examples/LongitudinalLiNGAM.ipynb

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   "source": [
    "# Longitudinal LiNGAM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import and settings\n",
    "In this example, we need to import `numpy`, `pandas`, and `graphviz` in addition to `lingam`."
   ]
  },
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    {
     "name": "stdout",
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     "text": [
      "['1.24.4', '2.0.3', '0.20.3', '1.9.1']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import graphviz\n",
    "import lingam\n",
    "from lingam.utils import print_causal_directions, print_dagc, make_dot\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\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 5 variables. The causal model at each timepoint is as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
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   "source": [
    "# setting\n",
    "n_features = 5\n",
    "n_samples = 200\n",
    "n_lags = 1\n",
    "n_timepoints = 3\n",
    "\n",
    "causal_orders = []\n",
    "B_t_true = np.empty((n_timepoints, n_features, n_features))\n",
    "B_tau_true = np.empty((n_timepoints, n_lags, n_features, n_features))\n",
    "X_t = np.empty((n_timepoints, n_samples, n_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    "# B(0,0)\n",
    "B_t_true[0] = np.array([[0.0, 0.5,-0.3, 0.0, 0.0],\n",
    "                        [0.0, 0.0,-0.3, 0.4, 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",
    "                        [0.1,-0.7, 0.0, 0.0, 0.0]])\n",
    "causal_orders.append([3, 2, 1, 0, 4])\n",
    "make_dot(B_t_true[0], labels=[f'x{i}(0)' for i in range(5)])"
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    "# B(1,1)\n",
    "B_t_true[1] = np.array([[0.0, 0.2,-0.1, 0.0,-0.5],\n",
    "                        [0.0, 0.0, 0.0, 0.4, 0.0],\n",
    "                        [0.0, 0.3, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0,-0.4, 0.0, 0.0, 0.0]])\n",
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       "</g>\n",
       "<!-- x2(2)&#45;&gt;x1(2) -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>x2(2)&#45;&gt;x1(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M78.22,-87.79C85.09,-77.78 94.38,-64.82 103.45,-54 106.9,-49.88 110.72,-45.66 114.52,-41.64\"/>\n",
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       "<!-- x3(2) -->\n",
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       "<text text-anchor=\"middle\" x=\"34.45\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x3(2)</text>\n",
       "</g>\n",
       "<!-- x2(2)&#45;&gt;x3(2) -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>x2(2)&#45;&gt;x3(2)</title>\n",
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       "</g>\n",
       "<!-- x4(2)&#45;&gt;x1(2) -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>x4(2)&#45;&gt;x1(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M151.01,-86.8C148.68,-75.16 145.56,-59.55 142.89,-46.24\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"146.28,-45.29 140.88,-36.18 139.41,-46.67 146.28,-45.29\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fd3e069ffd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# B(2,2)\n",
    "B_t_true[2] = np.array([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0,-0.7, 0.0, 0.5],\n",
    "                        [0.2, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0,-0.4, 0.0, 0.0],\n",
    "                        [0.3, 0.0, 0.0, 0.0, 0.0]])\n",
    "causal_orders.append([0, 2, 4, 3, 1])\n",
    "make_dot(B_t_true[2], labels=[f'x{i}(2)' for i in range(5)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create B(t,t-τ) and X\n",
    "for t in range(n_timepoints):\n",
    "    # external influence\n",
    "    expon = 0.1\n",
    "    ext = np.empty((n_features, n_samples))\n",
    "    for i in range(n_features):\n",
    "        ext[i, :] = np.random.normal(size=(1, n_samples));\n",
    "        ext[i, :] = np.multiply(np.sign(ext[i, :]), abs(ext[i, :]) ** expon);\n",
    "        ext[i, :] = ext[i, :] - np.mean(ext[i, :]);\n",
    "        ext[i, :] = ext[i, :] / np.std(ext[i, :]);\n",
    "\n",
    "    # create B(t,t-τ)\n",
    "    for tau in range(n_lags):\n",
    "        value = np.random.uniform(low=0.01, high=0.5, size=(n_features, n_features))\n",
    "        sign = np.random.choice([-1, 1], size=(n_features, n_features))\n",
    "        B_tau_true[t, tau] = np.multiply(value, sign)\n",
    "\n",
    "    # create X(t)\n",
    "    X = np.zeros((n_features, n_samples))\n",
    "    for co in causal_orders[t]:\n",
    "        X[co] = np.dot(B_t_true[t][co, :], X) + ext[co]\n",
    "        if t > 0:\n",
    "            for tau in range(n_lags):\n",
    "                X[co] = X[co] + np.dot(B_tau_true[t, tau][co, :], X_t[t-(tau+1)].T)\n",
    "    \n",
    "    X_t[t] = X.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Discovery\n",
    "To run causal discovery, we create a `LongitudinalLiNGAM` object by specifying the `n_lags` parameter. Then, we call the `fit` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = lingam.LongitudinalLiNGAM(n_lags=n_lags)\n",
    "model = model.fit(X_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `causal_orders_` property, we can see the causal ordering in time-points as a result of the causal discovery. \n",
    "All elements are nan because the causal order of B(t,t) at t=0 is not calculated.\n",
    "So access to the time points above t=1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[nan, nan, nan, nan, nan]\n",
      "[3, 1, 2, 4, 0]\n",
      "[0, 4, 2, 3, 1]\n"
     ]
    }
   ],
   "source": [
    "print(model.causal_orders_[0]) # nan at t=0\n",
    "print(model.causal_orders_[1])\n",
    "print(model.causal_orders_[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, using the `adjacency_matrices_` property, we can see the adjacency matrix as a result of the causal discovery.\n",
    "As with the causal order, all elements are nan because the B(t,t) and B(t,t-τ) at t=0 is not calculated. \n",
    "So access to the time points above t=1.\n",
    "Also, if we run causal discovery with n_lags=2, B(t,t-τ) at t=1 is also not computed, so all the elements are nan."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B(0,0):\n",
      "[[nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]]\n",
      "B(0,-1):\n",
      "[[nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]\n",
      " [nan nan nan nan nan]]\n",
      "B(1,1):\n",
      "[[ 0.     0.     0.     0.    -0.611]\n",
      " [ 0.     0.     0.     0.398  0.   ]\n",
