examples/DirectLiNGAM(Kernel).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DirectLiNGAM by Kernel Method"
   ]
  },
  {
   "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": {
    "ExecuteTime": {
     "end_time": "2019-09-09T02:01:39.097825Z",
     "start_time": "2019-09-09T02:01:33.841227Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1.16.2', '0.24.2', '0.11.1', '1.3']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import graphviz\n",
    "import lingam\n",
    "from lingam.utils import make_dot\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": [
    "## Test data\n",
    "We create test data consisting of 6 variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-09T02:01:39.159633Z",
     "start_time": "2019-09-09T02:01:39.110757Z"
    }
   },
   "outputs": [
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   "source": [
    "n = 1000\n",
    "e = lambda n: np.random.laplace(0, 1, n)\n",
    "x3 = e(n)\n",
    "x2 = 0.3*x3 + e(n)\n",
    "x1 = 0.3*x3 + 0.3*x2 + e(n)\n",
    "x0 = 0.3*x2 + 0.3*x1 + e(n)\n",
    "x4 = 0.3*x1 + 0.3*x0 + e(n)\n",
    "X = pd.DataFrame(np.array([x0, x1, x2, x3, x4]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4'])\n",
    "X.head()"
   ]
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   "source": [
    "m = np.array([[0.0, 0.3, 0.3, 0.0, 0.0],\n",
    "              [0.0, 0.0, 0.3, 0.3, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.3, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "              [0.3, 0.3, 0.0, 0.0, 0.0]])\n",
    "\n",
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Discovery\n",
    "To run causal discovery, we create a `DirectLiNGAM` object by specifying 'kernel' in the `measure` parameter. Then, we call the `fit` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-09T02:01:39.557802Z",
     "start_time": "2019-09-09T02:01:39.423164Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lingam.direct_lingam.DirectLiNGAM at 0x1bba4a38550>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lingam.DirectLiNGAM(measure='kernel')\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `causal_order_` properties, we can see the causal ordering as a result of the causal discovery."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-09T02:01:39.568772Z",
     "start_time": "2019-09-09T02:01:39.560796Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 2, 1, 0, 4]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "model.causal_order_"
   ]
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  {
   "cell_type": "markdown",
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     "end_time": "2019-09-09T01:24:30.429100Z",
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   },
   "source": [
    "Also, using the `adjacency_matrix_` properties, we can see the adjacency matrix as a result of the causal discovery."
   ]
  },
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   "cell_type": "code",
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     "start_time": "2019-09-09T02:01:39.574757Z"
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   },
   "outputs": [
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     "data": {
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       "array([[0.   , 0.34 , 0.273, 0.   , 0.   ],\n",
       "       [0.   , 0.   , 0.304, 0.275, 0.   ],\n",
       "       [0.   , 0.   , 0.   , 0.261, 0.   ],\n",
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   "cell_type": "markdown",
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   "source": [
    "We can draw a causal graph by utility funciton."
   ]
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   "cell_type": "code",
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