statistics_concepts.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy.stats import norm\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concept 1 - Why is CDF uniformly distributed?\n",
    "\n",
    "CDF of any continuous random variable follows a standard uniform distribution.\n",
    "\n",
    "The proof is as follows:\n",
    "$$\n",
    "\\begin{gathered}\n",
    "F_{Y}(y)=P(Y \\leq y) \\\\\n",
    "F_{Y}(y)=P(F_{X}(x) \\leq y) \\\\\n",
    "F_{Y}(y)=P\\left(X \\leq F^{-1}_{X}(y)\\right) \\\\\n",
    "F_{Y}(y)=F_{X}\\left(F^{-1}_{X}(y)\\right) \\\\\n",
    "F_{Y}(y)=y\n",
    "\\end{gathered}\n",
    "$$\n",
    "\n",
    "The last equation is property of uniform distribution.\n",
    "$$\n",
    "Y \\sim U(0, 1)\n",
    "$$\n",
    "\n",
    "Here we will test with normal distribution but you can try any other continuous distribution as well and it should work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pdf(x, mu, sigma):\n",
    "    z = (x - mu) / sigma\n",
    "    prob = 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-z**2 / 2)\n",
    "    return prob \n",
    "\n",
    "def get_cdf(data, n_pts):\n",
    "    cdf = []\n",
    "    X = np.linspace(0,1,n_pts)\n",
    "    for x in X:\n",
    "        percentile = np.sum(data<x) / len(data)\n",
    "        cdf.append(percentile)\n",
    "    return cdf    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_pts = 10000\n",
    "data = np.random.normal(size=(n_pts,))\n",
    "probs = list(map(lambda x: pdf(x, 0, 1), data))\n",
    "cdf = get_cdf(data, n_pts)\n",
    "\n",
    "plt.scatter(data, probs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(cdf)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concept 2 - How to sample random variables from a distribution?\n",
    "\n",
    "We can use the above result to sample numbers from any continuous distribution. For example, given `mu` and `sigma`, if you want to generate normally distributed samples, you can calculate the inverse of CDF and use it. \n",
    "\n",
    "Note that $X$ is a random variable parametrized by $x$, which is a value that $X$ takes.\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "z=\\frac{x-\\mu}{\\sigma} \\\\\n",
    "\\phi_{Z}(z)=y=P_{Y}(y) \\\\\n",
    "z=\\phi_{Z}^{-1}(y) \\\\\n",
    "x=\\sigma * \\phi_{Z}^{-1}(y)+\\mu \n",
    "\\end{gathered}\n",
    "$$\n",
    "\n",
    "Now, as we know that $Y$ follows a standard uniform distribution, we can generate uniformly distributed random numbers and substitute for $y$ in the below equation to get normally distributed samples $x$ for random variable $X$.\n",
    "\n",
    "$$\n",
    "x=\\sigma * \\phi^{-1}(U_{Y}(y))+\\mu\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_norm_samples(mu, sigma, n_pts):\n",
    "    data = np.random.uniform(size=(n_pts,))\n",
    "    X = list(map(lambda x: sigma * norm.ppf(x) + mu, data))\n",
    "    return X\n",
    "\n",
    "n_pts = 1000\n",
    "mu = 50\n",
    "sigma = 1000\n",
    "X = generate_norm_samples(mu, sigma, n_pts)    \n",
    "sns.displot(X)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same procedure can be used to generate samples for any distribution. Let’s consider another example of generating samples for **exponential distribution**.\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "f(x)=\\lambda e^{-\\lambda x} \\\\\n",
    "F_{X}(x)=1-e^{-\\lambda x} \\\\\n",
    "-\\lambda x=\\log \\left(1-F_{X}(x)\\right) \\\\\n",
    "x=\\frac{- \\log \\left(1-F_{x}(x)\\right)}{\\lambda}\n",
    "\\end{gathered}\n",
    "$$\n",
    "\n",
    "Since $F_{X}(x)$ follows uniform distribution,\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "x=\\frac{- \\log \\left(1-U_{Y}(y)\\right)}{\\lambda}\n",
    "\\end{gathered}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_exp_samples(n_pts, lamda):\n",
    "    U = np.random.uniform(size=(n_pts,))\n",
    "    X = -np.log(1 - U) / lamda\n",
