Chapter_02.ipynb

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     ]
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   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install numpy\n",
    "!{sys.executable} -m pip install scipy\n",
    "!{sys.executable} -m pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d885824b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a2494ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "COLORS = [\n",
    "    '#00B0F0',\n",
    "    '#FF0000'\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0fd06fd",
   "metadata": {},
   "source": [
    "# Chapter 02\n",
    "\n",
    "This chapter introduces the concept of “the ladder of causation”. We focus on highlighting differences between three main concepts: associations, interventions and counterfactuals. We provide the reader with a couple of thought experiments to strengthen the understanding of these concepts and implement these experiments in Python. Finally, we demonstrate how counterfactuals can be used for model prediction explanations (e.g. in finance)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6c49b0c",
   "metadata": {},
   "source": [
    "## Association"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2be8da82",
   "metadata": {},
   "source": [
    "### Bookstore example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b47b8b1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "xx = stats.uniform()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aa115ac1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.40356048, 0.7976445 , 0.824071  , 0.80100555, 0.34749881])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx.rvs(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "053921a7",
   "metadata": {},
   "source": [
    "Normal Distribution is a probability distribution where probability of x is highest at centre and lowest in the ends whereas in Uniform Distribution probability of x is constant.\n",
    "\n",
    "\n",
    "![image info](./img/distributions.jpeg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7f5e9d21",
   "metadata": {},
   "outputs": [],
   "source": [
    "# First, we'll build a structural causal model (SCM)\n",
    "class BookSCM:\n",
    "    \n",
    "    def __init__(self, random_seed=None):\n",
    "        self.random_seed = random_seed\n",
    "        self.u_0 = stats.uniform()\n",
    "        self.u_1 = stats.norm()\n",
    "        \n",
    "    def sample(self, sample_size=100):\n",
    "        \"\"\"Samples from the SCM\"\"\"\n",
    "        if self.random_seed:\n",
    "            np.random.seed(self.random_seed)\n",
    "        \n",
    "        # Generate random variates of given size\n",
    "        u_0 = self.u_0.rvs(sample_size)\n",
    "        u_1 = self.u_1.rvs(sample_size)\n",
    "        a = u_0 > .61\n",
    "        b = (a + .5 * u_1) > .2\n",
    "        \n",
    "        return a, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5e1ea2e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's initialize our SCM\n",
    "scm = BookSCM(random_seed=45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fbf25307",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ...and sample from it\n",
    "buy_book_a, buy_book_b = scm.sample(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9a42fd00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100,), (100,))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sanity check\n",
    "buy_book_a.shape, buy_book_b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9cfaa047",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of buying book A: 0.390\n",
      "Probability of buying book B: 0.580\n",
      "Probability of buying book A given B: 0.638\n",
      "Probability of buying book B given A: 0.949\n"
     ]
    }
   ],
   "source": [
    "# Let's compute probabilities\n",
    "proba_book_a = buy_book_a.sum() / buy_book_a.shape[0]\n",
    "proba_book_b = buy_book_b.sum() / buy_book_b.shape[0]\n",
    "\n",
    "print(f'Probability of buying book A: {proba_book_a:0.3f}')\n",
    "print(f'Probability of buying book B: {proba_book_b:0.3f}')\n",
    "\n",
    "# ...and conditional probailities\n",
    "proba_book_a_given_book_b = np.where(buy_book_b, buy_book_a, 0).sum() / buy_book_b.sum()\n",
    "proba_book_b_given_book_a = np.where(buy_book_a, buy_book_b, 0).sum() / buy_book_a.sum()\n",
    "\n",
    "print(f'Probability of buying book A given B: {proba_book_a_given_book_b:0.3f}')\n",
    "print(f'Probability of buying book B given A: {proba_book_b_given_book_a:0.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "735d33fe",
   "metadata": {},
   "source": [
    "## Intervention"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "id": "125275ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of B before any intervention: -0.620\n",
