examples/utils.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# lingam.utils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we need to import `numpy`, `pandas`, and `lingam`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:13.343192Z",
     "start_time": "2021-06-25T06:55:08.877776Z"
    }
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   "outputs": [],
   "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",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define utility functions to draw the directed acyclic graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:13.379744Z",
     "start_time": "2021-06-25T06:55:13.343192Z"
    }
   },
   "outputs": [],
   "source": [
    "def make_prior_knowledge_graph(prior_knowledge_matrix):\n",
    "    d = graphviz.Digraph(engine='dot')\n",
    "    \n",
    "    labels = [f'x{i}' for i in range(prior_knowledge_matrix.shape[0])]\n",
    "    for label in labels:\n",
    "        d.node(label, label)\n",
    "\n",
    "    dirs = np.where(prior_knowledge_matrix > 0)\n",
    "    for to, from_ in zip(dirs[0], dirs[1]):\n",
    "        d.edge(labels[from_], labels[to])\n",
    "\n",
    "    dirs = np.where(prior_knowledge_matrix < 0)\n",
    "    for to, from_ in zip(dirs[0], dirs[1]):\n",
    "        d.edge(labels[from_], labels[to], style='dashed')\n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## print_causal_directions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create test data consisting of 6 variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:13.425622Z",
     "start_time": "2021-06-25T06:55:13.383735Z"
    }
   },
   "outputs": [
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       "         x0         x1        x2        x3         x4        x5\n",
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     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "x3 = np.random.uniform(size=10000)\n",
    "x0 = 3.0*x3 + np.random.uniform(size=10000)\n",
    "x2 = 6.0*x3 + np.random.uniform(size=10000)\n",
    "x1 = 3.0*x0 + 2.0*x2 + np.random.uniform(size=10000)\n",
    "x5 = 4.0*x0 + np.random.uniform(size=10000)\n",
    "x4 = 8.0*x0 - 1.0*x2 + np.random.uniform(size=10000)\n",
    "X = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5'])\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run booststrap and get the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.779808Z",
     "start_time": "2021-06-25T06:55:13.428616Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "model = lingam.DirectLiNGAM()\n",
    "result = model.bootstrap(X, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the ranking of the causal directions extracted by `get_causal_direction_counts()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.795244Z",
     "start_time": "2021-06-25T06:55:38.779808Z"
    }
   },
   "outputs": [],
   "source": [
    "cdc = result.get_causal_direction_counts(n_directions=8, min_causal_effect=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we import `lingam.utils` and check the results with the `print_causal_directions` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.809482Z",
     "start_time": "2021-06-25T06:55:38.797238Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0 <--- x3  (100.0%)\n",
      "x1 <--- x0  (100.0%)\n",
      "x1 <--- x2  (100.0%)\n",
      "x2 <--- x3  (100.0%)\n",
      "x4 <--- x0  (100.0%)\n",
      "x4 <--- x2  (100.0%)\n",
      "x5 <--- x0  (100.0%)\n",
      "x0 <--- x2  (15.0%)\n"
     ]
    }
   ],
   "source": [
    "from lingam.utils import print_causal_directions\n",
    "print_causal_directions(cdc, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-21T01:40:55.324356Z",
     "start_time": "2019-11-21T01:40:55.318373Z"
    }
   },
   "source": [
    "We can also output by specifying the variable name."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.825098Z",
     "start_time": "2021-06-25T06:55:38.809482Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 <--- X4  (100.0%)\n",
      "X2 <--- X1  (100.0%)\n",
      "X2 <--- X3  (100.0%)\n",
      "X3 <--- X4  (100.0%)\n",
      "X5 <--- X1  (100.0%)\n",
      "X5 <--- X3  (100.0%)\n",
      "X6 <--- X1  (100.0%)\n",
      "X1 <--- X3  (15.0%)\n"
     ]
    }
   ],
   "source": [
    "labels = ['X1', 'X2', 'X3', 'X4', 'X5', 'X6']\n",
    "print_causal_directions(cdc, 100, labels=labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## print_dags"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the bootstrap results above to get the ranking of the DAGs extracted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.841942Z",
