1_Intervention_in_2D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "76bc83dc-72d6-471e-be74-252a257c6a65",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90e2880e-3dca-4a46-81e6-8384346895c5",
   "metadata": {},
   "source": [
    "# Original Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4606cc95-4fce-4e95-8a96-ed47d9ba6a20",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f6b050ef-eaef-4993-ae3d-206f5a93151d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x01 = np.linspace(0, 10, N)\n",
    "x02 = x01 + 2 * x01\n",
    "y0 = x01**2 + x02"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "292c80fb-0ba6-48d6-bee6-41370cdb8a5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x01, y0, 'k.')\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a7075054-b563-468a-9876-81eab14f9354",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x02, y0, 'k.')\n",
    "plt.xlabel(\"x2\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d6e5e822-6c0a-4b6e-b7fe-ce59559da296",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x01, x02, 'k.')\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3a55090-b99b-4980-92ed-a2fe297db360",
   "metadata": {},
   "source": [
    "So, there is a path x1 -- x2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "717a547c-46c1-40b0-8496-53cd929db54a",
   "metadata": {},
   "source": [
    "# do(x2 = a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "35d3b0aa-41ff-4159-828e-1e13e87a8c17",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "05a3e630-329f-4705-8ab2-4342094d2096",
   "metadata": {},
   "outputs": [],
   "source": [
    "x11 = x01\n",
    "x12 = [a] * N\n",
    "y1 = x11**2 + x12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "33c2adb9-d7e0-43b0-a4ef-24a15743f6b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x01, y1, 'r.', label = 'do(x2 = a)')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87effa40-0e7f-4620-a14d-78f3ceb57bb0",
   "metadata": {},
   "source": [
    "Since x1 ~ y, the path direction is x1 --> x2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362f7f90-06fc-4e38-97ce-0517997a8ffa",
   "metadata": {},
   "source": [
    "# do(x1 = a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "aaabc161-8135-4b94-89d0-04f1c911b645",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 15\n",
    "x21 = a * np.ones(N)\n",
    "x22 = x21 + 2 * x21 \n",
