examples/CAMUV_f-correlation.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CAM-UV | Comparison of HSIC and F-correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import lingam\n",
    "from lingam.utils import print_causal_directions, print_dagc, make_dot\n",
    "\n",
    "from IPython.display import display, Markdown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_noise(n):\n",
    "    noise = ((np.random.rand(1, n)-0.5)*5).reshape(n)\n",
    "    mean = get_random_constant(0.0,2.0)\n",
    "    noise += mean\n",
    "    return noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def causal_func(cause):\n",
    "    a = get_random_constant(-5.0,5.0)\n",
    "    b = get_random_constant(-1.0,1.0)\n",
    "    c = int(random.uniform(2,3))\n",
    "    return ((cause+a)**(c))+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_random_constant(s,b):\n",
    "    constant = random.uniform(-1.0, 1.0)\n",
    "    if constant>0:\n",
    "        constant = random.uniform(s, b)\n",
    "    else:\n",
    "        constant = random.uniform(-b, -s)\n",
    "    return constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_data(n):\n",
    "    causal_pairs = [[0,1],[0,3],[2,4]]\n",
    "    intermediate_pairs = [[2,5]]\n",
    "    confounder_pairs = [[3,4]]\n",
    "\n",
    "    n_variables = 6\n",
    "\n",
    "    data = np.zeros((n, n_variables)) # observed data\n",
    "    confounders = np.zeros((n, len(confounder_pairs))) # data of unobserced common causes\n",
    "\n",
    "    # Adding external effects\n",
    "    for i in range(n_variables):\n",
    "        data[:,i] = get_noise(n)\n",
    "    for i in range(len(confounder_pairs)):\n",
    "        confounders[:,i] = get_noise(n)\n",
    "        confounders[:,i] = confounders[:,i] / np.std(confounders[:,i])\n",
    "\n",
    "    # Adding the effects of unobserved common causes\n",
    "    for i, cpair in enumerate(confounder_pairs):\n",
    "        cpair = list(cpair)\n",
    "        cpair.sort()\n",
    "        data[:,cpair[0]] += causal_func(confounders[:,i])\n",
    "        data[:,cpair[1]] += causal_func(confounders[:,i])\n",
    "\n",
    "    for i1 in range(n_variables)[0:n_variables]:\n",
    "        data[:,i1] = data[:,i1] / np.std(data[:,i1])\n",
    "        for i2 in range(n_variables)[i1+1:n_variables+1]:\n",
    "            # Adding direct effects between observed variables\n",
    "            if [i1, i2] in causal_pairs:\n",
    "                data[:,i2] += causal_func(data[:,i1])\n",
    "            # Adding undirected effects between observed variables mediated through unobserved variables\n",
    "            if [i1, i2] in intermediate_pairs:\n",
    "                interm = causal_func(data[:,i1])+get_noise(n)\n",
    "                interm = interm / np.std(interm)\n",
    "                data[:,i2] += causal_func(interm)\n",
    "    \n",
    "    return data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note that the sample size set below is $n=2000$. Please reduce the sample size if the execution time is too long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_size = 2000\n",
    "X = create_data(sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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    "m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "              [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
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    "\n",
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Discovery by HSIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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   "source": [
    "model = lingam.CAMUV()\n",
    "model.fit(X)\n",
    "dot = make_dot(model.adjacency_matrix_)\n",
    "display(dot)"
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  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal Discovery by F-correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### F-correlation threshold=0.7"
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       "### F-correlation threshold=0.6"
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       "### F-correlation threshold=0.2"
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    "for ind_corr in np.linspace(0.7, 0.1, 7):\n",
    "    display(Markdown(f\"### F-correlation threshold={ind_corr:.1f}\"))\n",
    "    model = lingam.CAMUV(independence='fcorr', ind_corr=ind_corr)\n",
    "    model.fit(X)\n",
    "    dot = make_dot(model.adjacency_matrix_)\n",
    "    display(dot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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