable\n",
    "def fit_lor_disc(Research,UR,GPA,n_samples):\n",
    "    LR_lor = smf.ols('LOR ~ C(Research) + C(UR) + GPA', data = df).fit()\n",
    "    pred = LR_lor.predict(pd.DataFrame({'Research':Research,'UR':UR,'GPA':GPA})[['Research','UR','GPA']])\n",
    "    pred = pd.qcut(pred,9,labels=False)+1  # generate integers from 1 to 9\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same as fit_ad_cont except that now\n",
    "# UR,SOP,LOR are treated as categorical variables\n",
    "def fit_ad_disc(Research,GRE,TF,UR,GPA,SOP,LOR,n_samples):\n",
    "    dataset = df.copy(deep=True)\n",
    "    dataset['SOP'] = dataset['SOP'] * 2 - 1\n",
    "    dataset['LOR'] = dataset['LOR'] * 2 - 1\n",
    "    LR_ad = smf.ols('Admit ~ C(Research) + GRE + TF + C(UR) + GPA + C(SOP) + C(LOR)', data = dataset).fit()\n",
    "    pred = LR_ad.predict(pd.DataFrame({'Research':Research,'GRE':GRE,'TF':TF,'UR':UR,'GPA':GPA,\n",
    "                                      'SOP':SOP,'LOR':LOR})[['Research','GRE','TF','UR','GPA','SOP','LOR']])\n",
    "    pred[pred < 0] = 0\n",
    "    pred[pred > 1] = 1\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_disc = StructuralCausalModel({\n",
    "    \"AB\": lambda n_samples: np.random.normal(size = n_samples),\n",
    "    \"GRE\": lambda AB, n_samples: fit_gre_disc(AB,n_samples),\n",
    "    \"TF\": lambda AB, n_samples: fit_tf_disc(AB,n_samples),\n",
    "    \"UR\": lambda AB, n_samples: fit_ur_disc_1(AB,n_samples),\n",
    "    \"GPA\": lambda AB, UR, n_samples: fit_gpa_disc(AB,UR,n_samples),\n",
    "    \"Research\": lambda UR, n_samples: fit_re_disc(UR,n_samples),\n",
    "    \"SOP\": lambda Research, n_samples: fit_sop_disc(Research,n_samples),\n",
    "    \"LOR\": lambda Research, UR, GPA, n_samples: fit_lor_disc(Research,UR,GPA,n_samples),\n",
    "    \"Admit\": lambda Research, GRE, TF, UR, GPA, SOP, LOR, n_samples: fit_ad_disc(Research,GRE,TF,UR,GPA,SOP,LOR,n_samples)\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>UR</th>\n",
       "      <th>Research</th>\n",
       "      <th>SOP</th>\n",
       "      <th>GPA</th>\n",
       "      <th>LOR</th>\n",
       "      <th>TF</th>\n",
       "      <th>GRE</th>\n",
       "      <th>Admit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.498560</td>\n",
       "      <td>2</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>0.627321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.503058</td>\n",
       "      <td>4</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>0.690064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.498520</td>\n",
       "      <td>6</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>0.726188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.494979</td>\n",
       "      <td>1</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>0.609097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>6.0</td>\n",
       "      <td>8.505800</td>\n",
       "      <td>9</td>\n",
       "      <td>107.0</td>\n",
       "      <td>316.0</td>\n",
       "      <td>0.739896</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UR  Research  SOP       GPA  LOR     TF    GRE     Admit\n",
       "0   3         0  3.0  8.498560    2  107.0  316.0  0.627321\n",
       "1   3         0  7.0  8.503058    4  107.0  316.0  0.690064\n",
       "2   3         1  8.0  8.498520    6  107.0  316.0  0.726188\n",
       "3   3         0  3.0  8.494979    1  107.0  316.0  0.609097\n",
       "4   3         1  6.0  8.505800    9  107.0  316.0  0.739896"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs_disc = grad_disc.sample(500).drop(columns = ['AB'])\n",
    "gs_disc.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(gs_disc.corr(), cmap='Blues', annot=True)\n",
    "plt.title('Correlation in the Discrete Model')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intervention Query"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are interested in the intervention query $P(\\mathbf{Admit}|do(\\mathbf{Research}=1))$, which is the probability of admittance if we force a student to have reasearch experience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\r\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<!-- Generated by graphviz version 2.38.0 (20140413.2041)\r\n",
