examples/BottomUpParceLiNGAM_f-correlation.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BottomUpParceLiNGAM | Comparison of HSIC and F-correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import and settings\n",
    "In this example, we need to import `numpy`, `pandas`, and `graphviz` in addition to `lingam`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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     "end_time": "2021-06-25T06:59:57.385770Z",
     "start_time": "2021-06-25T06:59:57.370810Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1.26.1', '2.1.3', '0.20.1', '1.8.3']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import graphviz\n",
    "import lingam\n",
    "from lingam.utils import print_causal_directions, print_dagc, make_dot\n",
    "\n",
    "from IPython.display import display, Markdown\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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test data\n",
    "First, we generate a causal structure with 7 variables. Then we create a dataset with 6 variables from x0 to x5, with x6 being the latent variable for x2 and x3."
   ]
  },
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     "start_time": "2021-06-25T06:59:59.059854Z"
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x0</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>x4</th>\n",
       "      <th>x5</th>\n",
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       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>1.505949</td>\n",
       "      <td>2.667827</td>\n",
       "      <td>2.029420</td>\n",
       "      <td>1.463708</td>\n",
       "      <td>0.615387</td>\n",
       "      <td>1.157907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.379130</td>\n",
       "      <td>1.721744</td>\n",
       "      <td>0.965613</td>\n",
       "      <td>0.801952</td>\n",
       "      <td>0.919654</td>\n",
       "      <td>0.957148</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.436825</td>\n",
       "      <td>2.845166</td>\n",
       "      <td>2.773506</td>\n",
       "      <td>2.533417</td>\n",
       "      <td>-0.616746</td>\n",
       "      <td>0.903326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.562885</td>\n",
       "      <td>2.205270</td>\n",
       "      <td>1.080121</td>\n",
       "      <td>1.192257</td>\n",
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       "      <td>2.974182</td>\n",
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       "      <td>1.886342</td>\n",
       "      <td>0.451992</td>\n",
       "      <td>1.770786</td>\n",
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       "  </tbody>\n",
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       "         x0        x1        x2        x3        x4        x5\n",
       "0  1.505949  2.667827  2.029420  1.463708  0.615387  1.157907\n",
       "1  1.379130  1.721744  0.965613  0.801952  0.919654  0.957148\n",
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       "3  1.562885  2.205270  1.080121  1.192257  1.240595  1.411295\n",
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   "source": [
    "np.random.seed(1000)\n",
    "\n",
    "x6 = np.random.uniform(size=1000)\n",
    "x3 = 2.0*x6 + np.random.uniform(size=1000)\n",
    "x0 = 0.5*x3 + np.random.uniform(size=1000)\n",
    "x2 = 2.0*x6 + np.random.uniform(size=1000)\n",
    "x1 = 0.5*x0 + 0.5*x2 + np.random.uniform(size=1000)\n",
    "x5 = 0.5*x0 + np.random.uniform(size=1000)\n",
    "x4 = 0.5*x0 - 0.5*x2 + np.random.uniform(size=1000)\n",
    "\n",
    "# The latent variable x6 is not included.\n",
    "X = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5]).T, columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5'])\n",
    "\n",
    "X.head()"
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   "source": [
    "## Causal Discovery by HSIC"
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    "model = lingam.BottomUpParceLiNGAM(independence='hsic')\n",
    "model.fit(X)\n",
    "dot = make_dot(model.adjacency_matrix_)\n",
    "display(dot)"
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    "## Causal Discovery by F-correlation"
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   "source": [
    "for ind_corr in np.linspace(0.15, 0.05, 11):\n",
    "    display(Markdown(f\"### threshold={ind_corr:.2f}\"))\n",
    "    model = lingam.BottomUpParceLiNGAM(independence='fcorr', ind_corr=ind_corr)\n",
    "    model.fit(X)\n",
    "    dot = make_dot(model.adjacency_matrix_)\n",
    "    display(dot)"
   ]
  },
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   "source": []
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