      "Variance of B before any intervention: 22.667\n",
      "Correlation between A and B:\n",
      "r = 0.978; p = 0.000\n",
      "\n",
      "Mean of B after the intervention on A: 7.575\n",
      "Variance of B after the intervention on A: 1.003\n",
      "\n",
      "Mean of B after the intervention on B: 0.186\n",
      "Variance of B after the intervention on B: 0.995\n",
      "Correlation between A and B after intervening on B:\n",
      "r = -0.023; p = 0.821\n",
      "\n"
     ]
    }
   ],
   "source": [
    "SAMPLE_SIZE = 100\n",
    "\n",
    "np.random.seed(45)\n",
    "\n",
    "u_0 = np.random.randn(SAMPLE_SIZE)\n",
    "u_1 = np.random.randn(SAMPLE_SIZE)\n",
    "a = u_0\n",
    "b = 5 * a + u_1\n",
    "\n",
    "r, p = stats.pearsonr(a, b)\n",
    "\n",
    "print(f'Mean of B before any intervention: {b.mean():.3f}')\n",
    "print(f'Variance of B before any intervention: {b.var():.3f}')\n",
    "print(f'Correlation between A and B:\\nr = {r:.3f}; p = {p:.3f}\\n')\n",
    "\n",
    "a = np.array([1.5] * SAMPLE_SIZE)\n",
    "b = 5 * a + u_1\n",
    "\n",
    "print(f'Mean of B after the intervention on A: {b.mean():.3f}')\n",
    "print(f'Variance of B after the intervention on A: {b.var():.3f}\\n')\n",
    "\n",
    "a = u_0\n",
    "b = np.random.randn(SAMPLE_SIZE)\n",
    "\n",
    "r, p = stats.pearsonr(a, b)\n",
    "\n",
    "print(f'Mean of B after the intervention on B: {b.mean():.3f}')\n",
    "print(f'Variance of B after the intervention on B: {b.var():.3f}')\n",
    "print(f'Correlation between A and B after intervening on B:\\nr = {r:.3f}; p = {p:.3f}\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d17be2b",
   "metadata": {},
   "source": [
    "## Counterfactuals"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64a2d342",
   "metadata": {},
   "source": [
    "We'll use the following SCM:\n",
    "\n",
    "$$\\large Y := TU + (T-1)(U-1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 494,
   "id": "ac4c9175",
   "metadata": {},
   "outputs": [],
   "source": [
    "class CounterfactualSCM:\n",
    "    \n",
    "    def abduct(self, t, y):\n",
    "        return (t + y - 1)/(2*t - 1)\n",
    "    \n",
    "    def modify(self, t):\n",
    "        return lambda u: t * u + (t - 1) * (u - 1)\n",
    "        \n",
    "    def predict(self, u, t):\n",
    "        return self.modify(t)(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "id": "060be2c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "coffee = CounterfactualSCM()\n",
    "t = 1\n",
    "y = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "id": "b40ca681",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 496,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = coffee.abduct(t=t, y=y)\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "id": "f0d28a6f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 497,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coffee.predict(u=u, t=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90f12e93",
   "metadata": {},
   "source": [
    "## Causation without correlation - plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa7369e",
   "metadata": {},
   "source": [
    "### Non-monotonic case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "9fe93c0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-2, 2, 5000)\n",
    "y = x**2 + 0.2*np.random.randn(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0dcc1649",
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y, alpha=.1)\n",
    "plt.xlabel('$X$', alpha=.5)\n",
    "plt.ylabel('$Y$', alpha=.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "6836fe51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=-0.0008669790541861908, pvalue=0.9562854975187957)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation coefficient\n",
    "stats.spearmanr(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b31a2fb0",
   "metadata": {},
   "source": [
    "### Bad sampling case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "233017fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get initial x\n",
    "x = np.random.uniform(-2, 2, 5000)\n",
    "\n",
    "# Filter samples\n",
    "x = x[np.where((x < -1.9) | (x > 1.9), True, False)]\n",
    "\n",
    "# Get y\n",
    "y = x**2 + 0.2*np.random.randn(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "218c2245",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y, alpha=.1)\n",
    "plt.xlabel('$X$', alpha=.5)\n",
    "plt.ylabel('$Y$', alpha=.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "1f458191",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.011041548093340922, pvalue=0.8618158306305002)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation coefficient\n",
    "stats.spearmanr(x, y)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}