      " [ 0.     0.328  0.     0.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.   ]\n",
      " [ 0.    -0.338  0.     0.     0.   ]]\n",
      "B(1,0):\n",
      "[[ 0.029  0.064 -0.27   0.065 -0.18 ]\n",
      " [ 0.139 -0.211 -0.43   0.558  0.051]\n",
      " [-0.181  0.178  0.466  0.214  0.079]\n",
      " [ 0.384 -0.083 -0.495 -0.072 -0.323]\n",
      " [-0.174 -0.383 -0.274 -0.275  0.457]]\n",
      "B(2,2):\n",
      "[[ 0.     0.     0.     0.     0.   ]\n",
      " [ 0.     0.    -0.696  0.     0.487]\n",
      " [ 0.231  0.     0.     0.     0.   ]\n",
      " [ 0.     0.    -0.409  0.     0.   ]\n",
      " [ 0.25   0.     0.     0.     0.   ]]\n",
      "B(2,1):\n",
      "[[ 0.194  0.2    0.031 -0.473 -0.002]\n",
      " [-0.376 -0.038  0.16   0.261  0.102]\n",
      " [ 0.117  0.266 -0.05   0.523 -0.019]\n",
      " [ 0.249 -0.448  0.473 -0.001 -0.177]\n",
      " [-0.177  0.309 -0.112  0.295 -0.273]]\n"
     ]
    }
   ],
   "source": [
    "t = 0 # nan at t=0\n",
    "print('B(0,0):')\n",
    "print(model.adjacency_matrices_[t, 0])\n",
    "print('B(0,-1):')\n",
    "print(model.adjacency_matrices_[t, 1])\n",
    "\n",
    "t = 1\n",
    "print('B(1,1):')\n",
    "print(model.adjacency_matrices_[t, 0])\n",
    "print('B(1,0):')\n",
    "print(model.adjacency_matrices_[t, 1])\n",
    "\n",
    "t = 2\n",
    "print('B(2,2):')\n",
    "print(model.adjacency_matrices_[t, 0])\n",
    "print('B(2,1):')\n",
    "print(model.adjacency_matrices_[t, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6Rw5YsADq1vVwwOksLXmtY30rn7Vrlz3aPnIEvv7ajtutlPJOfn5+9OjRgx49etxwOxEYNQpeeMFOS7loEZRM8p6AzMPHzz1UZrVsGdSrB+fOwcqVWqSVygiuXLGdxp5/3vbuXrdOizRooVY+5t+j7RYtoHRpe4vGvfc6HZVSKq1OnYJmzWDCBBg61M4Vnzu301F5B730rXzGlSv2SHvcOHu0PWOGJrJSGcGePdCyJRw6ZIcETeHqeKajZ9TKJ0RFQfPmtkgPHgzz5mmRVspXnTx5kl27dhETE8Py5baj2JkzEBqqRTopekatvN7evbbT2B9/wNSp0KuX0xEppW5FdHQ0Tz/9NAsXLiQwMJC//w7m4sVhVK7sx6JFtjlLXU/PqJVXW7HCHm2fOmWPtrVIK+W7nnnmGeLj41m+fCUXL35MdPTHxMcvAepz5co+p8PzWlqoldcaPx6aNoXixW2nsfvuczoipdStOnXqFAsWLODNN4fTqNE5jhwJ5sUXY5ky5TSxsVE8/PDDXLhwwekwvZIWauV1YmNh4EB7m0bTprBhAyQz251SymGrV6/m6aefpm/fvixatIj4+Pgkt9u9ezexsaW5664oLl2qR4MGXzJ48CmqV69CtmzZqFq1Kt99952Ho/cNN2yjNsa8eKP1IjI8fcNRmd2xY5do3DiCvXvLULjwDO677yjZsg0EApwOLUPR3FZpFR8fT9u2bfnxxx8pUaIE1atXZ+jQocybN4/JkydfM6nGZbp0mUh0dCjZs2elZcvxlCr1J02afEarVq2oX78+BQoU4M8//3TuC3mxlM6ob3M9goCnsXPKFgf6A3e7NzSVEUVHRzNr1izGjRvH3r17r1q3b59Qrtxx9u0rycsv72H27OJs2LCW1q1bJ3uUrm6Z5rZKk65du7JkyRJGjhzJp59+SnR0NIGBgaxdu5a1a9dete3Agds5fPgLihWzE+aEhw+nY8eOnDlzhnHjxvHSSy+xbNkyateu7dC38XIikuIDWAPcluj1bcCa1LzX04/atWuL8k7r16+XwMBAefTRR6V3795SqFAhGTRokMTHx8uqVSK33XZZ/P2j5KefYhPeExsbK9WqVZPly5c7GLlnYSeu8Ei+aG6rW/H7779L3rx5pWfPngnLYmNjpU6dOtKpUycZPHiwa5nIf/4jAiJly+6R06dFQkJCpECBApI/f3656667pHv37tK1a1dp0KCBxMbGJveRPi8teZ3aNurCwOVEry+7limVKrGxsXTq1Ikvv/ySxYsXM3nyZPbs2cOCBQv4z3+289BDEBBwhj59JtGkiX/C+/z9/WnZsiUbN250MPoMTXNb3bTly5dz1113cfbs2YRl/v7+tG/fnj179nDbbbdx9qy9rXLECGjRYi8lSjxN3rzQvHlz/vrrL55++mn++usvQkNDueOOO/jhhx/w9/dP/kMzsdTeRz0dCDPGzHO9fgyY5paIVIa0bt06ihQpwqOPPpqwLE+e/JQoMZuRI6vTtCm0bv0jy5atA1656r27du2iVatWHo4409DcVilau3YtU6dO5fTp05w+fZpNmzYRGxvLli1bGDJkCB9++CEAP//8M3v37qVBgx7ce68dA2H8eHjiidLUqnWMQYMGMWjQIMC2W5cpU4atW7eSNWtWJ7+e10vVGbWIvAc8AUS5Hk+IyPvuDExlLFeuXCEg4H8dws6etcOArlhRk/Llf2DxYujZszXh4eFMnjyZuLg44uLimDJlCps3b6ZDhw4ORp9xaW6rlIwYMYLu3btTrVo1zp8/z7Zt26hevTqFChWie/fufPTRR1SvXp06derw7bff0q/fV3ToUIqICDt5zlNPQbZs2VixYgXHjh2jVKlS3HHHHRw/fpzQ0FAt0qmR2mvkwH3YJAYoBJS51evt7nxoO5Z3io6OloIFC0p4eLgcPChSpYqIv3+8lC79gcycOTNhu23btkmdOnUkMDBQAgMDJSgoSH777TcHI/c8PNhGLZrb6gb27t0ruXPnll27dsm5c+ckb968cuzYMXnggQfk//7v/6Rq1apy++23S/bs2eX222+X5577RbJmFalQQWTv3qT3GR8fL/Hx8Z79Il4gLXmdqkvfxpi3sL1DKwJTgKzA10CD9DxoUBlXzpw5mTRpEg8++CaXL88B/ClRYgBBQWfp2PF/l7qrVatGWFgYhw4dQkS44447nAs6E9DcVkmJiYlhwIABzJw5Ez8/P+rXr0/fvn3JnTs3hQsXpmfPnixfvpxt27axcOFCBg58gfbt9zN8uB8PPQTffAP58ye978S3banUSW1nsjZAayAaQET+xvYOVSrVzp5tw6VLi8mVK4auXUcycWIn5syZk2QHkn8vjym309xW1xk0aBCRkZHMmTOH8uXL8+uvv/LDDz8kXPo+duwY+fLlwxjDtm1/EBc3l+HD/XjmGQgJSb5Iq1uT2s5kl0VEjDECYIzJ5caYVAYTFwevvgoffQRNmhi+/bYg+fMPdjosZWluq6tcunSJadOmsXv3bgoVKsQLL7xAaGgon3zyCf3796dly5acO3eOiRMn8tprExk27GGgMqNHw7PPOh19xpTaQv2NMWYCkM8Y8yTQG/jCfWGpjOL8eejWDRYuhP79YeRI0L4jXkVzW13l/PnzGGMoXLgwxhgWLFhAmzZtMMYQERFBlixZKFmyJC+88A3Hjo0jLi4LWbI8yvTpJ6lW7WMaNWrk9FfIcFLb6/sTYC7wHbYt600RGenOwJTvO3QIGjSAxYth1CgYO1aLtLfR3FbXKliwIIGBgaxevRqAypUrs2vXLh5++GHq1q3L33//zauv7iIiYiZZslygUqXeFCu2g6xZs9KmTRt27Njh8DfIgFLT4wwYlppl3vDQnqHeYcMGkcBAkTx5RJYudToa34JnRybT3FbXmTdvnhQpUkTGjRsnGzdulP/+979SqFAh2bbtdxk6VARE/PxWSYUK9SQkJET2798vn3zyieTMmVM6derkdPheKS15ndrOZA8nsax52g8TVEY0YwY88ADkzg2bNtkZsJTX0txW13nssceYO3cuoaGhDBw4kKNHj/Ljj+t5660qfPABNG9+BGOasXTpTJo3b86dd97JSy+9RLt27a4b51ulXUqzZz0NPAOUNcZsS7TqNmC9OwNTvic+Ht58E957Dxo3hu++g4IFnY5KJUVzW6WkQYMGNGhg79I7fNgOULRtmx0StGbNgyxbdpm8efNe9R5jDLGxsQ5Em7Gl1JlsJvAD8AEwJNHycyJyym1RKZ8THQ09e8L330OfPrY9Ols2p6NSN6C5rVIlLAyCg22OL14MzZvDqVNVyZIlCy1btmTEiBHccccdzJo1i3nz5lG/fn2nQ85wblioReQMcAboAmCMCcRODJzbGJNbRA65P0Tl7Y4csYm8dSsMHw7/+Q/omAbeTXNbpcbs2dCrVxzZsp2iceNPOHOmFnFxHShQoADdu3dn8+bNdO3alaioKKpWrUpAQACvvvqq02FnOKlqozbGtDLG7AP+AFYDf2KPxlUmt2UL3HMP7Ntnb8F64QUt0r5Ec1slJT4e3noLunQBP7+fGTLkex57rDyfffYZHTt2JD4+njFjxvDggw9y4sQJjDEcPXqUsWPH6u1Z7pCaHmfAb0BB4FfX6weAybfag82dD+0Z6j5AwiMyMlLmzBEJCBApXVpk+3ano8s48Gyvb83tDCQ+Pl5+/fVXWbVqlURHR1+17tKlS7JkyRL55ptv5MSJE8nuIzpapEMHERDJlu1rOXTon4R1MTExUqNGDVmyZEnCsgsXLsixY8ckLi4u/b9QBpKWvE5tr+8rInIS8DPG+InISuz4wGlijGlmjNljjNlvjBmSxPrsxpg5rvWbjTGl0/qZ6uYNGjTouvF5CxUaRadOEBRk27CqVnUoOJVWmtsZxIEDB6hduzbt27dnyJAhlCxZkqlTpwKwceNGypQpw4cffshXX31FuXLlGD9+/HX7OHoUGjWCuXOhQ4fNtGsXQsmSgQnrs2XLRvfu3Vm6dGnCshw5clC4cGH8/FJbTtRNS001B34CcgOjgFnA58CGWz06cO3THzgAlAWyYY/sK1+zzTPAeNfzzsCclParR93pD9dZ9KJFi+TCBZHHHrskIAJT5NIlp6PLePDsGbXmdgYQHx8vVatWlREjRiTMTLVjxw4pWrSorF27VooUKSKLFy9O2P7gwYNStGhR+eWXXxKWhYeLFCsmkitXnDRq9LFky5ZN/P39pXfv3hIZGZmw3SuvvCKvv/66575cBpGWvE7tIVAwcBF4AVjqSsJWN3NAkIR7gP0iclBELgOzXZ9z7ef+O4n9XKCJ0alXHOHn58fdd7ekcWNYsCA7ZctOAJ5g5MiPnQ5NpY3mdgawadMm4uPjGThwYMLVr8qVKzNw4EDee+89KlasyKOPPpqwfZkyZXjqqaf46quvAHsG3bAh+PvHU7BgMA0bnubAgQPkyZOHNWvWULlyZUJCQti2bRtTpkyhR48ejnzPzCq1Q4hGi0gckBNYhJ0GT9L42cWBw4leH3EtS3IbEYnF9lK97s5cY0w/Y0y4MSY8MjIyjWGppAQE1Oeee2DnTpg3D/r3PwvAoUPaOdiXaW5nDAcOHODSpUu0aNGCfv36sXXrVgBKlixJVFQUBQoUuO49+fPn5/z5aN59Fzp0gFq1YPDg76hcOZZ3332X5cuXAxAREcGZM2do27YtQUFBDB8+nAoVKnjy62V6qe31/ZQx5hiwDQgHfnb99QoiMlFEgkQkqFChQk6HkwG15cKFZfj5wfr19lasQYMGATBq1CiHY1Npobnt+44cOcLQoUM5cuQInTp14s4776Rp06YsXLiQGTNm0LZtW0JDQ686qL58+TJTpsxm9+7XeeMN6NEDVqyAo0d/pUGDBpw+fZoXX3yRTZs2ERUVRatWrejUqROVKlUiT548Dn7bzCm1s2e9DFQVkRPp+NlHgZKJXpdwLUtqmyPGmCxAXuBkOsagbkAE3n8f7HwNGzl8uA01a/6TsD6peaSVz9Hc9nEffvghXbp0ITAwkHfeeYdBgwYxYMAAunTpQpUqVRgwYADZs2enfv36PPPMM+TLl48JExZw+PBUoqJK8sEHMHiwva2ycuXKfP3111SqVIn69etToUIFRIRDhw7x9ttvU6dOHRYtWkRw8LUtGcqdUttGfQC4kM6fvQUob4wpY4zJhu1QsvCabRYCvVzP2wOhrkZ55WaXLtmj7Ndft9NUdu48Efhfka5ataoOFZgxaG77uNDQULp168bLL7/MxIkTWbNmDRs3biRLlixMmzaNnDlz8vzzz/P9999z7NgxfvzxOH//PY+YmPJ8/z0MGfK/sQ/at2/PH3/8wezZszl9+jQRERE899xzxMXF0bRpU6KjowkICHD2C2dGqelxBtQCtgITgJH/Pm61B1ui/bYA9mL/Z/Gaa9k7QGvX8wDgW2A/EAaUTWmf2jM07Y4dE6lXTwRE3n1XxNWJVHkInu31rbnt4+67776renSLiJw9e1by5Mkjp06dSlh2+fJlGTcuQnLmjJcSJUQSdfi+ytGjR6Vz584CSM6cOaVv375y4sQJiYiIkFKlSsn69evd+XUyrLTktZFUHMQaY8KAdcB2ID5RkZ+W7JscEhQUJOHhXtPE5nN++w1atYKTJ2H6dGjXzumIMh9jzM8ikuZ7mVP5WZrbPm7atGmMGDGCpUuXUrhwYS5fvszzzz9PVFQUs2fPBmDq1GkMHHiEc+eG4uf3Cx07zmTy5HfJmTNnsvtds2YN7du3p3bt2hQoUIClS5fyyiuvMGTIdbfFq1RIS16nto06q4i8eCsfoHzHwoXQtSvkywdr18LddzsdkfIAzW0f17NnT/bt20fFihWpUaMGe/fupVatWsycOROAJUt+4tlnc3Hhwmt07gyffnonL70UwTPPPJMwIEpSGjVqxB9//EFISAjnz59n2LBhlChRwkPfSiWW2jPq97FjAC8CYv5dLl44y44edd88Efj4Y9tWFRQECxZA0aJOR5V5efiMWnM7gzh58iTbtm2jRIkSlC9fHoDjx+Guu3YRFVWJd96xfU6MgTNnzlC6dGn2799PQZ2L1iM8cUbdxfV3aKJlgh15SPmwmBjo3x+mToVOnWDKFMiRw+molAdpbmcQBQsW5IEHHkh4vX27bcY6fbo077+/n6FDyyWsy5s3L4ULF+aff/7RQu0DUlWoRaSMuwNRnhcZCW3bwrp18Pbb8OabOvNVZqO57XtEhM2bNxMREUGdOnUSLkefOXOGFStWkDVrVi5ffoTHH89OnjzQps0ILl68iO3LZ+3evZtTp05Rtqwej/mCGxZqY8yDIhJqjGmb1HoR+d49YSl3+/13e7R97Jidc7ZTJ6cjUp6kue2bjhw5QnBwMBcuXKB8+fL06dOHPn36UL16dQYOHEi9eveyb18rDhzISvnyZ1m5Mg8xMZ2oX78+/v7+tGnThj179jB06FDeeustvdXKR6R0Rt0YCCXpsX8F0GT2QUuW2Hlmc+eGNWugTh2nI1IO0Nz2QY8//jjBwcG88cYbGGOIioqiQYMGjB8/nrVrNzNqVGWWLoXGjSPZvv1ubrttB8WLl2XdunUJA6MUK1aMTz75hMcee8zpr6NSKzX3cAFlUrPMGx56r2Xy4uNFPv1UxBiRWrVEDh92OiKVFDx7H7Xmto84dOiQ3H777RITE3PV8k6dOkmxYtWlUSMREHnjDZG4OJHg4GD56quvHIpWXSsteZ3akcm+S2LZ3LQfJihPuXwZ+vWDl16CNm3s7Vd6p4VCc9tnnDt3jrx585ItW7Zrlpfkn38WsHkzzJwJ77wDfn5QoEABzp8/71C0Kj2l1EZ9F1AFyHtNW1Ye7MhCygecPGkHLlm9Gl577X+JrDIvzW3fU7FiRWJjY1m9ejWNGzcGYOlS+PHHt4mPP8+yZZdo3Nj+p4uMjGTRokW88cYbToas0klKbdQVgZZAPq5uyzoHPOmmmFQ62rXLdho7cgS+/tqO260Umts+x9/fn9GjR9OhQweefLIfhw4F8/XXdxMQcJgWLUbz3HNrePLJJ7l06RJjx45lwIABlCmjnfozghsWahFZACwwxtwrIhs9FJNKJ8uWQceOEBAAK1fCvfc6HZHyFprbvqlly5ZMmjSVF1/MysGDdahe/SDLlpUgMHAkISEhLFiwgKxZszJ9+nQaNmzodLgqnaR2wJM2xpgdwEVgKVAdeEFEvnZbZOqWicDo0fCf/0C1anZo0FKlnI5KeSnNbR8RERFBmzZ92Lr1VWJi7iMgYDhPPJGFIkUGAraIt2zZ0uEolTuktqXyERE5i71U9idQDnjFXUGpW3flCjz7LAwcCC1b2sFMtEirG9Dc9hHBwYPYu/crRBowfTrs2PEYn3/+GcuXL3c6NOVmqS3UWV1/HwW+FZEzbopHpUFUFDRvDuPG2Yng582z90ordQOa2z5g6tSjhIePJkuWAoSGGnr0gLJly/Lqq68yadIkp8NTbpbaS9+LjDG7sZfHnjbGFAIuuS8sdbP27rWdxv74w47b3auX0xEpH6G57eXGjoWBA4uRPfsBwsLyUrr0/9aVLFmSkydPOhab8oxUnVGLyBCgPhAkIleAC0CwOwNTqbdiBdStC6dOQWioFmmVeprb3is2FgYMsE1ZjzwST86cD3Hx4q6rtpk1a9ZVE3GojOmGhdoYMyjRyyYiEgcgItHAQHcGplJnwgRo2hSKF4ewMLjvPqcjUr5Ac9u7nT4NLVrAmDHw8suwaJE/w4a9ziOPPMLo0aNZvHgx3bt3JywsjGeffdbpcJWbpXRG3TnR86HXrGuWzrGomxAbazuM9e9vC/WGDaC3TKqboLntpfbvh3r1YNUqmDzZzhXv7w99+/Zl5syZhIWFMXr0aKpUqcLGjRvJnz+/0yErN0upjdok8zyp18pDTp+2s139+CO8+CJ89JFNZKVugua2F1q50o4i6OcHy5cL0dE/0Lv3XESEdu3a8eijj+r90ZlQSmfUkszzpF4rD9i/3w5cEhoKkybBp59qkVa3RHPby0yaBI88AkWL2masuXMH8vLLL1O7dm3q1KnDkCFD9DJ3JpXSGXUNY8xZ7BF2DtdzXK91PGAP2Lt3L3///Tc1atRg27b8tHWNyrx8Odx/v6OhKd+mue0l4uJsO/SIEdCsmZ0f/uDBX5k/fz47duwgT548APTs2ZMqVaoQHh5OUFCQs0Erj0ppCFE9V3PIyZMn6dy5Mzt27ODOO+/k559rEhMzggoV/Fi0yFCunNMRKl+mue0dzp6Fzp3hhx/sSIIffwxZssCyZcvo0KFDQpEGyJ07Nx07dmTZsmVaqDMZnUPJS/Xu3ZuqVaty8OBf3HPPWi5eHEWOHBsZPHiBFmmlMoCDB20z1vLlMH48fPaZLdIAefLkITIy8rr3REZGXlW8VeaghdoLHTt2jLVr1zJkyPu0a5eV4cNtD+8vvjjGzJljnQ5PKZVGa9bAPfdARISdPOeppyAuLo6lS5cyfvx4ypUrR0hICBs2bEh4z+bNm1m0aBEdO3Z0MHLlhNSOTKY86PTp09x2W3WaNMnB7t12SND+/WHTphI6CpFSPm7KFFuYy5SBxYuhfHk4evQoTZs2JWfOnNSsWZOPPvqIChUq0Lp1a6pUqYIxhh07djBt2jQKFy7s9FdQHqaF2gsdO1aOI0e+I1euWJYty0KTJnb5zJkzefDBB50NTil1S+LioE+fSKZNK0SFCn/x3XdZKF++OAD9+/enXbt2/Pe//wXgypUrtG3blqZNm1K3bl1EhAceeIAcOXI4+RWUQ7RQe5lp06BfvywULpyNK1cas3VrWy5erMj8+fMJDQ296lKYUso3nDsHd9+9i/37K1Gjxjpq1/6aRo2+YcyYMbRo0YJVq1YxZ86chO2zZs3K66+/Tu/evXn77bedC1x5BW2j9hLx8TBkCDz+ODRsCDt23EZIyAh27tzJmDFjKFWqFGFhYRQpUsTpUJVSN+Gvv6BWrWj27y/PsGHn2br1PiZPHs+aNWt45plniIyMxBhDtmzZrnpfrly5iImJcShq5U0cOaM2xhQA5gClsXPgdhSRqCS2iwO2u14eEpHWnorRk86fh+7dYcEC2xY9ciRkzQp16tShTp06ToenVKppbl9twwZo0wbOnPGjV69vGDSoa8K6qlWrcv/997N582aqVavG9OnT6d27NwAiwujRo2ndOkP+LOomOXXpewiwQkQ+NMYMcb0enMR2F0Wkpkcj87BDh6B1a9i+HUaNsjPlGB3AUfkuzW2Xr76Cvn2hZElo0WIkd955Jdltx4wZQ7NmzVi9ejU1atRg2bJlREREsHLlSg9GrLyVU5e+g4FprufTgMccisNRGzfaWzT++ANCQuyUdlqklY/L9LkdHw+vvgo9e0L9+rB5M/Tr14hJkyZx4sSJhO22b9/OqlWraNGiBTVr1uT333+nZs2aHDp0iG7duhEWFkbBggUd/CbKWzh1Rl1YRCJcz48Byd1vEGCMCQdigQ9FZH5SGxlj+gH9AEqVKpXOobrHjBnQp4+dnnLlSqhUyemIlEoXmTq3o6OhRw+YNw+efNJOU5k1K9x777307NmTatWq0bFjR86dO8f8+fOZMGFCwuxXt99+Oy+88ILD30B5IyPinvH3jTE/AUn1fHoNmCYi+RJtGyUi183VZowpLiJHjTFlgVDsvLkHbvS5QUFBEh4enrbg3Sg+Ht58E957Dxo3hu++Az1oVokZY34WEa8dI1JzO2mHD9tmrG3bSBik6NorZDt37mTx4sUEBATQvn17ihUr5kywyuPSktduO6MWkYeSW2eM+ccYU1REIowxRYHjyezjqOvvQWPMKqAWcMNk9mbR0fZy2Pff27arMWPgmo6eSnk9ze3rhYVBcLDN8cWLoXnzpLerXLkylStX9mxwyuc51Ua9EOjlet4LWHDtBsaY/MaY7K7ntwMNgJ0eizCdHTkCjRrB/Pn2aHviRC3SKkPKdLk9e7a9OpYjh+13klyRVupWOVWoPwQeNsbsAx5yvcYYE2SM+cK1TSUg3BjzG7AS247lk8m8ZYvtNLZvHyxcCC+8oJ3GVIaVaXI7Ph7eegu6dIE6dexZdZUqTkelMiJHOpOJyEmgSRLLw4G+rucbgGoeDi3dffMN9OoFRYrAjz9C1apOR6SU+2SW3L5wwQ5O9O238MQTdjz+7NmdjkplVDoymZuIwH//C506QVCQPdrWIq2U7zt61DZjzZ1r54+ePFmLtHIvHevbDS5etEfZc+bYs+kJEzSRlcoIfv7Z9uw+e9aOJNiqldMRqcxAz6jTWUSE7VjyzTcwbJid0k6LtFK+b+5cOw5/liywfr0WaeU5WqjT0a+/2k4lO3faAQ8GDdJOY0r5OhF4913o0AFq1rTNWNWrOx2Vyky0UN+iM2fOcOHChYTX338P990Hfn72aDs42MHglFLp4uJF6NYN3njDTpwTGgqFkxtrTSk30UJ9k3799VcaNmxI8eLFCQwMpGPHTgwdep527exRdlgY1KjhdJRKqbQ6dgweeABmzYL334fp0yEgwOmoVGakhfom/PPPPzRr1ozevXsTFRXFwYN/s337ID78MDfdugkrV9rbsJRSvm3rVjv2wfbt9mrZ0KHajKWco4X6JkyZMoXg4GCeeOIJTp3KSnBwHnbvrk1g4Ej69VunR9tKZQDz50ODBrZtet06O5+0Uk7SQn0TDh48yN13381vv9lOY9u22Z6gjzyyhT///MPp8JRSaSACH34IbdvaMQ/CwqBWLaejUkoL9U2pVasW06ZF0aCBHT5w7Vpo1eoyq1atombNmk6Hp5S6RTExdsyDoUPtIEWrVkHRok5HpZSlA56kkgicONGbTZuyUrjwIWbPvkJ8fBRt275N3bp1qa73ayjlk44ft5e3N2yAd96B11/X9mjlXbRQp0JMDPTvD1OnZic4+CKBgZ/Stes8cubMSffu3Rk0aJDTISqlbsH27XbgkuPH7SBFHTo4HZFS19NCnYLISNtmtW4dvP02vPlmDoz5HPjc6dCUUmmweLGd+SpPHlizxo7Jr5Q30jbqG/j9d3uLRni4nXP2rbf0kphSvk4EPv3UjtldoYLtNKZFWnkzLdTJCAmB+vXtZe81a2wHE6WUb7t8Gfr2hZdfhnbtbIfQ4sWdjkqpG9NCfQ0R+Owz225Vrpw92q5Tx+molFJpdeIEPPwwfPmlHRJ0zhzImdPpqJRKmbZRJ3L5MgwYAJMm2Xbp6dMhVy6no1JKpdXOnfbg++hRmDEDunZ1OiKlUk/PqF1OnoRHHrFF+rXX4NtvtUgrlREsXQr33gvR0bB6tRZp5Xu0UAO7dkHdurBpE3z9tZ3Szk9/GaV8mgiMHAmPPgplythmrLp1nY5KqZuX6cvRsmVQrx6cOwcrV9op7ZRSvu3KFXj6aXj+edu7e906KFXK6aiUujWZtlCLwKhR0KKFPdressVeHlNK+bZTp6BZM5gwwQ4J+t13kDu301EpdesyZWeyK1fskfa4cfZoe8YMTWSlMoI9e6BlSzh0yHYG7dHD6YiUSrtMV6ijouwwgStWwODBdkJ4bY9WyvctX25zO1s2CA21U1UqlRFkqhK1d69tj16zBqZOtVPaaZFWyveNHQvNm0PJkrbTmBZplZFkmjK1YoXt8XnqlD3a7tXL6YiUUmkVG2vHPnj2WVuoN2yA0qWdjkqp9JUpCvWECdC0qR0qMCwM7rvP6YiUUml1+rTtDDpmjB0SdP58uO02p6NSKv1l6Dbq2Fh46SV7L2WLFjBrlp0pRynl2/bvt53GDh6EyZOhd2+nI1LKfTJsoT5zxk6ksWwZvPgifPQR+