examples/CausalEffect(LassoCV).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Causal Effect"
   ]
  },
  {
   "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', '1.2.0']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import graphviz\n",
    "import lingam\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 'Auto MPG Data Set' (http://archive.ics.uci.edu/ml/datasets/Auto+MPG) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(392, 6)\n"
     ]
    },
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693.0</td>\n",
       "      <td>11.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436.0</td>\n",
       "      <td>11.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449.0</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration\n",
       "0  18.0        8.0         307.0       130.0  3504.0          12.0\n",
       "1  15.0        8.0         350.0       165.0  3693.0          11.5\n",
       "2  18.0        8.0         318.0       150.0  3436.0          11.0\n",
       "3  16.0        8.0         304.0       150.0  3433.0          12.0\n",
       "4  17.0        8.0         302.0       140.0  3449.0          10.5"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data-original',\n",
    "                   delim_whitespace=True, header=None,\n",
    "                   names = ['mpg', 'cylinders', 'displacement',\n",
    "                            'horsepower', 'weight', 'acceleration',\n",
    "                            'model year', 'origin', 'car name'])\n",
    "X.dropna(inplace=True)\n",
    "X.drop(['model year', 'origin', 'car name'], axis=1, inplace=True)\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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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lingam.DirectLiNGAM()\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 linear regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=None, copy_X=True, cv=5, eps=0.001, fit_intercept=True,\n",
       "    max_iter=1000, n_alphas=100, n_jobs=None, normalize=False,\n",
       "    positive=False, precompute='auto', random_state=0, selection='cyclic',\n",
       "    tol=0.0001, verbose=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "target = 0 # mpg\n",
    "features = [i for i in range(X.shape[1]) if i != target]\n",
    "reg = LassoCV(cv=5, random_state=0)\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": [
    {
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       "      <th></th>\n",
       "      <th>feature</th>\n",
       "      <th>effect_plus</th>\n",
       "      <th>effect_minus</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>mpg</td>\n",
       "      <td>2.040563</td>\n",
       "      <td>2.040563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>cylinders</td>\n",
       "      <td>5.872194</td>\n",
       "      <td>5.872194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>displacement</td>\n",
       "      <td>1.315913</td>\n",
       "      <td>1.315913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>horsepower</td>\n",
       "      <td>1.047548</td>\n",
       "      <td>1.047548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>weight</td>\n",
       "      <td>5.632157</td>\n",
       "      <td>5.632157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>acceleration</td>\n",
       "      <td>0.350074</td>\n",
       "      <td>0.350074</td>\n",
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       "        feature  effect_plus  effect_minus\n",
       "0           mpg     2.040563      2.040563\n",
       "1     cylinders     5.872194      5.872194\n",
       "2  displacement     1.315913      1.315913\n",
       "3    horsepower     1.047548      1.047548\n",
       "4        weight     5.632157      5.632157\n",
       "5  acceleration     0.350074      0.350074"
      ]
     },
     "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": [
      "cylinders\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",
    "To estimate of the intervention such that the expectation of the prediction of the post-intervention observations is equal or close to a specified value, we use `estimate_optimal_intervention` method of `CausalEffect`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal intervention: 7.922\n"
     ]
    }
   ],
   "source": [
    "# mpg = 15\n",
    "c = ce.estimate_optimal_intervention(X, target, reg, 1, 15)\n",
    "print(f'Optimal intervention: {c:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal intervention: 6.182\n"
     ]
    }
   ],
   "source": [
    "# mpg = 21\n",
    "c = ce.estimate_optimal_intervention(X, target, reg, 1, 21)\n",
    "print(f'Optimal intervention: {c:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal intervention: 3.571\n"
     ]
    }
   ],
   "source": [
    "# mpg = 30\n",
    "c = ce.estimate_optimal_intervention(X, target, reg, 1, 30)\n",
    "print(f'Optimal intervention: {c:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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