ipm.ipynb

{
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    "<h1> Empirical estimation of IPMs (integral probability metrics)<span class=\"tocSkip\"></span></h1>\n",
    "\n",
    "Author: [Sylvain Combettes](https://github.com/sylvaincom).\n",
    "\n",
    "Last update: Feb 3, 2020.\n",
    "\n",
    "GitHub repository: [here](https://github.com/sylvaincom/comparison-distributions).\n",
    "\n",
    "---\n",
    "This notebook deals with the empirical estimation of IPMs (integral probability metrics) and completes my report on the _Comparison of Empirical Probability Distributions_. As $f$-divergences input probability distributions, IPMs input samples drawn from the probability distributions. Actually, for IPMs, we only focus on the Kantorovich metric.\n",
    "\n",
    "If needed, please take a look at `ipm-prerequisite.ipynb` which introduces the `PuLP` library for solving linear programming problems and gives more details about how our function for computing the Kantorovich metric was built.\n",
    "\n",
    "<br/>\n",
    "\n",
    "<div class=\"alert alert-info\"><h4>README<span class=\"tocSkip\"></span></h4>\n",
    "<p> We recommend reading the report before reading this notebook, as most explanations are not duplicated here.</p>\n",
    "\n",
    "<p>\n",
    "The best way to open this Jupyter Notebook is to use the table of contents from the extensions called <code>nbextensions</code>. See <a href=\"https://towardsdatascience.com/4-awesome-tips-for-enhancing-jupyter-notebooks-4d8905f926c5\">4 Awesome Tips for Enhancing Jupyter Notebooks</a> by George Seif.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "In your current directory:\n",
    "<ul>\n",
    "  <li>create a <code>img</code> folder (in which the generated images will be saved)</li>\n",
    "  <li>create another <code>data</code> folder in move the download the <a href=\"https://github.com/sylvaincom/comparison-distributions/tree/master/data\">data from my GitHub</a> into it</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "The Python version is 3.7.3.\n",
    "</p>\n",
    "</div>"
   ]
  },
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   "metadata": {
    "toc": true
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   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Defining-a-generic-function-for-computing-the-estimate-of-the-Kantorovich-metric-$W$\" data-toc-modified-id=\"Defining-a-generic-function-for-computing-the-estimate-of-the-Kantorovich-metric-$W$-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Defining a generic function for computing the estimate of the Kantorovich metric $W$</a></span><ul class=\"toc-item\"><li><span><a href=\"#Defining-the-generic-function\" data-toc-modified-id=\"Defining-the-generic-function-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Defining the generic function</a></span></li><li><span><a href=\"#The-memory-error-due-to-the-linear-programming-problem\" data-toc-modified-id=\"The-memory-error-due-to-the-linear-programming-problem-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>The memory error due to the linear programming problem</a></span></li></ul></li><li><span><a href=\"#Running-several-simulations-to-interpret-$W$\" data-toc-modified-id=\"Running-several-simulations-to-interpret-$W$-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Running several simulations to interpret $W$</a></span><ul class=\"toc-item\"><li><span><a href=\"#Comparing-two-normal-distributions\" data-toc-modified-id=\"Comparing-two-normal-distributions-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Comparing two normal distributions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Influence-of-the-difference-of-means-$\\mu_q-\\mu_p$-on-$W$\" data-toc-modified-id=\"Influence-of-the-difference-of-means-$\\mu_q-\\mu_p$-on-$W$-2.1.1\"><span class=\"toc-item-num\">2.1.1&nbsp;&nbsp;</span>Influence of the difference of means $\\mu_q-\\mu_p$ on $W$</a></span></li><li><span><a href=\"#Influence-of-the-difference-of-standard-deviations-$\\sigma_q-\\sigma_p$-on-$W$\" data-toc-modified-id=\"Influence-of-the-difference-of-standard-deviations-$\\sigma_q-\\sigma_p$-on-$W$-2.1.2\"><span class=\"toc-item-num\">2.1.2&nbsp;&nbsp;</span>Influence of the difference of standard deviations $\\sigma_q-\\sigma_p$ on $W$</a></span></li><li><span><a href=\"#Influence-of-the-number-of-samples-on-$W$\" data-toc-modified-id=\"Influence-of-the-number-of-samples-on-$W$-2.1.3\"><span class=\"toc-item-num\">2.1.3&nbsp;&nbsp;</span>Influence of the number of samples on $W$</a></span></li></ul></li><li><span><a href=\"#Comparison-of-two-exponential-distributions\" data-toc-modified-id=\"Comparison-of-two-exponential-distributions-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Comparison of two exponential distributions</a></span></li><li><span><a href=\"#Comparison-of-two-uniform-distributions\" data-toc-modified-id=\"Comparison-of-two-uniform-distributions-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Comparison