examples/CausalEffect(LogisticRegression).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Causal Effect for Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import and settings\n",
    "In this example, we need to import `numpy`, `pandas`, and `graphviz` in addition to `lingam`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1.16.2', '0.24.2', '0.11.1', '1.4.1']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import graphviz\n",
    "import lingam\n",
    "from lingam.utils import make_prior_knowledge\n",
    "\n",
    "print([np.__version__, pd.__version__, graphviz.__version__, lingam.__version__])\n",
    "\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility function\n",
    "We define a utility function to draw the directed acyclic graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_graph(adjacency_matrix, labels=None):\n",
    "    idx = np.abs(adjacency_matrix) > 0.01\n",
    "    dirs = np.where(idx)\n",
    "    d = graphviz.Digraph(engine='dot')\n",
    "    names = labels if labels else [f'x{i}' for i in range(len(adjacency_matrix))]\n",
    "    for to, from_, coef in zip(dirs[0], dirs[1], adjacency_matrix[idx]):\n",
    "        d.edge(names[from_], names[to], label=f'{coef:.2f}')\n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test data\n",
    "We use 'Wine Quality Data Set' (https://archive.ics.uci.edu/ml/datasets/Wine+Quality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1599, 12)\n"
     ]
    },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "      <th>quality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.4</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.076</td>\n",
       "      <td>11.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.9978</td>\n",
       "      <td>3.51</td>\n",
       "      <td>0.56</td>\n",
       "      <td>9.4</td>\n",
       "      <td>0</td>\n",
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       "      <th>1</th>\n",
       "      <td>7.8</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2.6</td>\n",
       "      <td>0.098</td>\n",
       "      <td>25.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>0.9968</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0.68</td>\n",
       "      <td>9.8</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.8</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.04</td>\n",
       "      <td>2.3</td>\n",
       "      <td>0.092</td>\n",
       "      <td>15.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.9970</td>\n",
       "      <td>3.26</td>\n",
       "      <td>0.65</td>\n",
       "      <td>9.8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.2</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.56</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.075</td>\n",
       "      <td>17.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.9980</td>\n",
       "      <td>3.16</td>\n",
       "      <td>0.58</td>\n",
       "      <td>9.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.4</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.076</td>\n",
       "      <td>11.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.9978</td>\n",
       "      <td>3.51</td>\n",
       "      <td>0.56</td>\n",
       "      <td>9.4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "   fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
       "0            7.4              0.70         0.00             1.9      0.076   \n",
       "1            7.8              0.88         0.00             2.6      0.098   \n",
       "2            7.8              0.76         0.04             2.3      0.092   \n",
       "3           11.2              0.28         0.56             1.9      0.075   \n",
       "4            7.4              0.70         0.00             1.9      0.076   \n",
       "\n",
       "   free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
       "0                 11.0                  34.0   0.9978  3.51       0.56   \n",
       "1                 25.0                  67.0   0.9968  3.20       0.68   \n",
       "2                 15.0                  54.0   0.9970  3.26       0.65   \n",
       "3                 17.0                  60.0   0.9980  3.16       0.58   \n",
       "4                 11.0                  34.0   0.9978  3.51       0.56   \n",
       "\n",
       "   alcohol  quality  \n",
       "0      9.4        0  \n",
       "1      9.8        0  \n",
       "2      9.8        0  \n",
       "3      9.8        1  \n",
       "4      9.4        0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv', sep=';')\n",
    "X['quality'] = np.where(X['quality']>5, 1, 0)\n",
    "print(X.shape)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Discovery\n",
    "To run causal discovery, we create a `DirectLiNGAM` object and call the `fit` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<graphviz.dot.Digraph at 0x22d72bbb4e0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk = make_prior_knowledge(\n",
    "    n_variables=len(X.columns),\n",
    "    sink_variables=[11])\n",
    "\n",
    "model = lingam.DirectLiNGAM(prior_knowledge=pk)\n",
    "model.fit(X)\n",
    "labels = [f'{i}. {col}' for i, col in enumerate(X.columns)]\n",
    "make_graph(model.adjacency_matrix_, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction Model\n",
    "We create the logistic regression model because the target is a discrete variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='warn',\n",
       "          n_jobs=None, penalty='l2', random_state=None, solver='liblinear',\n",
       "          tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "target = 11 # quality\n",
    "features = [i for i in range(X.shape[1]) if i != target]\n",
    "reg = LogisticRegression(solver='liblinear')\n",
    "reg.fit(X.iloc[:, features], X.iloc[:, target])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identification of Feature with Greatest Causal Influence on Prediction\n",
    "To identify of the feature having the greatest intervention effect on the prediction, we create a `CausalEffect` object and call the `estimate_effects_on_prediction` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>feature</th>\n",
       "      <th>effect_plus</th>\n",
       "      <th>effect_minus</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>fixed acidity</td>\n",
       "      <td>0.108700</td>\n",
       "      <td>0.111510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>volatile acidity</td>\n",
       "      <td>0.283712</td>\n",
       "      <td>0.266202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>citric acid</td>\n",
       "      <td>0.204237</td>\n",
       "      <td>0.214388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>residual sugar</td>\n",
       "      <td>0.013498</td>\n",
       "      <td>0.013540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>chlorides</td>\n",
       "      <td>0.013722</td>\n",
       "      <td>0.013679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>free sulfur dioxide</td>\n",
       "      <td>0.088231</td>\n",
       "      <td>0.086463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>total sulfur dioxide</td>\n",
       "      <td>0.403675</td>\n",
       "      <td>0.369129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>density</td>\n",
       "      <td>0.542298</td>\n",
       "      <td>0.481731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>pH</td>\n",
       "      <td>0.131429</td>\n",
       "      <td>0.135560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>sulphates</td>\n",
       "      <td>0.242358</td>\n",
       "      <td>0.256786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>alcohol</td>\n",
       "      <td>0.411940</td>\n",
       "      <td>0.455436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>quality</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 feature  effect_plus  effect_minus\n",
       "0          fixed acidity     0.108700      0.111510\n",
       "1       volatile acidity     0.283712      0.266202\n",
       "2            citric acid     0.204237      0.214388\n",
       "3         residual sugar     0.013498      0.013540\n",
       "4              chlorides     0.013722      0.013679\n",
       "5    free sulfur dioxide     0.088231      0.086463\n",
       "6   total sulfur dioxide     0.403675      0.369129\n",
       "7                density     0.542298      0.481731\n",
       "8                     pH     0.131429      0.135560\n",
       "9              sulphates     0.242358      0.256786\n",
       "10               alcohol     0.411940      0.455436\n",
       "11               quality     0.000000      0.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ce = lingam.CausalEffect(model)\n",
    "effects = ce.estimate_effects_on_prediction(X, target, reg)\n",
    "\n",
    "df_effects = pd.DataFrame()\n",
    "df_effects['feature'] = X.columns\n",
    "df_effects['effect_plus'] = effects[:, 0]\n",
    "df_effects['effect_minus'] = effects[:, 1]\n",
    "df_effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "density\n"
     ]
    }
   ],
   "source": [
    "max_index = np.unravel_index(np.argmax(effects), effects.shape)\n",
    "print(X.columns[max_index[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation of Optimal Intervention\n",
    "`estimate_optimal_intervention` method of `CausalEffect` is available only for linear regression models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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