Ps7HZVSKq1WrrQTavj52Q5kjRs7HZFS7uXIpW9jTAdjzA5jTLwxJtkJ5owxzYwxe4wx+40xQ1K7/wMH7D3RK1bYIUE//VSLtFKe4O7cnjTJDvVbpAhs3qxFWmUOTrVR/w60BdYkt4Exxh8YAzQHKgNdjDGVU9rxuXN2Dul//rFH2337plfISqlUcFtuHz4M/fpBkyawcSPceWd6hayUd3OkUIvILhHZk8Jm9wD7ReSgiFwGZgPBKe17714IDLRH2/ffnw7BKqVSzZ25ffy4Haho8WLImzc9olXKN3hzG3Vx4HCi10eAJIfUN8b0A/q5Xsbs3m1+L1/ezdGlr9uBE04HcRM0Xveq6HQAbnbLuf355+b3zz93c3Tpx9f+3Wm87nXLee22Qm2M+QkoksSq10RkQXp+lohMBCa6PjdcRJJtG/NGvhazxutexphwp2O4Ec3t1NF43csX473V97qtUIvIQ2ncxVGgZKLXJVzLlFIO0txWyrO8ecCTLUB5Y0wZY0w2oDOw0OGYlFJpp7mt1E1w6vasNsaYI8C9wBJjzDLX8mLGmBAAEYkFBgDLgF3ANyKyIxW7n+imsN3J12LWeN3L1+JNoLl9FY3XvTJNvEZE0jMQpZRSSqUjb770rZRSSmV6WqiVUkopL+bzhdrdQxamN2NMAWPMcmPMPtff/MlsF2eM2ep6eLyjTUq/lzEmuzFmjmv9ZmNMaU/HeE08KcX7uDEmMtFv6uiYdcaYL40xx40xvyez3hhjRrq+zzZjzN2ejtFpmttui1Nz203cltci4tMPoBL2RvJVQFAy2/gDB4CyQDbgN6CyQ/F+BAxxPR8CDEtmu/MO/qYp/l7AM8B41/POwBwvj/dxYLRTMSYRcyPgbuD3ZNa3AH4ADFAP2Ox0zA78Rprb6R+j5rZ743VLXvv8GbW4cchCNwkGprmeTwMecyiOG0nN75X4e8wFmhhjjAdjTMyb/vumioisAU7dYJNgYLpYm4B8xpiinonOO2huu4Xmthu5K699vlCnUlJDFhZ3KJbCIhLhen4MKJzMdgHGmHBjzCZjzGOeCS1Ban6vhG3E3m5zBijokeiul9r/vu1cl5vmGmNKJrHem3jTv1lv5k2/k+Z2+stouX1L/169eazvBMaDQxamhxvFm/iFiIgxJrn74+4QkaPGmLJAqDFmu4gcSO9YM5FFwCwRiTHGPIU9Y3jQ4ZgyPc1tze10kOFz2ycKtfjYkIU3itcY848xpqiIRLgueRxPZh9HXX8PGmNWAbWwbTWekJrf699tjhhjsgB5gZOeCe86KcYrIolj+wLbnujNMsUwm5rbmtspyGi5fUv/XjPLpW9vGrJwIdDL9bwXcN1ZgzEmvzEmu+v57UADYKfHIkzd75X4e7QHQsXVW8IBKcZ7TTtQa+yIWN5sIdDT1Uu0HnAm0WVV9T+a2zdHc9tZt5bXTveSS4dedm2w1/ljgH+AZa7lxYCQa3rb7cUeub7mYLwFgRXAPuAnoIBreRDwhet5fWA7tofjdqCPA3Fe93sB7wCtXc8DgG+B/UAYUNbhfwcpxfsBsMP1m64E7nI43llABHDF9e+3D9Af6O9ab4Axru+znWR6PWfkh+a22+LU3HZfrG7Jax1CVCmllPJimeXSt1JKKeWTtFArpZRSXkwLtVJKKeXFtFArpZRSXkwLtVJKKeXFfGLAE+V+xph/by0BO/JSHBDpen2P2HF2lVI+RnPb9+ntWeo6xpi3sTP8fJJoWRax4/4qpXyU5rZv0jNqlSxjzFTgEnaIw/XGmLMkSnLXnKstReRPY0x3YCB2KrrNwDMiEudM5EqpG9Hc9i3aRq1SUgKoLyIvJreBMaYS0AloICI1sZfWunkmPKXULdLc9hF6Rq1S8m0qjp6bALWBLa5pa3OQzIQESimvobntI7RQq5REJ3oey9VXYQJcfw0wTUSGeiwqpVRaaW77CL30rW7Gn8DdAMaYu4EyruUrgPbGmEDXugLGmDsciVApdSv+RHPba2mhVjfjO6CAMWYHMAA7ow0ishN4HfjRGLMNWA4UTXYvSilvo7ntxfT2LKWUUsqL6Rm1Ukop5cW0UCullFJeTAu1Ukop5cW0UCullFJeTAu1Ukop5cW0UCullFJeTAu1Ukop5cX+HwJl09d1rhaVAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for t in range(1, n_timepoints):\n",
    "    B_t, B_tau = model.adjacency_matrices_[t]\n",
    "    plt.figure(figsize=(7, 3))\n",
    "\n",
    "    plt.subplot(1,2,1)\n",
    "    plt.plot([-1, 1],[-1, 1], marker=\"\", color=\"blue\", label=\"support\")\n",
    "    plt.scatter(B_t_true[t], B_t, facecolors='none', edgecolors='black')\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1, 1)\n",
    "    plt.xlabel('True')\n",
    "    plt.ylabel('Estimated')\n",
    "    plt.title(f'B({t},{t})')\n",
    "\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.plot([-1, 1],[-1, 1], marker=\"\", color=\"blue\", label=\"support\")\n",
    "    plt.scatter(B_tau_true[t], B_tau, facecolors='none', edgecolors='black')\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1, 1)\n",
    "    plt.xlabel('True')\n",
    "    plt.ylabel('Estimated')\n",
    "    plt.title(f'B({t},{t-1})')\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Independence between error variables\n",
    "To check if the LiNGAM assumption is broken, we can get p-values of independence between error variables. The value in the i-th row and j-th column of the obtained matrix shows the p-value of the independence of the error variables $e_i$ and $e_j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_values_list = model.get_error_independence_p_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.    0.026 0.064 0.289 0.051]\n",
      " [0.026 0.    0.363 0.821 0.581]\n",
      " [0.064 0.363 0.    0.067 0.098]\n",
      " [0.289 0.821 0.067 0.    0.059]\n",
      " [0.051 0.581 0.098 0.059 0.   ]]\n"
     ]
    }
   ],
   "source": [
    "t = 1\n",
    "print(p_values_list[t])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.    0.715 0.719 0.593 0.564]\n",
      " [0.715 0.    0.78  0.7   0.504]\n",
      " [0.719 0.78  0.    0.532 0.591]\n",
      " [0.593 0.7   0.532 0.    0.401]\n",
      " [0.564 0.504 0.591 0.401 0.   ]]\n"
     ]
    }
   ],
   "source": [
    "t = 2\n",
    "print(p_values_list[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrapping\n",
    "We call `bootstrap()` method instead of `fit()`. Here, the second argument specifies the number of bootstrap sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = lingam.LongitudinalLiNGAM()\n",
    "result = model.bootstrap(X_t, n_sampling=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Directions\n",
    "Since `LongitudinalBootstrapResult` object is returned, we can get the ranking of the causal directions extracted by `get_causal_direction_counts()` method. In the following sample code, `n_directions` option is limited to the causal directions of the top 8 rankings, and `min_causal_effect` option is limited to causal directions with a coefficient of 0.01 or more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "cdc_list = result.get_causal_direction_counts(n_directions=12, min_causal_effect=0.01, split_by_causal_effect_sign=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x2(1) <--- x0(0) (b<0) (100.0%)\n",
      "x4(1) <--- x1(0) (b<0) (100.0%)\n",
      "x4(1) <--- x1(1) (b<0) (100.0%)\n",
      "x3(1) <--- x4(0) (b<0) (100.0%)\n",
      "x3(1) <--- x2(0) (b<0) (100.0%)\n",
      "x3(1) <--- x0(0) (b>0) (100.0%)\n",
      "x2(1) <--- x2(0) (b>0) (100.0%)\n",
      "x1(1) <--- x3(0) (b>0) (100.0%)\n",
      "x1(1) <--- x2(0) (b<0) (100.0%)\n",
      "x1(1) <--- x3(1) (b>0) (100.0%)\n",
      "x4(1) <--- x4(0) (b>0) (100.0%)\n",
      "x0(1) <--- x4(1) (b<0) (100.0%)\n"
     ]
    }
   ],
   "source": [
    "t = 1\n",
    "labels = [f'x{i}({u})' for u in [t, t-1] for i in range(5)]\n",
    "print_causal_directions(cdc_list[t], 100, labels=labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0(2) <--- x0(1) (b>0) (100.0%)\n",
      "x4(2) <--- x1(1) (b>0) (100.0%)\n",
      "x4(2) <--- x0(1) (b<0) (100.0%)\n",
      "x3(2) <--- x2(1) (b>0) (100.0%)\n",
      "x3(2) <--- x1(1) (b<0) (100.0%)\n",
      "x3(2) <--- x0(1) (b>0) (100.0%)\n",
      "x3(2) <--- x2(2) (b<0) (100.0%)\n",
      "x2(2) <--- x3(1) (b>0) (100.0%)\n",
      "x4(2) <--- x3(1) (b>0) (100.0%)\n",
      "x1(2) <--- x3(1) (b>0) (100.0%)\n",
      "x1(2) <--- x2(1) (b>0) (100.0%)\n",
      "x1(2) <--- x0(1) (b<0) (100.0%)\n"
     ]
    }
   ],
   "source": [
    "t = 2\n",
    "labels = [f'x{i}({u})' for u in [t, t-1] for i in range(5)]\n",
    "print_causal_directions(cdc_list[t], 100, labels=labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Directed Acyclic Graphs\n",