    "y2 = x21**2 + x22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4d270c10-bdc8-47ab-bfd7-de4f23eb1f29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEGCAYAAACKB4k+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAAU9ElEQVR4nO3df5BdZZ3n8feX/JgEwo8MNC7SYRtHoGLGmEiL/DAhIqysrrJoOYSqgUQs2KGYWYIU7oIzClNkUQpwtsranUKhCi1+GCU66C7lgpUgSIB0oAmGHkyUCD2kQiAoWBJCwnf/uCePl6Q7dNJ9cnPT71dVV+59zjnP/T596P7wPOfc25GZSJIEsF+rC5Ak7T0MBUlSYShIkgpDQZJUGAqSpGJsqwsYjsMOOyy7urpaXYYktZUVK1a8lJkdA21r61Do6uqip6en1WVIUluJiN8Ots3lI0lSYShIkgpDQZJUtPU1BUnt7c0336S/v59Nmza1upR90oQJE+js7GTcuHFDPsZQkNQy/f39HHjggXR1dRERrS5nn5KZvPzyy/T393P00UcP+TiXjyS1zKZNmzj00EMNhBpEBIceeuguz8IMBUktZSDUZ3e+t4aCJKkwFCRJhaEgSZWrr76aG2644R33W7BgAT//+c93us+Xv/xlpkyZwqRJk0aqvEHNnTuX1atXj0hfhoKktrLs+WVc9+B1LHt+WUtef+PGjTzyyCPMnj17p/t96lOf4rHHHtsjNV188cVcf/31I9KXoSCpbSx7fhkf+87H+Icl/8DHvvOxEQmGhQsXctxxx3H66afzzDPPlPbe3l5OPPFEpk+fztlnn80rr7wCwA9+8APOPPNMAH7/+99z3HHHlePOPfdcvvWtbwFw4okncsQRRwy7vmYXX3wx3d3dTJs2ja9+9aulfdasWdx///1s2bJl2K9hKEhqG0vXLmXz1s1sza1s3rqZpWuXDqu/FStWcNddd/HEE0+wePFili9fXradf/75fP3rX2flypW8//3v55prrgHgF7/4BccffzwABx98MN/85jeZP38+d911F6+88goXXnjhkF9/yZIlzJgxY4evk08+ecD9Fy5cSE9PDytXruSBBx5g5cqVAOy33368973v5cknn9zdb0Xhm9cktY05XXMYP2Y8m7duZvyY8czpmjOs/h588EHOPvts9t9/fwA+/elPA40ZwO9+9ztOPfVUAObNm8fnPvc5ANatW0dHx58+dfqMM87g+9//Ppdccsku/1L+6Ec/Sm9v75D3X7RoETfffDNbtmxh3bp1PP3000yfPh2Aww8/nBdeeKEE1u4yFCS1jZOmnMTPzv8ZS9cuZU7XHE6actKw+9zVe/knTpz4tjeEvfXWW/T19TFx4kQ2btxIZ2fnkPtasmQJl1122Q7t+++/Pw8//PDb2p599lluuOEGli9fzuTJk5k/f/7b6ti0aRMTJ07cpbEMxOUjSW3lpCknceWsK0ckEGbPns0Pf/hDXn/9dV577TV+/OMfA41locmTJ/Pggw8C8N3vfrfMGqZOncqaNWtKH9/4xjeYOnUqd955JxdccAFvvvnmkF9/20xh+6/tAwHg1Vdf5YADDuDggw9m/fr13HvvvW/b/qtf/Ypp06bt8vdge4aCpFHrgx/8IOeccw4zZszgs5/9LLNmzSrbbrvtNq644gqmT59Ob28vX/nKVwD45Cc/ydKlS4HGL+Jvf/vb3HjjjcyaNYvZs2dz7bXXAvClL32Jzs5O/vjHP9LZ2cnVV189rFo/8IEPMHPmTKZNm8YFF1zAKaecUratX7+eiRMnjsiF7cjMYXfSKt3d3elfXpPaV19fH1OnTm11GbvsIx/5CD/5yU845JBDWl0K0JitHHTQQXzhC1/YYdtA3+OIWJGZ3QP15UxBknbRjTfeyHPPPdfqMopDDjmEefPmjUhfXmiW1FKZ2XYfivfhD3+41SW8zec///kB23dnJciZgqSWmTBhAi+//PJu/fLSzm37ewoTJkzYpeOcKUhqmc7OTvr7+9mwYUOrS9knbfvLa7vCUJDUMuPGjdulvwqm+rl8JEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJRW2hEBFTImJJRPRFxKqIuLRqnxERj0REb0T0RMQJTcdcGRFrIuKZiPh4XbVJkgZW5zuatwCXZ+bjEXEgsCIi7gOuB67JzHsj4hPV8zkR8T5gLjANeDdwf0Qcm5lba6xRktSktplCZq7LzMerx68BfcCRQAIHVbsdDLxQPT4LuCsz38jMZ4E1wAlIkvaYPfLZRxHRBcwEHgUWAD+NiBtohNLJ1W5HAo80HdZftW3f10XARQBHHXVUbTVL0mhU+4XmiJgE3A0syMxXgYuByzJzCnAZcMu2XQc4fIfP083MmzOzOzO7Ozo66ipbkkalWkMhIsbRCITbM3Nx1TwP2Pb4+/xpiagfmNJ0eCd/WlqSJO0Bdd59FDRmAX2ZeVPTpheAU6vHpwGrq8f3AHMj4s8i4mjgGOCxuuqTJO2ozmsKpwDnAU9FRG/VdhVwIfA/I2IssInq+kBmroqIRcDTNO5cusQ7jyRpz6otFDLzIQa+TgBw/CDHLAQW1lWTJGnnfEezJKkwFCRJhaEgSSoMBUlSYShIkgpDQZJUGAqSpMJQkCQVhoIkqTAUJEmFoSBJKgwFSVJhKEiSCkNBklQYCpKkwlCQJBWGgiSpMBQkSYWhIEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJhaEgSSpqC4WImBIRSyKiLyJWRcSlVfv3IqK3+lobEb1Ve1dEvN607Z/rqk2SNLCxNfa9Bbg8Mx+PiAOBFRFxX2aes22HiLgR+H3TMb/OzBk11iRJ2onaQiEz1wHrqsevRUQfcCTwNEBEBPBXwGl11SBJ2jV75JpCRHQBM4FHm5pnAeszc3VT29ER8UREPBARswbp66KI6ImIng0bNtRXtCSNQrWHQkRMAu4GFmTmq02bzgXubHq+DjgqM2cCXwTuiIiDtu8vM2/OzO7M7O7o6KizdEkadWoNhYgYRyMQbs/MxU3tY4HPAN/b1paZb2Tmy9XjFcCvgWPrrE+S9HZ13n0UwC1AX2betN3m04F/zcz+pv07ImJM9fg9wDHAb+qqT5K0ozpnCqcA5wGnNd1m+olq21zevnQEMBtYGRFPAj8A/iYzN9ZYnyRpO3XeffQQEINsmz9A2900lpokSS3iO5olSYWhIEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJhaEgSSoMBUlSYShIkgpDQZJUGAqSpMJQkCQVhoIkqTAUJEmFoSBJKgwFSVJhKEiSCkNBklQYCpKkwlCQJBWGgiSpMBQkSYWhIEkqDAVJUmEoSJKK2kIhIqZExJKI6IuIVRFxadX+vYjorb7WRkRv0zFXRsSaiHgmIj5eV22SpIHVOVPYAlyemVOBE4FLIuJ9mXlOZs7IzBnA3cBigIh4HzAXmAacCfyviBhTV3HLnl/GdQ9ex7Lnl43IfvY5sn3ua+OxT/tsRZ+7JTN3+gX8LTD5nfYbQj//ApzR9DyA54FjqudXAlc2bf8pcNLO+jz++ONzdzz83MM58dqJOeaaMTnx2on58HMPD2s/+xzZPve18dinfbaiz50BenKQ36tDmSn8O2B5RCyKiDMjInY1eCKiC5gJPNrUPAtYn5mrq+dHViGxTX/Vtn1fF0VET0T0bNiwYVdLAWDp2qVs3rqZrbmVzVs3s3Tt0mHtZ58j2+e+Nh77tM9W9Lm73jEUMvPvgWOAW4D5wOqI+B8R8RdDeYGImERjmWhBZr7atOlc4M7mXQd6+QHquTkzuzOzu6OjYygl7GBO1xzGjxnPmBjD+DHjmdM1Z1j72efI9rmvjcc+7bMVfe6uaMwkhrBjxAeAz9NY719C4zrBfZn5pZ0cMw74CfDTzLypqX0s8G/A8ZnZX7VdCZCZ11XPfwpcnZmDLpp1d3dnT0/PkOrf3rLnl7F07VLmdM3hpCknDXs/+xzZPve18dinfbaiz8FExIrM7B5w2zuFQkT8V2Ae8BLwbeBHmflmROwHrM7MAWcM1TLTbcDGzFyw3bYzaVw/OLWpbRpwB3AC8G7gZzSuN2wdrLbhhIIkjVY7C4WxQzj+MOAzmfnb5sbMfCsi/tNOjjsFOA94qum206sy8//SuMuoeemIzFwVEYuAp2ncuXTJzgJBkjTyhrx8tDdypiBJu25nMwXf0SxJKgwFSVJhKEiSCkNBklQYCpKkwlCQJBWGgiSpMBQkSYWhIEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJhaEgSSoMBUlSYShIkgpDQZJUGAqSpMJQkCQVhoIkqTAUJEmFoSBJKgwFSVJhKEiSCkNBklTUFgoRMSUilkREX0SsiohLm7b9XUQ8U7VfX7V1RcTrEdFbff1zXbVJkgY2tsa+twCXZ+bjEXEgsCIi7gPeBZwFTM/MNyLi8KZjfp2ZM2qsSZK0E7WFQmauA9ZVj1+LiD7gSOBC4GuZ+Ua17cW6apAk7Zo9ck0hIrqAmcCjwLHArIh4NCIeiIgPNe16dEQ8UbXPGqSviyKiJyJ6NmzYUH/xkjSK1B4KETEJuBtYkJmv0pidTAZOBK4AFkVE0JhVHJWZM4EvAndExEHb95eZN2dmd2Z2d3R01F2+JI0qtYZCRIyjEQi3Z+biqrkfWJwNjwFvAYdl5huZ+TJAZq4Afk1jViFJ2kPqvPsogFuAvsy8qWnTj4DTqn2OBcYDL0VER0SMqdrfAxwD/Kau+iRJO6rz7qNTgPOApyKit2q7CrgVuDUifglsBuZlZkbEbOAfI2ILsBX4m8zcWGN9kqTt1Hn30UNADLL5rwfY/24aS02SpBbxHc2SpMJQkCQVhoIkqTAUJEmFoSBJKgwFSVJhKEiSCkNBklQYCpKkwlCQJBWGgiSpMBQkSYWhIEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJhaEgSSoMBUlSYShIkgpDQZJUGAqSpMJQkCQVhoIkqagtFCJiSkQsiYi+iFgVEZc2bfu7iHimar++qf3KiFhTbft4XbVJkgY2tsa+twCXZ+bjEXEgsCIi7gPeBZwFTM/MNyLicICIeB8wF5gGvBu4PyKOzcytNdYoSWpS20whM9dl5uPV49eAPuBI4GLga5n5RrXtxeqQs4C7