examples/MultiGroupRCD_f-correlation.ipynb

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  {
   "cell_type": "markdown",
   "id": "4a19bdfc",
   "metadata": {},
   "source": [
    "# MultiGroupRCD | Comparison of HSIC and F-correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97ed724d",
   "metadata": {},
   "source": [
    "## Import and settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9457975",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "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",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e1f0a6e",
   "metadata": {},
   "source": [
    "## Test data\n",
    "We generate two datasets consisting of 6 variables and 1 latent variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0d5f04d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_coef():\n",
    "    coef = random.random()\n",
    "    return coef if coef >= 0.5 else coef - 1.0\n",
    "get_external_effect = lambda n: np.random.normal(0.0, 0.5, n) ** 3"
   ]
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   "execution_count": 3,
   "id": "8d9500f5",
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   "source": [
    "B1 = np.array([[       0.0,        0.0,        0.0,        0.0,        0.0, get_coef(),        0.0],\n",
    "               [       0.0,        0.0,        0.0,        0.0,        0.0, get_coef(),        0.0],\n",
    "               [get_coef(), get_coef(),        0.0,        0.0,        0.0,        0.0,        0.0],\n",
    "               [       0.0,        0.0, get_coef(),        0.0,        0.0,        0.0, get_coef()],\n",
    "               [       0.0,        0.0, get_coef(),        0.0,        0.0,        0.0, get_coef()],\n",
    "               [       0.0,        0.0,        0.0,        0.0,        0.0,        0.0,        0.0],\n",
    "               [       0.0,        0.0,        0.0,        0.0,        0.0,        0.0,        0.0]])\n",
    "\n",
    "samples = 1000\n",
    "x5 = get_external_effect(samples)\n",
    "x6 = get_external_effect(samples)\n",
    "x0 = x5 * B1[0, 5] + get_external_effect(samples)\n",
    "x1 = x5 * B1[1, 5] + get_external_effect(samples)\n",
    "x2 = x0 * B1[2, 0] + x1 * B1[2, 1] + get_external_effect(samples)\n",
    "x3 = x2 * B1[3, 2] + x6 * B1[3, 6] + get_external_effect(samples)\n",
    "x4 = x2 * B1[4, 2] + x6 * B1[4, 6] + get_external_effect(samples)\n",
    "\n",
    "# x5, x6 is a latent variable.\n",
    "X1 = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5'])"
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    "B2 = np.array([[       0.0,        0.0,        0.0,        0.0,        0.0, get_coef(),        0.0],\n",
    "               [       0.0,        0.0,        0.0,        0.0,        0.0, get_coef(),        0.0],\n",
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    "\n",
    "samples = 1000\n",
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    "x6 = get_external_effect(samples)\n",
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    "x1 = x5 * B2[1, 5] + get_external_effect(samples)\n",
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    "x3 = x2 * B2[3, 2] + x6 * B2[3, 6] + get_external_effect(samples)\n",
    "x4 = x2 * B2[4, 2] + x6 * B2[4, 6] + get_external_effect(samples)\n",
    "\n",
    "# x5, x6 is a latent variable.\n",
    "X2 = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5'])"
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     "execution_count": 6,
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   "source": [
    "make_dot(B2, labels=['x0', 'x1', 'x2', 'x3', 'x4', 'x5', 'U'])"
   ]
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  {
   "cell_type": "markdown",
   "id": "3b225e1a",
   "metadata": {},
   "source": [
    "We create a list variable that contains two datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "382b5222",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_list = [X1, X2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ca6382a",
   "metadata": {},
   "source": [
    "## Causal Discovery by HSIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7c26654c",
   "metadata": {},
   "outputs": [
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    "model = lingam.MultiGroupRCD()\n",
    "model.fit(X_list)\n",
    "\n",
    "display(make_dot(model.adjacency_matrices_[0]))"
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   "cell_type": "code",
   "execution_count": 9,
   "id": "5ffac66b-b7ac-4fae-b96c-d3149558a555",
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    "model = lingam.MultiGroupRCD()\n",
    "model.fit(X_list)\n",
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   "source": [
    "## Causal Discovery by F-correlation"
   ]
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       "### F-correlation threshold=0.7"
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   "source": [
    "for ind_corr in np.linspace(0.7, 0.2, 6):\n",
    "    display(Markdown(f\"### F-correlation threshold={ind_corr:.1f}\"))\n",
    "    model = lingam.MultiGroupRCD(independence='fcorr', ind_corr=ind_corr)\n",
    "    model.fit(X_list)\n",
    "    display(make_dot(model.adjacency_matrices_[0]))"
   ]
  },
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   "cell_type": "code",
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   "id": "fd800950-bbe6-4a3d-9d94-6d00ad82395a",
   "metadata": {},
   "outputs": [],
   "source": []
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