    "Also, using the `get_directed_acyclic_graph_counts()` method, we can get the ranking of the DAGs extracted. In the following sample code, `n_dags` option is limited to the dags of the top 3 rankings, and `min_causal_effect` option is limited to causal directions with a coefficient of 0.01 or more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "dagc_list = result.get_directed_acyclic_graph_counts(n_dags=3, min_causal_effect=0.01, split_by_causal_effect_sign=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DAG[0]: 2.0%\n",
      "\tx0(1) <--- x1(1) (b>0)\n",
      "\tx0(1) <--- x3(1) (b>0)\n",
      "\tx0(1) <--- x4(1) (b<0)\n",
      "\tx0(1) <--- x0(0) (b<0)\n",
      "\tx0(1) <--- x1(0) (b>0)\n",
      "\tx0(1) <--- x2(0) (b<0)\n",
      "\tx0(1) <--- x3(0) (b<0)\n",
      "\tx0(1) <--- x4(0) (b<0)\n",
      "\tx1(1) <--- x3(1) (b>0)\n",
      "\tx1(1) <--- x0(0) (b>0)\n",
      "\tx1(1) <--- x1(0) (b<0)\n",
      "\tx1(1) <--- x2(0) (b<0)\n",
      "\tx1(1) <--- x3(0) (b>0)\n",
      "\tx1(1) <--- x4(0) (b>0)\n",
      "\tx2(1) <--- x1(1) (b>0)\n",
      "\tx2(1) <--- x0(0) (b<0)\n",
      "\tx2(1) <--- x1(0) (b>0)\n",
      "\tx2(1) <--- x2(0) (b>0)\n",
      "\tx2(1) <--- x3(0) (b>0)\n",
      "\tx2(1) <--- x4(0) (b>0)\n",
      "\tx3(1) <--- x0(0) (b>0)\n",
      "\tx3(1) <--- x1(0) (b<0)\n",
      "\tx3(1) <--- x2(0) (b<0)\n",
      "\tx3(1) <--- x3(0) (b<0)\n",
      "\tx3(1) <--- x4(0) (b<0)\n",
      "\tx4(1) <--- x1(1) (b<0)\n",
      "\tx4(1) <--- x0(0) (b<0)\n",
      "\tx4(1) <--- x1(0) (b<0)\n",
      "\tx4(1) <--- x2(0) (b<0)\n",
      "\tx4(1) <--- x3(0) (b<0)\n",
      "\tx4(1) <--- x4(0) (b>0)\n",
      "DAG[1]: 2.0%\n",
      "\tx0(1) <--- x1(1) (b>0)\n",
      "\tx0(1) <--- x4(1) (b<0)\n",
      "\tx0(1) <--- x0(0) (b<0)\n",
      "\tx0(1) <--- x1(0) (b>0)\n",
      "\tx0(1) <--- x2(0) (b<0)\n",
      "\tx0(1) <--- x3(0) (b<0)\n",
      "\tx0(1) <--- x4(0) (b<0)\n",
      "\tx1(1) <--- x3(1) (b>0)\n",
      "\tx1(1) <--- x0(0) (b>0)\n",
      "\tx1(1) <--- x1(0) (b<0)\n",
      "\tx1(1) <--- x2(0) (b<0)\n",
      "\tx1(1) <--- x3(0) (b>0)\n",
      "\tx1(1) <--- x4(0) (b>0)\n",
      "\tx2(1) <--- x1(1) (b>0)\n",
      "\tx2(1) <--- x0(0) (b<0)\n",
      "\tx2(1) <--- x1(0) (b>0)\n",
      "\tx2(1) <--- x2(0) (b>0)\n",
      "\tx2(1) <--- x3(0) (b>0)\n",
      "\tx2(1) <--- x4(0) (b>0)\n",
      "\tx3(1) <--- x0(0) (b>0)\n",
      "\tx3(1) <--- x1(0) (b<0)\n",
      "\tx3(1) <--- x2(0) (b<0)\n",
      "\tx3(1) <--- x3(0) (b<0)\n",
      "\tx3(1) <--- x4(0) (b<0)\n",
      "\tx4(1) <--- x1(1) (b<0)\n",
      "\tx4(1) <--- x0(0) (b<0)\n",
      "\tx4(1) <--- x1(0) (b<0)\n",
      "\tx4(1) <--- x2(0) (b<0)\n",
      "\tx4(1) <--- x3(0) (b<0)\n",
      "\tx4(1) <--- x4(0) (b>0)\n",
      "DAG[2]: 2.0%\n",
      "\tx0(1) <--- x4(1) (b<0)\n",
      "\tx0(1) <--- x0(0) (b<0)\n",
      "\tx0(1) <--- x1(0) (b>0)\n",
      "\tx0(1) <--- x2(0) (b<0)\n",
      "\tx0(1) <--- x3(0) (b>0)\n",
      "\tx0(1) <--- x4(0) (b<0)\n",
      "\tx1(1) <--- x3(1) (b>0)\n",
      "\tx1(1) <--- x0(0) (b>0)\n",
      "\tx1(1) <--- x1(0) (b<0)\n",
      "\tx1(1) <--- x2(0) (b<0)\n",
      "\tx1(1) <--- x3(0) (b>0)\n",
      "\tx1(1) <--- x4(0) (b>0)\n",
      "\tx2(1) <--- x1(1) (b>0)\n",
      "\tx2(1) <--- x3(1) (b<0)\n",
      "\tx2(1) <--- x4(1) (b<0)\n",
      "\tx2(1) <--- x0(0) (b<0)\n",
      "\tx2(1) <--- x1(0) (b>0)\n",
      "\tx2(1) <--- x2(0) (b>0)\n",
      "\tx2(1) <--- x3(0) (b>0)\n",
      "\tx2(1) <--- x4(0) (b>0)\n",
      "\tx3(1) <--- x0(0) (b>0)\n",
      "\tx3(1) <--- x1(0) (b>0)\n",
      "\tx3(1) <--- x2(0) (b<0)\n",
      "\tx3(1) <--- x3(0) (b<0)\n",
      "\tx3(1) <--- x4(0) (b<0)\n",
      "\tx4(1) <--- x1(1) (b<0)\n",
      "\tx4(1) <--- x3(1) (b>0)\n",
      "\tx4(1) <--- x0(0) (b<0)\n",
      "\tx4(1) <--- x1(0) (b<0)\n",
      "\tx4(1) <--- x2(0) (b<0)\n",
      "\tx4(1) <--- x3(0) (b<0)\n",
      "\tx4(1) <--- x4(0) (b>0)\n"
     ]
    }
   ],
   "source": [
    "t = 1\n",
    "labels = [f'x{i}({u})' for u in [t, t-1] for i in range(5)]\n",
    "print_dagc(dagc_list[t], 100, labels=labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DAG[0]: 5.0%\n",
      "\tx0(2) <--- x0(1) (b>0)\n",
      "\tx0(2) <--- x1(1) (b>0)\n",
      "\tx0(2) <--- x2(1) (b>0)\n",
      "\tx0(2) <--- x3(1) (b<0)\n",
      "\tx0(2) <--- x4(1) (b>0)\n",
      "\tx1(2) <--- x2(2) (b<0)\n",
      "\tx1(2) <--- x4(2) (b>0)\n",
      "\tx1(2) <--- x0(1) (b<0)\n",
      "\tx1(2) <--- x1(1) (b<0)\n",
      "\tx1(2) <--- x2(1) (b>0)\n",
      "\tx1(2) <--- x3(1) (b>0)\n",
      "\tx1(2) <--- x4(1) (b>0)\n",
      "\tx2(2) <--- x0(2) (b>0)\n",
      "\tx2(2) <--- x0(1) (b>0)\n",
      "\tx2(2) <--- x1(1) (b>0)\n",
      "\tx2(2) <--- x2(1) (b<0)\n",
      "\tx2(2) <--- x3(1) (b>0)\n",
      "\tx2(2) <--- x4(1) (b<0)\n",
      "\tx3(2) <--- x2(2) (b<0)\n",
      "\tx3(2) <--- x0(1) (b>0)\n",
      "\tx3(2) <--- x1(1) (b<0)\n",
      "\tx3(2) <--- x2(1) (b>0)\n",
      "\tx3(2) <--- x3(1) (b>0)\n",
      "\tx3(2) <--- x4(1) (b<0)\n",
      "\tx4(2) <--- x0(2) (b>0)\n",
      "\tx4(2) <--- x0(1) (b<0)\n",
      "\tx4(2) <--- x1(1) (b>0)\n",
      "\tx4(2) <--- x2(1) (b<0)\n",
      "\tx4(2) <--- x3(1) (b>0)\n",
      "\tx4(2) <--- x4(1) (b<0)\n",
      "DAG[1]: 2.0%\n",
      "\tx0(2) <--- x0(1) (b>0)\n",
      "\tx0(2) <--- x1(1) (b>0)\n",
      "\tx0(2) <--- x2(1) (b>0)\n",
      "\tx0(2) <--- x3(1) (b<0)\n",
      "\tx0(2) <--- x4(1) (b<0)\n",
      "\tx1(2) <--- x2(2) (b<0)\n",
      "\tx1(2) <--- x4(2) (b>0)\n",
      "\tx1(2) <--- x0(1) (b<0)\n",
      "\tx1(2) <--- x1(1) (b<0)\n",
      "\tx1(2) <--- x2(1) (b>0)\n",
      "\tx1(2) <--- x3(1) (b>0)\n",
      "\tx1(2) <--- x4(1) (b>0)\n",
      "\tx2(2) <--- x0(2) (b>0)\n",
      "\tx2(2) <--- x0(1) (b>0)\n",
      "\tx2(2) <--- x1(1) (b>0)\n",
      "\tx2(2) <--- x3(1) (b>0)\n",
      "\tx2(2) <--- x4(1) (b<0)\n",
      "\tx3(2) <--- x2(2) (b<0)\n",
      "\tx3(2) <--- x0(1) (b>0)\n",
      "\tx3(2) <--- x1(1) (b<0)\n",
      "\tx3(2) <--- x2(1) (b>0)\n",
      "\tx3(2) <--- x3(1) (b>0)\n",
      "\tx3(2) <--- x4(1) (b<0)\n",
      "\tx4(2) <--- x0(2) (b>0)\n",
      "\tx4(2) <--- x0(1) (b<0)\n",
      "\tx4(2) <--- x1(1) (b>0)\n",
      "\tx4(2) <--- x2(1) (b<0)\n",
      "\tx4(2) <--- x3(1) (b>0)\n",
      "\tx4(2) <--- x4(1) (b<0)\n",
      "DAG[2]: 2.0%\n",
      "\tx0(2) <--- x0(1) (b>0)\n",
      "\tx0(2) <--- x1(1) (b>0)\n",
      "\tx0(2) <--- x2(1) (b<0)\n",
      "\tx0(2) <--- x3(1) (b<0)\n",
      "\tx0(2) <--- x4(1) (b<0)\n",
      "\tx1(2) <--- x2(2) (b<0)\n",
      "\tx1(2) <--- x4(2) (b>0)\n",
      "\tx1(2) <--- x0(1) (b<0)\n",
      "\tx1(2) <--- x1(1) (b<0)\n",