of two uniform distributions</a></span></li></ul></li><li><span><a href=\"#Application-of-the-Kantorovich-metric-to-the-data-generated-from-two-methods-for-computing-the-Choquet-integral\" data-toc-modified-id=\"Application-of-the-Kantorovich-metric-to-the-data-generated-from-two-methods-for-computing-the-Choquet-integral-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Application of the Kantorovich metric to the data generated from two methods for computing the Choquet integral</a></span><ul class=\"toc-item\"><li><span><a href=\"#For-the-Choquet-integral-of-normal-distributions\" data-toc-modified-id=\"For-the-Choquet-integral-of-normal-distributions-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>For the Choquet integral of normal distributions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Presenting-the-data\" data-toc-modified-id=\"Presenting-the-data-3.1.1\"><span class=\"toc-item-num\">3.1.1&nbsp;&nbsp;</span>Presenting the data</a></span></li><li><span><a href=\"#Computing-the-Kantorovich-metric\" data-toc-modified-id=\"Computing-the-Kantorovich-metric-3.1.2\"><span class=\"toc-item-num\">3.1.2&nbsp;&nbsp;</span>Computing the Kantorovich metric</a></span></li></ul></li><li><span><a href=\"#For-the-Choquet-integral-of-exponential-distributions\" data-toc-modified-id=\"For-the-Choquet-integral-of-exponential-distributions-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>For the Choquet integral of exponential distributions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Presenting-the-data\" data-toc-modified-id=\"Presenting-the-data-3.2.1\"><span class=\"toc-item-num\">3.2.1&nbsp;&nbsp;</span>Presenting the data</a></span></li><li><span><a href=\"#Computing-the-Kantorovich-metric\" data-toc-modified-id=\"Computing-the-Kantorovich-metric-3.2.2\"><span class=\"toc-item-num\">3.2.2&nbsp;&nbsp;</span>Computing the Kantorovich metric</a></span></li></ul></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Imports<span class=\"tocSkip\"></span></h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install pulp\n",
    "from pulp import *\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "from time import process_time\n",
    "import datetime\n",
    "\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We configure the size of the plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (8,6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining a generic function for computing the estimate of the Kantorovich metric $W$\n",
    "\n",
    "## Defining the generic function\n",
    "\n",
    "We duplicate the functions created in `ipm-prerequisite.ipynb`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_c(X_p, X_q):\n",
    "    m = len(X_p)\n",
    "    n = len(X_q)\n",
    "    \n",
    "    Y = [1/m]*m + [-1/n]*n\n",
    "    \n",
    "    return np.asarray(Y)\n",
    "\n",
    "\n",
    "def rho(x,y):\n",
    "    return abs(x-y)\n",
    "\n",
    "\n",
    "def construct_b(X_p, X_q):\n",
    "    \n",
    "    X = np.concatenate((X_p, X_q), axis=0)\n",
    "    N = len(X)\n",
    "    \n",
    "    b_part = []\n",
    "    for i in range(N):\n",
    "        for j in range(i+1, N):\n",
    "            b_part.append(rho(X[i], X[j]))\n",
    "    \n",
    "    # Now, we duplicate each row to obtain a list of size 2*N\n",
    "    b = []\n",
    "    for i in range(N):\n",
    "        b.append(b_part[i])\n",
    "        b.append(b_part[i])\n",
    "    \n",
    "    return b\n",
    "\n",
    "\n",
    "def construct_M(X_p, X_q):\n",
    "    \n",
    "    X = np.concatenate((X_p, X_q), axis=0)\n",
    "    N = len(X)\n",
    "    \n",
    "    M = []\n",
    "    for i in range(N):\n",
    "        for j in range(i+1, N):\n",
    "            l_M_1 = [0]*N\n",
    "            l_M_1[i] = 1\n",
    "            l_M_1[j] = -1\n",
    "            M.append(l_M_1)\n",
    "            l_M_2 = [0]*N\n",
    "            l_M_2[i] = -1\n",
    "            l_M_2[j] = 1\n",
    "            M.append(l_M_2)\n",
    "    M = np.asarray(M)\n",
    "\n",
    "    return M.astype(int)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we regroup them under one function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kantorovich_metric(X_p, X_q):\n",
    "    \n",
    "    X = np.concatenate((X_p, X_q), axis=0)\n",
    "    m = len(X_p)\n",
    "    n = len(X_q)\n",
    "    N = m+n\n",
    "    \n",
    "    c = construct_c(X_p, X_q)\n",
    "    b = construct_b(X_p, X_q)\n",
    "    M = construct_M(X_p, X_q)\n",
    "    \n",
    "    prob = LpProblem(\"LP_problem_for_estimating_the_Kantorovich_metric\", LpMaximize)\n",
    "    a = LpVariable.matrix(\"a\", list(range(N)))\n",
    "    prob += lpDot(c, a)\n",
    "    p = 2*N\n",
    "    for i in range(p):\n",
    "        prob += lpDot(M[i], a) <= b[i]\n",
    "    prob.solve()\n",
    "    \n",
    "#     for v in prob.variables():\n",
    "#         print(v.name, \"=\", v.varValue)\n",