     "start_time": "2021-06-25T06:55:38.826320Z"
    }
   },
   "outputs": [],
   "source": [
    "dagc = result.get_directed_acyclic_graph_counts(n_dags=3, min_causal_effect=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-21T01:44:23.032001Z",
     "start_time": "2019-11-21T01:44:23.025049Z"
    }
   },
   "source": [
    "Then, we import `lingam.utils` and check the results with the `print_dagc` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.857898Z",
     "start_time": "2021-06-25T06:55:38.841942Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DAG[0]: 77.0%\n",
      "\tx0 <--- x3 \n",
      "\tx1 <--- x0 \n",
      "\tx1 <--- x2 \n",
      "\tx2 <--- x3 \n",
      "\tx4 <--- x0 \n",
      "\tx4 <--- x2 \n",
      "\tx5 <--- x0 \n",
      "DAG[1]: 14.0%\n",
      "\tx0 <--- x2 \n",
      "\tx0 <--- x3 \n",
      "\tx1 <--- x0 \n",
      "\tx1 <--- x2 \n",
      "\tx2 <--- x3 \n",
      "\tx4 <--- x0 \n",
      "\tx4 <--- x2 \n",
      "\tx5 <--- x0 \n",
      "DAG[2]: 3.0%\n",
      "\tx0 <--- x3 \n",
      "\tx1 <--- x0 \n",
      "\tx1 <--- x2 \n",
      "\tx2 <--- x3 \n",
      "\tx4 <--- x0 \n",
      "\tx4 <--- x2 \n",
      "\tx4 <--- x5 \n",
      "\tx5 <--- x0 \n"
     ]
    }
   ],
   "source": [
    "from lingam.utils import print_dagc\n",
    "print_dagc(dagc, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.876016Z",
     "start_time": "2021-06-25T06:55:38.859916Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DAG[0]: 77.0%\n",
      "\tX1 <--- X4 \n",
      "\tX2 <--- X1 \n",
      "\tX2 <--- X3 \n",
      "\tX3 <--- X4 \n",
      "\tX5 <--- X1 \n",
      "\tX5 <--- X3 \n",
      "\tX6 <--- X1 \n",
      "DAG[1]: 14.0%\n",
      "\tX1 <--- X3 \n",
      "\tX1 <--- X4 \n",
      "\tX2 <--- X1 \n",
      "\tX2 <--- X3 \n",
      "\tX3 <--- X4 \n",
      "\tX5 <--- X1 \n",
      "\tX5 <--- X3 \n",
      "\tX6 <--- X1 \n",
      "DAG[2]: 3.0%\n",
      "\tX1 <--- X4 \n",
      "\tX2 <--- X1 \n",
      "\tX2 <--- X3 \n",
      "\tX3 <--- X4 \n",
      "\tX5 <--- X1 \n",
      "\tX5 <--- X3 \n",
      "\tX5 <--- X6 \n",
      "\tX6 <--- X1 \n"
     ]
    }
   ],
   "source": [
    "labels = ['X1', 'X2', 'X3', 'X4', 'X5', 'X6']\n",
    "print_dagc(dagc, 100, labels=labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## make_prior_knowledge\n",
    "In order to perform causal discovery using prior knowledge of causal relations, `make_prior_knowledge` function that creates a prior knowledge matrix is provided. First, we import `lingam.utils` to use `make_prior_knowledge` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.891638Z",
     "start_time": "2021-06-25T06:55:38.876016Z"
    }
   },
   "outputs": [],
   "source": [
    "from lingam.utils import make_prior_knowledge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exogenous variables\n",
    "If the exogenous variable is known, specify the variable index in the `exogenous_variables` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:38.906859Z",
     "start_time": "2021-06-25T06:55:38.891638Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1  0  0]\n",
      " [ 0 -1  0]\n",
      " [-1 -1 -1]]\n"
     ]
    }
   ],
   "source": [
    "pk = make_prior_knowledge(n_variables=3, exogenous_variables=[0, 1])\n",
    "print(pk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:39.241135Z",
     "start_time": "2021-06-25T06:55:38.910798Z"
    }
   },
   "outputs": [
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   "source": [
    "make_prior_knowledge_graph(pk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sink variables\n",
    "If the sink variable such as the target variable of the predictive model is already known, specify the variable index in the `sink_variables` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
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      "[[-1  0  0]\n",
      " [-1 -1  0]\n",
      " [-1  0 -1]]\n"
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   "source": [
    "pk = make_prior_knowledge(n_variables=3, sink_variables=[1, 2])\n",
    "print(pk)"
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    "make_prior_knowledge_graph(pk)"
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   "metadata": {},
   "source": [
    "### Directed path\n",
    "If the causal direction between variables is already known, specify the variable index pair in the `paths` argument."