      "\tx1(2) <--- x2(1) (b>0)\n",
      "\tx1(2) <--- x3(1) (b>0)\n",
      "\tx1(2) <--- x4(1) (b>0)\n",
      "\tx2(2) <--- x0(1) (b>0)\n",
      "\tx2(2) <--- x1(1) (b>0)\n",
      "\tx2(2) <--- x2(1) (b<0)\n",
      "\tx2(2) <--- x3(1) (b>0)\n",
      "\tx2(2) <--- x4(1) (b<0)\n",
      "\tx3(2) <--- x2(2) (b<0)\n",
      "\tx3(2) <--- x0(1) (b>0)\n",
      "\tx3(2) <--- x1(1) (b<0)\n",
      "\tx3(2) <--- x2(1) (b>0)\n",
      "\tx3(2) <--- x3(1) (b>0)\n",
      "\tx3(2) <--- x4(1) (b<0)\n",
      "\tx4(2) <--- x0(2) (b>0)\n",
      "\tx4(2) <--- x0(1) (b<0)\n",
      "\tx4(2) <--- x1(1) (b>0)\n",
      "\tx4(2) <--- x2(1) (b<0)\n",
      "\tx4(2) <--- x3(1) (b>0)\n",
      "\tx4(2) <--- x4(1) (b<0)\n"
     ]
    }
   ],
   "source": [
    "t = 2\n",
    "labels = [f'x{i}({u})' for u in [t, t-1] for i in range(5)]\n",
    "print_dagc(dagc_list[t], 100, labels=labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability\n",
    "Using the `get_probabilities()` method, we can get the probability of bootstrapping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[0.   0.37 0.1  0.12 1.  ]\n",
      "  [0.   0.   0.   1.   0.  ]\n",
      "  [0.   0.98 0.   0.5  0.24]\n",
      "  [0.   0.   0.   0.   0.  ]\n",
      "  [0.   1.   0.11 0.28 0.  ]]\n",
      "\n",
      " [[0.91 0.93 1.   0.94 0.97]\n",
      "  [0.99 0.99 1.   1.   0.94]\n",
      "  [1.   1.   1.   0.99 0.84]\n",
      "  [1.   0.98 1.   0.92 1.  ]\n",
      "  [0.98 1.   1.   1.   1.  ]]]\n"
     ]
    }
   ],
   "source": [
    "probs = result.get_probabilities(min_causal_effect=0.01)\n",
    "print(probs[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B(1,1):\n",
      "[[0.   0.37 0.1  0.12 1.  ]\n",
      " [0.   0.   0.   1.   0.  ]\n",
      " [0.   0.98 0.   0.5  0.24]\n",
      " [0.   0.   0.   0.   0.  ]\n",
      " [0.   1.   0.11 0.28 0.  ]]\n",
      "B(1,0):\n",
      "[[0.91 0.93 1.   0.94 0.97]\n",
      " [0.99 0.99 1.   1.   0.94]\n",
      " [1.   1.   1.   0.99 0.84]\n",
      " [1.   0.98 1.   0.92 1.  ]\n",
      " [0.98 1.   1.   1.   1.  ]]\n",
      "B(2,2):\n",
      "[[0.   0.   0.   0.   0.  ]\n",
      " [0.06 0.   1.   0.04 1.  ]\n",
      " [0.8  0.   0.   0.   0.07]\n",
      " [0.03 0.02 1.   0.   0.1 ]\n",
      " [0.91 0.   0.01 0.01 0.  ]]\n",
      "B(2,1):\n",
      "[[1.   1.   0.91 1.   0.92]\n",
      " [1.   0.86 1.   1.   0.96]\n",
      " [0.95 1.   0.95 1.   0.82]\n",
      " [1.   1.   1.   0.92 0.99]\n",
      " [1.   1.   0.97 1.   1.  ]]\n"
     ]
    }
   ],
   "source": [
    "t = 1\n",
    "print('B(1,1):')\n",
    "print(probs[t, 0])\n",
    "print('B(1,0):')\n",
    "print(probs[t, 1])\n",
    "\n",
    "t = 2\n",
    "print('B(2,2):')\n",
    "print(probs[t, 0])\n",
    "print('B(2,1):')\n",
    "print(probs[t, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Total Causal Effects\n",
    "Using the `get_total_causal_effects()` method, we can get the list of total causal effect. The total causal effects we can get are dictionary type variable.\n",
    "We can display the list nicely by assigning it to pandas.DataFrame. Also, we have replaced the variable index with a label below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>from</th>\n",
       "      <th>to</th>\n",
       "      <th>effect</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x0(1)</td>\n",
       "      <td>0.257084</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>-0.201297</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>0.319831</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>0.373447</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>x2(2)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.428210</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.299875</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.331575</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>0.495256</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.294184</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>0.186140</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.543159</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.352668</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.161875</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>x2(2)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>-0.692908</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>0.299131</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>-0.563879</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>x4(2)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>0.476373</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x0(1)</td>\n",
       "      <td>-0.586968</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x1(1)</td>\n",
       "      <td>0.388875</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x2(1)</td>\n",
       "      <td>0.357268</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>-0.387450</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x4(1)</td>\n",
       "      <td>-0.356674</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.202197</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.258939</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>-0.181191</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>-0.115873</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>0.163286</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x4(1)</td>\n",
       "      <td>-0.108293</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>-0.146124</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x0(1)</td>\n",
       "      <td>0.080405</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>-0.130167</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>-0.092469</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>-0.068454</td>\n",
       "      <td>0.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x2(1)</td>\n",
       "      <td>0.032170</td>\n",
       "      <td>0.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.023336</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>0.000911</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>x0(2)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>0.261939</td>\n",
       "      <td>0.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>x0(2)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>-0.029275</td>\n",
       "      <td>0.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>x0(2)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.106739</td>\n",
       "      <td>0.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>x0(2)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.250640</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x2(1)</td>\n",