       " -->\r\n",
       "<!-- Title: %3 Pages: 1 -->\r\n",
       "<svg width=\"359pt\" height=\"332pt\"\r\n",
       " viewBox=\"0.00 0.00 359.43 332.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 328)\">\r\n",
       "<title>%3</title>\r\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-328 355.427,-328 355.427,4 -4,4\"/>\r\n",
       "<!-- Research -->\r\n",
       "<g id=\"node1\" class=\"node\"><title>Research</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"272.247\" cy=\"-162\" rx=\"44.393\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"272.247\" y=\"-158.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">Research</text>\r\n",
       "</g>\r\n",
       "<!-- LOR -->\r\n",
       "<g id=\"node2\" class=\"node\"><title>LOR</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"181.247\" cy=\"-90\" rx=\"29.4969\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"181.247\" y=\"-86.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">LOR</text>\r\n",
       "</g>\r\n",
       "<!-- Research&#45;&gt;LOR -->\r\n",
       "<g id=\"edge16\" class=\"edge\"><title>Research&#45;&gt;LOR</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M252.502,-145.811C239.13,-135.525 221.335,-121.836 206.873,-110.712\"/>\r\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"208.862,-107.826 198.802,-104.503 204.594,-113.375 208.862,-107.826\"/>\r\n",
       "</g>\r\n",
       "<!-- SOP -->\r\n",
       "<g id=\"node4\" class=\"node\"><title>SOP</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"295.247\" cy=\"-90\" rx=\"28.6953\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"295.247\" y=\"-86.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">SOP</text>\r\n",
       "</g>\r\n",
       "<!-- Research&#45;&gt;SOP -->\r\n",
       "<g id=\"edge17\" class=\"edge\"><title>Research&#45;&gt;SOP</title>\r\n",
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       "</g>\r\n",
       "<!-- Admit -->\r\n",
       "<g id=\"node9\" class=\"node\"><title>Admit</title>\r\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"181.247\" cy=\"-18\" rx=\"33.2948\" ry=\"18\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"181.247\" y=\"-14.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">Admit</text>\r\n",
       "</g>\r\n",
       "<!-- Research&#45;&gt;Admit -->\r\n",
       "<g id=\"edge15\" class=\"edge\"><title>Research&#45;&gt;Admit</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M262.891,-144.34C252.608,-126.262 235.4,-96.6769 219.247,-72 212.951,-62.3803 205.67,-52.053 199.177,-43.093\"/>\r\n",
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       "</g>\r\n",
       "<!-- LOR&#45;&gt;Admit -->\r\n",
       "<g id=\"edge12\" class=\"edge\"><title>LOR&#45;&gt;Admit</title>\r\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M181.247,-71.6966C181.247,-63.9827 181.247,-54.7125 181.247,-46.1124\"/>\r\n",
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       "<g id=\"edge1\" class=\"edge\"><title>AB&#45;&gt;GRE</title>\r\n",
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       "<g id=\"edge2\" class=\"edge\"><title>AB&#45;&gt;TF</title>\r\n",
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     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_latent.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## the Multilated Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_doResearch = grad_latent.do(\"Research\")\n",
    "grad_doResearch.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "frozenset({frozenset({'UR'}),\n",
       "           frozenset({'GRE', 'UR'}),\n",
       "           frozenset({'GPA', 'GRE', 'UR'}),\n",
       "           frozenset({'AB', 'UR'}),\n",
       "           frozenset({'AB', 'GPA', 'UR'}),\n",
       "           frozenset({'TF', 'UR'}),\n",
       "           frozenset({'GPA', 'UR'}),\n",
       "           frozenset({'AB', 'TF', 'UR'}),\n",
       "           frozenset({'AB', 'GPA', 'TF', 'UR'}),\n",
       "           frozenset({'AB', 'GRE', 'TF', 'UR'}),\n",
       "           frozenset({'GPA', 'TF', 'UR'}),\n",
       "           frozenset({'GRE', 'TF', 'UR'}),\n",