    "    return X\n",
    "\n",
    "lamda = 0.2 \n",
    "X = generate_exp_samples(n_pts, lamda)\n",
    "sns.displot(X)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Concept 3: Law of Large Numbers (LLN)\n",
    "\n",
    "According to **Law of Large Numbers (LLN)**, if you conduct an experiment a number of times and compute a measure, the average of sample measures should be close to population measure. \n",
    "\n",
    "For an example, assume we want to find the centroid of a large number of points. However, we do not have enough computing power and memory to do it. So, instead of computing mean of entire data, we compute mean of a large number of bootsrapped samples and take their expectation. \n",
    "\n",
    "The expected value should get closer to the actual mean of all points and the variance of sample mean should decrease as more trials are performed.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([49.96598, 50.02411, 49.82545])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# population size\n",
    "N = 100000 \n",
    "# max value\n",
    "max_value = 100\n",
    "\n",
    "X=np.random.choice(np.arange(1,max_value), N, replace=True)\n",
    "Y=np.random.choice(np.arange(1,max_value), N, replace=True)\n",
    "Z=np.random.choice(np.arange(1,max_value), N, replace=True)\n",
    "\n",
    "data=np.array([X,Y,Z]).transpose()\n",
    "population_mean = np.mean(data,axis=0)\n",
    "population_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sample_measure(data, sample_size):\n",
    "    return np.mean(np.random.choice(data, sample_size, replace=True))\n",
    "\n",
    "def get_sampling_dist(data, sample_size, n_iters):\n",
    "    return np.array(list(map(lambda x: get_sample_measure(data, sample_size), range(n_iters))))\n",
    "\n",
    "def get_mean_var(sample):\n",
    "    mean = np.mean(sample)\n",
    "    var = np.var(sample)\n",
    "    return mean, var\n",
    "\n",
    "def get_expected_value(data, sample_size, n_iters):\n",
    "    X = data[:,0]\n",
    "    Y = data[:,1]\n",
    "    Z = data[:,2]\n",
    "\n",
    "    sample_x = get_sampling_dist(X, sample_size, n_iters)\n",
    "    sample_y = get_sampling_dist(Y, sample_size, n_iters)\n",
    "    sample_z = get_sampling_dist(Z, sample_size, n_iters)\n",
    "\n",
    "    mean_x, var_x = get_mean_var(sample_x)\n",
    "    mean_y, var_y = get_mean_var(sample_y)\n",
    "    mean_z, var_z = get_mean_var(sample_z)\n",
    "\n",
    "    exp_value = np.array([mean_x, mean_y, mean_z])\n",
    "    total_var = (var_x + var_y + var_z) / n_iters\n",
    "    return exp_value, total_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [01:27<00:00,  2.28it/s]\n"
     ]
    }
   ],
   "source": [
    "# sample size\n",
    "sample_size_pct = 0.1\n",
    "sample_size = int(sample_size_pct * N) \n",
    "\n",
    "L2_norm = []\n",
    "total_vars = []\n",
    "for n_iters in tqdm(range(10, 2000, 10)):\n",
    "    exp_value, total_var = get_expected_value(data, sample_size, n_iters)\n",
    "    l2_norm = np.linalg.norm(population_mean - exp_value)\n",
    "    L2_norm.append(l2_norm)\n",
    "    total_vars.append(total_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "plt.subplot(121)\n",
    "plt.plot(L2_norm)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(total_vars)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Observations:\n",
    "1. We see than the deviation between sample mean and population mean decreases with increasing number of trials\n",
    "2. We see that variance converges with increasing number of trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "951daa5e1959839fcb325fff331f52e72634f7a1be998f6081ed7f433b63f1b3"
  },
  "kernelspec": {
   "display_name": "Python 3.8.11 64-bit ('base': conda)",
   "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": "3.8.11"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}