       "      <td>-0.169832</td>\n",
       "      <td>0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x0(1)</td>\n",
       "      <td>0.015604</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>x4(2)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.147539</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x4(1)</td>\n",
       "      <td>-0.171814</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>x4(2)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.155502</td>\n",
       "      <td>0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>x3(2)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>-0.155433</td>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>x2(2)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>0.084880</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>x1(2)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>-0.174134</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>x3(2)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>-0.146344</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     from     to    effect  probability\n",
       "0   x1(1)  x0(1)  0.257084         1.00\n",
       "1   x4(1)  x4(2) -0.201297         1.00\n",
       "2   x3(1)  x4(2)  0.319831         1.00\n",
       "3   x1(1)  x4(2)  0.373447         1.00\n",
       "4   x2(2)  x3(2) -0.428210         1.00\n",
       "5   x4(1)  x3(2) -0.299875         1.00\n",
       "6   x3(1)  x3(2) -0.331575         1.00\n",
       "7   x2(1)  x3(2)  0.495256         1.00\n",
       "8   x1(1)  x3(2) -0.294184         1.00\n",
       "9   x0(1)  x3(2)  0.186140         1.00\n",
       "10  x3(1)  x2(2)  0.543159         1.00\n",
       "11  x1(1)  x2(2)  0.352668         1.00\n",
       "12  x0(1)  x2(2)  0.161875         1.00\n",
       "13  x2(2)  x1(2) -0.692908         1.00\n",
       "14  x4(1)  x1(2)  0.299131         1.00\n",
       "15  x0(1)  x1(2) -0.563879         1.00\n",
       "16  x4(2)  x1(2)  0.476373         1.00\n",
       "17  x4(1)  x0(1) -0.586968         1.00\n",
       "18  x3(1)  x1(1)  0.388875         1.00\n",
       "19  x1(1)  x2(1)  0.357268         1.00\n",
       "20  x3(1)  x0(2) -0.387450         1.00\n",
       "21  x1(1)  x4(1) -0.356674         1.00\n",
       "22  x0(1)  x0(2)  0.202197         1.00\n",
       "23  x1(1)  x0(2)  0.258939         1.00\n",
       "24  x1(1)  x1(2) -0.181191         0.99\n",
       "25  x4(1)  x2(2) -0.115873         0.99\n",
       "26  x2(1)  x1(2)  0.163286         0.99\n",
       "27  x3(1)  x4(1) -0.108293         0.98\n",
       "28  x0(1)  x4(2) -0.146124         0.97\n",
       "29  x3(1)  x0(1)  0.080405         0.97\n",
       "30  x4(1)  x0(2) -0.130167         0.97\n",
       "31  x2(1)  x4(2) -0.092469         0.97\n",
       "32  x2(1)  x2(2) -0.068454         0.95\n",
       "33  x3(1)  x2(1)  0.032170         0.94\n",
       "34  x2(1)  x0(2)  0.023336         0.92\n",
       "35  x3(1)  x1(2)  0.000911         0.92\n",
       "36  x0(2)  x4(2)  0.261939         0.91\n",
       "37  x0(2)  x1(2) -0.029275         0.90\n",
       "38  x0(2)  x3(2) -0.106739         0.84\n",
       "39  x0(2)  x2(2)  0.250640         0.80\n",
       "40  x4(1)  x2(1) -0.169832         0.24\n",
       "41  x2(1)  x0(1)  0.015604         0.20\n",
       "42  x4(2)  x3(2) -0.147539         0.18\n",
       "43  x2(1)  x4(1) -0.171814         0.11\n",
       "44  x4(2)  x2(2)  0.155502         0.07\n",
       "45  x3(2)  x1(2) -0.155433         0.05\n",
       "46  x2(2)  x4(2)  0.084880         0.02\n",
       "47  x1(2)  x3(2) -0.174134         0.02\n",
       "48  x3(2)  x4(2) -0.146344         0.01"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "causal_effects = result.get_total_causal_effects(min_causal_effect=0.01)\n",
    "\n",
    "df = pd.DataFrame(causal_effects)\n",
    "\n",
    "labels = [f'x{i}({t})' for t in range(3) for i in range(5)]\n",
    "df['from'] = df['from'].apply(lambda x : labels[x])\n",
    "df['to'] = df['to'].apply(lambda x : labels[x])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily perform sorting operations with pandas.DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>from</th>\n",
       "      <th>to</th>\n",
       "      <th>effect</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x2(2)</td>\n",
       "      <td>0.543159</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x3(2)</td>\n",
       "      <td>0.495256</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>x4(2)</td>\n",
       "      <td>x1(2)</td>\n",
       "      <td>0.476373</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x1(1)</td>\n",
       "      <td>0.388875</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x4(2)</td>\n",
       "      <td>0.373447</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     from     to    effect  probability\n",
       "10  x3(1)  x2(2)  0.543159          1.0\n",
       "7   x2(1)  x3(2)  0.495256          1.0\n",
       "16  x4(2)  x1(2)  0.476373          1.0\n",
       "18  x3(1)  x1(1)  0.388875          1.0\n",
       "3   x1(1)  x4(2)  0.373447          1.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_values('effect', ascending=False).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And with pandas.DataFrame, we can easily filter by keywords. The following code extracts the causal direction towards x0(2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>from</th>\n",
       "      <th>to</th>\n",
       "      <th>effect</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>x3(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>-0.387450</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>x0(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.202197</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>x1(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.258939</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>x4(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>-0.130167</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>x2(1)</td>\n",
       "      <td>x0(2)</td>\n",
       "      <td>0.023336</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     from     to    effect  probability\n",
       "20  x3(1)  x0(2) -0.387450         1.00\n",
       "22  x0(1)  x0(2)  0.202197         1.00\n",
       "23  x1(1)  x0(2)  0.258939         1.00\n",
       "30  x4(1)  x0(2) -0.130167         0.97\n",
       "34  x2(1)  x0(2)  0.023336         0.92"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df['to']=='x0(2)'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because it holds the raw data of the total causal effect (the original data for calculating the median), it is possible to draw a histogram of the values of the causal effect, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6.,  8., 13., 12., 19., 16.,  9., 10.,  6.,  1.]),\n",