       "           frozenset({'AB', 'GRE', 'UR'}),\n",
       "           frozenset({'GPA', 'GRE', 'TF', 'UR'}),\n",
       "           frozenset({'AB', 'GPA', 'GRE', 'UR'}),\n",
       "           frozenset({'AB', 'GPA', 'GRE', 'TF', 'UR'})})"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# backdoor criterion\n",
    "grad_latent.get_all_backdoor_adjustment_sets(\"Research\", \"Admit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ATE Estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# copied from the third notebook of causal inference\n",
    "def estimate_conditional_expectation(df, x, y):\n",
    "    \"\"\"\n",
    "    Estimate E[Y|X=1] - E[Y|X=0]\n",
    "    \n",
    "    from a dataframe `df` of samples.\n",
    "    \n",
    "    Arguments\n",
    "    ---------\n",
    "    df: pandas.DataFrame\n",
    "    \n",
    "    x: str\n",
    "    \n",
    "    y: str\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    estimates: tuple[float, float]\n",
    "        estiamted difference and standard deviation\n",
    "    \"\"\"\n",
    "    a = df.loc[lambda df: df[x] == 0]\n",
    "    b = df.loc[lambda df: df[x] == 1]\n",
    "    \n",
    "    n_a = a.shape[0]\n",
    "    n_b = b.shape[0]\n",
    "    \n",
    "    delta = b[y].mean() - a[y].mean()\n",
    "    delta_std = np.sqrt(a[y].var() / n_a + b[y].var() / n_b)\n",
    "    \n",
    "    return (delta, delta_std)\n",
    "\n",
    "\n",
    "def ab_test(scm, x, y, n=10000):\n",
    "    \"\"\"\n",
    "    Simulate an A/B on StructuralCausalModel scm\n",
    "    to estimate the quantity:\n",
    "    \n",
    "    E[Y|do(X) = 1] - E[Y|do(X) = 0]\n",
    "    \n",
    "    Arguments\n",
    "    ---------\n",
    "    scm: StructuralCausalmodel\n",
    "    \n",
    "    x: str\n",
    "    \n",
    "    y: str\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    estimate: tuple[estimates, estiamte_std]\n",
    "    \n",
    "    \"\"\"\n",
    "    scm_do = scm.do(x)\n",
    "    \n",
    "    n_a = int(n / 2)\n",
    "    n_b = n - n_a\n",
    "    set_variable = np.array([0]*n_a + [1]*n_b)\n",
    "    \n",
    "    samp = (\n",
    "        scm_do\n",
    "        .sample(\n",
    "            set_values={x: set_variable}, \n",
    "            n_samples=n)\n",
    "    )\n",
    "    \n",
    "    return estimate_conditional_expectation(samp, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated ATE: 0.035\n"
     ]
    }
   ],
   "source": [
    "# ATE based on the continuous model\n",
    "print(\"Estimated ATE: {:.3f}\".format(ab_test(grad_cont, \"Research\", \"Admit\")[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated ATE: 0.073\n"
     ]
    }
   ],
   "source": [
    "# ATE based on the discrete model\n",
    "print(\"Estimated ATE: {:.3f}\".format(ab_test(grad_disc, \"Research\", \"Admit\")[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "Both the continuous and the discrete models show that intervening on the variable **Research** will increase a student's chance of admittance **Admit**, but it does not have much influence on it (the ATE value is small)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contribution\n",
    "\n",
    "The correlation map -- credit to Elliot Brown\n",
    "\n",
    "The idea of using customized function in StructuralCausalModel -- credit to Cory Glover\n",
    "\n",
    "The discrete densities of **Research** and **SOP** -- credit to Joseph Drapeau\n",
    "\n",
    "My own work: \n",
    "\n",
    "1. propose a confounding variable **AB**\n",
    "\n",
    "2. propose a continuous model with specified structural assumptions\n",
    "\n",
    "3. propose a discrete model (treat categorical variables) with specified structural assumptions\n",
    "\n",
    "4. for both two models, write customized fitting functions that not only fit the corresponding distribution, but also process the prediction values to obey certain constraint. For example, in the continuous model, the continuous values of **UR** are forced to be integers from 1 to 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working Hours: 12"
   ]
  }
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