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    "pk = make_prior_knowledge(n_variables=3, paths=[[0, 1]])\n",
    "print(pk)"
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    "make_prior_knowledge_graph(pk)"
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   "source": [
    "### No directed path\n",
    "If there is no causal direction between variables is already known, specify the variable index pair in the `no_paths` argument."
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    "pk = make_prior_knowledge(n_variables=3, no_paths=[[0, 1]])\n",
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     "execution_count": 19,
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   "source": [
    "make_prior_knowledge_graph(pk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mix all knowledge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All prior knowledge can be specified at the same time. A prior knowledge matrix is created with priorities in the order of `exogenous_variables`, `sink_variables`, `paths`, `no_paths`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
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     "end_time": "2021-06-25T06:55:40.359270Z",
     "start_time": "2021-06-25T06:55:40.348100Z"
    }
   },
   "outputs": [],
   "source": [
    "pk = make_prior_knowledge(\n",
    "    n_variables=4,\n",
    "    exogenous_variables=[3],\n",
    "    sink_variables=[0],\n",
    "    paths=[[1, 0]],\n",
    "    no_paths=[[3, 0]],\n",
    ")"
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    "make_prior_knowledge_graph(pk)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## remove_effect\n",
    "If it is considered that there are hidden common causes in X0(categorical variable) and X1 in following DAG, we want to run causal discovery excluding the effects of X0 and X1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
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    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:41.000026Z",
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    "m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
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       "    x0        x1        x2        x3        x4\n",
       "0  0.0  0.050261  0.463783 -1.126735 -1.158823\n",
       "1  1.0  1.178004  3.267241 -6.887056 -5.598983\n",
       "2  1.0  0.540158  4.043353 -9.351763 -9.743842\n",
       "3  1.0  1.349468  2.777060 -6.244626 -4.675765\n",
       "4  1.0  0.794132  3.493286 -7.697956 -6.991642"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# x0 = np.random.uniform(size=10000)\n",
    "x0 = np.random.randint(2, size=10000)\n",
    "x1 = 0.5*x0 + np.random.uniform(size=10000)\n",
    "x2 = 4.0*x0 - 1.0*x1 + np.random.uniform(size=10000)\n",
    "x3 = 2.0*x0 - 3.0*x2 + np.random.uniform(size=10000)\n",
    "x4 = 1.0*x1 + 2.0*x2 + 2.0*x3 + np.random.uniform(size=10000)\n",
    "X = pd.DataFrame(np.array([x0, x1, x2, x3, x4]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4'])\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this cases, we can import `lingam.utils` and use `remove_effect` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:41.036440Z",
     "start_time": "2021-06-25T06:55:41.020819Z"
    }
   },
   "outputs": [],
   "source": [
    "from lingam.utils import remove_effect\n",
    "remove_features=[0, 1]\n",
    "X_removed = remove_effect(X, remove_features=remove_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run DirectLiNGAM on the dataset that excludes the effects of X0 and X1, we can get the following results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:41.518197Z",
     "start_time": "2021-06-25T06:55:41.036440Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 2, 1, 3, 4]\n",
      "[[ 0.     0.     0.     0.     0.   ]\n",
      " [ 0.493  0.     0.     0.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.   ]\n",
      " [ 0.     0.    -2.998  0.     0.   ]\n",
      " [ 0.     0.     2.023  2.012  0.   ]]\n"
     ]
    },
    {
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     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lingam.DirectLiNGAM()\n",
    "model.fit(X_removed)\n",
    "print(model.causal_order_)\n",
    "print(model.adjacency_matrix_)\n",
    "make_dot(model.adjacency_matrix_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To add causal coefficients from variables whose effects have been removed, regression for each variable may be performed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:41.548907Z",
     "start_time": "2021-06-25T06:55:41.523184Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.utils import check_array\n",
    "\n",
    "def get_reg_coef(X, features, target, gamma=1.0):\n",
    "    X = np.copy(check_array(X))\n",
    "    lr = linear_model.LinearRegression()\n",
    "    lr.fit(X[:, features], X[:, target])\n",
    "    weight = np.power(np.abs(lr.coef_), gamma)\n",
    "    reg = linear_model.LassoLarsIC(criterion='bic')\n",