       " array([0.026, 0.057, 0.088, 0.119, 0.15 , 0.181, 0.212, 0.243, 0.274,\n",
       "        0.304, 0.335]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "%matplotlib inline\n",
    "\n",
    "from_index = 5 # index of x0(1). (index:0)+(n_features:5)*(timepoint:1) = 5\n",
    "to_index = 12 # index of x2(2). (index:2)+(n_features:5)*(timepoint:2) = 12\n",
    "plt.hist(result.total_effects_[:, to_index, from_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prior knowledge\n",
    "\n",
    "### Prior knowledge matrix\n",
    "\n",
    "The shape of the prior knowledge is the same as for LongitudinalLiNGAM.adjacency_matrices_.\n",
    "\n",
    "The elements of prior knowledge matrix are defined as follows:\n",
    "* ``0`` : :math:`x_i` does not have a directed path to :math:`x_j`\n",
    "* ``1`` : :math:`x_i` has a directed path to :math:`x_j`\n",
    "* ``-1`` : No prior knowledge is available to know if either of the two cases above (0 or 1) is true.\n",
    "\n",
    "### Example\n",
    "\n",
    "In this example, the path from x2(2) to x1(2) in graph B(2, 2) is prohibited."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"250pt\" height=\"305pt\"\n",
       " viewBox=\"0.00 0.00 250.45 305.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 301)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-301 246.45,-301 246.45,4 -4,4\"/>\n",
       "<!-- x0(2) -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>x0(2)</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"34.45\" cy=\"-279\" rx=\"34.39\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"34.45\" y=\"-275.3\" font-family=\"Times,serif\" font-size=\"14.00\">x0(2)</text>\n",
       "</g>\n",
       "<!-- x2(2) -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>x2(2)</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"107.45\" cy=\"-18\" rx=\"34.39\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"107.45\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x2(2)</text>\n",
       "</g>\n",
       "<!-- x0(2)&#45;&gt;x2(2) -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>x0(2)&#45;&gt;x2(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M32.29,-260.87C29.5,-234.67 26.04,-183.25 35.45,-141 44.7,-99.46 51.92,-89.46 75.45,-54 78.2,-49.85 81.45,-45.7 84.79,-41.79\"/>\n",
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       "<text text-anchor=\"middle\" x=\"51.45\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\">0.14</text>\n",
       "</g>\n",
       "<!-- x4(2) -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>x4(2)</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"80.45\" cy=\"-192\" rx=\"34.39\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"80.45\" y=\"-188.3\" font-family=\"Times,serif\" font-size=\"14.00\">x4(2)</text>\n",
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       "<!-- x0(2)&#45;&gt;x4(2) -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>x0(2)&#45;&gt;x4(2)</title>\n",
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       "<text text-anchor=\"middle\" x=\"75.45\" y=\"-231.8\" font-family=\"Times,serif\" font-size=\"14.00\">0.21</text>\n",
       "</g>\n",
       "<!-- x1(2) -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>x1(2)</title>\n",
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       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>x1(2)&#45;&gt;x2(2)</title>\n",
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       "</g>\n",
       "<!-- x3(2) -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>x3(2)</title>\n",
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       "<text text-anchor=\"middle\" x=\"190.45\" y=\"-188.3\" font-family=\"Times,serif\" font-size=\"14.00\">x3(2)</text>\n",
       "</g>\n",
       "<!-- x3(2)&#45;&gt;x1(2) -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>x3(2)&#45;&gt;x1(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M182.3,-174.27C179.49,-168.49 176.33,-161.96 173.45,-156 169.64,-148.11 165.5,-139.51 161.76,-131.7\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"164.91,-130.18 157.43,-122.68 158.6,-133.21 164.91,-130.18\"/>\n",
       "<text text-anchor=\"middle\" x=\"189.45\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\">0.25</text>\n",
       "</g>\n",
       "<!-- x3(2)&#45;&gt;x2(2) -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>x3(2)&#45;&gt;x2(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M199.21,-174.36C201.74,-168.69 204.17,-162.22 205.45,-156 211.72,-125.43 204.64,-115.72 192.45,-87 185.65,-71 184.14,-65.88 171.45,-54 163.16,-46.25 152.84,-39.64 142.92,-34.32\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"144.5,-31.19 133.99,-29.8 141.33,-37.44 144.5,-31.19\"/>\n",
       "<text text-anchor=\"middle\" x=\"223.95\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">&#45;0.27</text>\n",
       "</g>\n",
       "<!-- x4(2)&#45;&gt;x1(2) -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>x4(2)&#45;&gt;x1(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M93.43,-175.01C103.74,-162.31 118.32,-144.34 130.02,-129.93\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"132.94,-131.89 136.53,-121.92 127.51,-127.47 132.94,-131.89\"/>\n",
       "<text text-anchor=\"middle\" x=\"134.45\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\">0.38</text>\n",
       "</g>\n",
       "<!-- x4(2)&#45;&gt;x2(2) -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>x4(2)&#45;&gt;x2(2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M76.54,-173.82C72.47,-152.99 67.56,-116.96 74.45,-87 77.89,-72.02 85.09,-56.51 91.89,-44.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"95.02,-45.68 96.94,-35.26 88.94,-42.2 95.02,-45.68\"/>\n",
       "<text text-anchor=\"middle\" x=\"90.45\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\">0.22</text>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fd3e069fac0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk = np.ones((3, 2, 5, 5)) * -1\n",
    "\n",
    "# T=2, tau=0\n",
    "pk[2, 0, 1, 2] = 0\n",
    "model = lingam.LongitudinalLiNGAM(n_lags=n_lags, prior_knowledge=pk)\n",
    "model = model.fit(X_t)\n",
    "\n",
    "make_dot(model.adjacency_matrices_[2, 0], labels=[f'x{i}(2)' for i in range(5)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Comparing with graph B(2, 2) above, we can confirm that the path from x2(2) to x1(2) has been eliminated."
   ]
  }
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