MvONzHwWWAOcUFd9kqQd7ZFrChHRBcwEHgWOBWZFxKMR8UBEfKja7Ujg+abD+qu27fu6KCJ6IqJnw4YNNVcuSaNL7aEQEZOAu4EFmfkqjSWrycCJwBXAoogIIAY4PHdoyLw5M7szs7ujo6PGyiVp9Kk1FCJiHI1AuD0zF1fN/cDibHgMeAs4rGqf0nR4J/BCnfVJkt6uzruPArgF6MvMm5o2/Qg4rdrnWGA88BJwDzA3Iv4sIo4GjgEeq6s+SdKO6rz76BTgPOCpiOit2q4CbgVujYhfApuBeZmZwKqIWAQ8TePOpUu880iS9qzaQiEzH2Lg6wQAfz3IMQuBhXXVJEnaOd/RLEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFYaCJKkwFCRJhaEgSSoMBUlSYShIkgpDQZJUGAqSpMJQkCQVhoIkqTAUJEmFoSBJKgwFSVJhKEiSCkNBklQYCpKkwlCQJBWGgiSpMBQkSYWhIEkqDAVJUmEoSJIKQ0GSVBgKkqTCUJAkFZGZra5ht0XEBuC3w+jiMOClESqnlfaVcYBj2RvtK+MAx7LNv8/MjoE2tHUoDFdE9GRmd6vrGK59ZRzgWPZG+8o4wLEMhctHkqTCUJAkFaM9FG5udQEjZF8ZBziWvdG+Mg5wLO9oVF9TkCS93WifKUiSmhgKkqRiVIZCRJwZEc9ExJqI+O+trmc4ImJtRDwVEb0R0dPqenZFRNwaES9GxC+b2v48Iu6LiNXVv5NbWeNQDDKOqyPi36rz0hsRn2hljUMVEVMiYklE9EXEqoi4tGpvx/My2Fja6txExISIeCwinqzGcU3VXss5GXXXFCJiDPAr4AygH1gOnJuZT7e0sN0UEWuB7sxsuzfkRMRs4A/AdzLzL6u264GNmfm1KrAnZ+Z/a2Wd72SQcVwN/CEzb2hlbbsqIo4AjsjMxyPiQGAF8J+B+bTfeRlsLH9FG52biAjggMz8Q0SMAx4CLgU+Qw3nZDTOFE4A1mTmbzJzM3AXcFaLaxqVMvPnwMbtms8Cbqse30bjh3ivNsg42lJmrsvMx6vHrwF9wJG053kZbCxtJRv+UD0dV30lNZ2T0RgKRwLPNz3vpw3/Q2mSwP+LiBURcVGrixkB78rMddD4oQYOb3E9w/G3EbGyWl7a65dbthcRXcBM4FHa/LxsNxZos3MTEWMiohd4EbgvM2s7J6MxFGKAtnZeQzslMz8I/EfgkmopQ633v4G/AGYA64AbW1rNLoqIScDdwILMfLXV9QzHAGNpu3OTmVszcwbQCZwQEX9Z12uNxlDoB6Y0Pe8EXmhRLcOWmS9U/74I/JDG8lg7W1+tBW9bE36xxfXslsxcX/0gvwV8izY6L9W69d3A7Zm5uGpuy/My0Fja+dxk5u+ApcCZ1HRORmMoLAeOiYijI2I8MBe4p8U17ZaIOKC6gEZEHAD8B+CXOz9qr3cPMK96PA/4lxbWstu2/bBWzqZNzkt1UfMWoC8zb2ra1HbnZbCxtNu5iYiOiDikejwROB34V2o6J6Pu7iOA6ha0fwLGALdm5sLWVrR7IuI9NGYHAGOBO9ppLBFxJzCHxkcArwe+CvwIWAQcBTwHfC4z9+qLuIOMYw6N5YkE1gL/Zdv6794sIj4CPAg8BbxVNV9FYy2+3c7LYGM5lzY6NxExncaF5DE0/kd+UWb+Y0QcSg3nZFSGgiRpYKNx+UiSNAhDQZJUGAqSpMJQkCQVhoIkqTAUpBpExIyIWFZ9quXKiDin1TVJQ+EtqVINIuJYGp9ltjoi3k3jEzqnVu9IlfZazhSkYYqID1WzgQnVu8xXAeMzczWUjyJ5EehoaaHSEDhTkEZARFwLTAAmAv2ZeV3TthNovCN1WvV5O9Jey1CQRkD1OVrLgU3AyZm5tWo/gsYHmM3LzEdaV6E0NC4fSSPjz4FJwIE0ZgxExEHA/wH+3kBQu3CmII2AiLiHxl/xOxo4AvgicC/w48z8pxaWJu2Ssa0uQGp3EXE+sCUz76j+BvjDND6SfTZwaETMr3adn5m9ralSGhpnCpKkwmsKkqTCUJAkFYaCJKkwFCRJhaEgSSoMBUlSYShIkor/Dxl9WQxTUbszAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x02, y2, 'g.', label = 'do(x1 = a)')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"x2\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1f00af0-b5b0-45f9-8819-33f071c889ae",
   "metadata": {},
   "source": [
    "Since y || x2, the path is x1 --> x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bfe75eda-aadf-4b89-80ee-1f37fa3436de",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}