    "    reg.fit(X[:, features] * weight, X[:, target])\n",
    "    return reg.coef_ * weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:41.955434Z",
     "start_time": "2021-06-25T06:55:41.557897Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.     0.     0.     0.     0.   ]\n",
      " [ 0.493  0.     0.     0.     0.   ]\n",
      " [ 3.987 -0.99   0.     0.     0.   ]\n",
      " [ 1.977  0.017 -2.998  0.     0.   ]\n",
      " [ 0.025  0.984  2.023  2.012  0.   ]]\n"
     ]
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   ],
   "source": [
    "B = model.adjacency_matrix_.copy()\n",
    "B[2, 0], B[2, 1] = get_reg_coef(X, [0, 1], 2)\n",
    "B[3, 0], B[3, 1], _ = get_reg_coef(X, [0, 1, 2], 3)\n",
    "B[4, 0], B[4, 1], _, _ = get_reg_coef(X, [0, 1, 2, 3], 4)\n",
    "print(B)\n",
    "make_dot(B, lower_limit=0.1) # To align the display, the causal direction of small coefficients is excluded."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## get_sink_variables\n",
    "By using the `get_sink_variables()` method, we can get the sink variables in the adjacent matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:42.324455Z",
     "start_time": "2021-06-25T06:55:41.958425Z"
    }
   },
   "outputs": [
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     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "              [0.5, 0.0, 0.0, 0.0, 0.0],\n",
    "              [4.0,-1.0, 0.0, 0.0, 0.0],\n",
    "              [2.0, 0.0,-3.0, 0.0, 0.0],\n",
    "              [0.0, 1.0, 2.0, 2.0, 0.0]])\n",
    "\n",
    "make_dot(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:42.339415Z",
     "start_time": "2021-06-25T06:55:42.328446Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lingam.utils import get_sink_variables\n",
    "\n",
    "get_sink_variables(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## get_exo_variables\n",
    "By using the `get_exo_variables()` method, we can get the exogenous variables in the adjacent matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
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     "end_time": "2021-06-25T06:55:42.668402Z",
     "start_time": "2021-06-25T06:55:42.343405Z"
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    "m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "              [0.5, 0.0, 0.0, 0.0, 0.0],\n",
    "              [4.0,-1.0, 0.0, 0.0, 0.0],\n",
    "              [2.0, 0.0,-3.0, 0.0, 0.0],\n",
    "              [0.0, 1.0, 2.0, 2.0, 0.0]])\n",
    "\n",
    "make_dot(m)"
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  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:42.687814Z",
     "start_time": "2021-06-25T06:55:42.671277Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0]"
      ]
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     "execution_count": 31,
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     "output_type": "execute_result"
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   ],
   "source": [
    "from lingam.utils import get_exo_variables\n",
    "\n",
    "get_exo_variables(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## find_all_paths\n",
    "Using the `find_all_paths()` method, we can explore all paths from any variable to any variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
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   "outputs": [
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       "</svg>\r\n"
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      "text/plain": [
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      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "              [0.5, 0.0, 0.0, 0.0, 0.0],\n",
    "              [4.0,-1.0, 0.0, 0.0, 0.0],\n",
    "              [2.0, 0.0,-3.0, 0.0, 0.0],\n",
    "              [0.0, 1.0, 2.0, 2.0, 0.0]])\n",
    "\n",
    "make_dot(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-25T06:55:43.088132Z",
     "start_time": "2021-06-25T06:55:43.059211Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>path</th>\n",
       "      <th>effect</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>[0, 1, 2, 3, 4]</td>\n",
       "      <td>3.0</td>\n",
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[0, 2, 3, 4]</td>\n",
       "      <td>-24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>[0, 2, 4]</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>[0, 3, 4]</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              path  effect\n",
       "0  [0, 1, 2, 3, 4]     3.0\n",
       "1     [0, 1, 2, 4]    -1.0\n",
       "2        [0, 1, 4]     0.5\n",
       "3     [0, 2, 3, 4]   -24.0\n",
       "4        [0, 2, 4]     8.0\n",
       "5        [0, 3, 4]     4.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lingam.utils import find_all_paths\n",
    "\n",
    "paths = find_all_paths(m, 0, 4)\n",
    "pd.DataFrame({'path': paths[0], 'effect': paths[1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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