    "        \n",
    "#     print(\"objective=\", value(prob.objective))\n",
    "\n",
    "    return value(prob.objective)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we check if we obtain the same result as formula (II.11) of the report:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical Kantorovich metric is: \n",
      " 0.629\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.uniform(0, 1, 10)\n",
    "np.random.seed(2) # random seed for reproducability\n",
    "X_q = np.random.uniform(1/2, 3/2, 10)\n",
    "W = kantorovich_metric(X_p, X_q)\n",
    "print('The empirical Kantorovich metric is: \\n', round(W, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is close to $1/2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The memory error due to the linear programming problem\n",
    "\n",
    "We take the same parameters as previsouly but with more samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical Kantorovich metric is: \n",
      " 0.6291911601\n",
      "The processing time is: \n",
      " 0:00:03.532529\n"
     ]
    }
   ],
   "source": [
    "t_start = process_time()\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.uniform(0, 1, 100)\n",
    "np.random.seed(2) # random seed for reproducability\n",
    "X_q = np.random.uniform(1/2, 3/2, 100)\n",
    "kantorovich_metric(X_p, X_q)\n",
    "t_stop = process_time()\n",
    "print('The empirical Kantorovich metric is: \\n', W)\n",
    "print('The processing time is: \\n', datetime.timedelta(seconds=t_stop-t_start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical Kantorovich metric is: \n",
      " 0.8252509367355002\n",
      "The processing time is: \n",
      " 0:00:18.127270\n"
     ]
    }
   ],
   "source": [
    "t_start = process_time()\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.uniform(0, 1, 200)\n",
    "np.random.seed(2) # random seed for reproducability\n",
    "X_q = np.random.uniform(1/2, 3/2, 200)\n",
    "W = kantorovich_metric(X_p, X_q)\n",
    "t_stop = process_time()\n",
    "print('The empirical Kantorovich metric is: \\n', W)\n",
    "print('The processing time is: \\n', datetime.timedelta(seconds=t_stop-t_start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# t_start = process_time()\n",
    "# np.random.seed(1) # random seed for reproducability\n",
    "# X_p = np.random.uniform(0, 1, 300)\n",
    "# np.random.seed(2) # random seed for reproducability\n",
    "# X_q = np.random.uniform(1/2, 3/2, 300)\n",
    "# W = kantorovich_metric(X_p, X_q)\n",
    "# t_stop = process_time()\n",
    "# print('The empirical Kantorovich metric is: \\n', W)\n",
    "# print('The processing time is: \\n', datetime.timedelta(seconds=t_stop-t_start))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We obtained a memory error for $300$ samples per distribution !\n",
    "\n",
    "The problem is that when we have more than $400$ total samples (for the two distributions), $M$ already has $400 \\times 399 \\times 400 = 63~840~000$ values and we have a memory problem if we go above $400$ total samples. Hence, we can not have more than $200$ samples per distribution.\n",
    "\n",
    "Note that the problem is not really about the computing time (which of course, we could have tried to improve)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running several simulations to interpret $W$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing two normal distributions\n",
    "\n",
    "Here we consider two normal distributions $\\mathbb{P} = \\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathbb{Q} = \\mathcal{N}(\\mu_q, \\sigma_q)$.\n",
    "\n",
    "### Influence of the difference of means $\\mu_q-\\mu_p$ on $W$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_p, sigma_p, n_p, mu_q, sigma_q, n_q = 0, 2, 50, 1, 2, 50\n",
    "np.random.seed(2) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "\n",
    "txt = 'Histograms of $X_p$ and $X_q$ from normal distributions '\n",
    "txt = txt + '$\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'The Kantorovich metric $W(X_p, X_q)$ is %1.3f' % kantorovich_metric(X_p, X_q)\n",
    "plt.title(txt)\n",
    "sns.distplot(X_p) ;\n",
    "sns.distplot(X_q) ;\n",
    "txt1 = '$\\mu_p = %1.1f$, $\\sigma_p = %1.0f$, $n_p= %1.0f$' % (mu_p, sigma_p, n_p)\n",
    "txt2 = '$\\mu_q = %1.1f$, $\\sigma_q = %1.0f$, $n_q= %1.0f$' % (mu_q, sigma_q, n_q)\n",
    "plt.legend([txt1, txt2]) ;\n",
    "plt.savefig('img/IPM_normal_histo_1.png', dpi=120) ; # to save the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_p, sigma_p, n_p, mu_q, sigma_q, n_q = 0, 2, 50, 5, 2, 50\n",
    "np.random.seed(2) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "\n",
    "txt = 'Histograms of $X_p$ and $X_q$ from normal distributions '\n",
    "txt = txt + '$\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'The Kantorovich metric $W(X_p, X_q)$ is %1.3f' % kantorovich_metric(X_p, X_q)\n",
    "plt.title(txt)\n",
    "sns.distplot(X_p) ;\n",
    "sns.distplot(X_q) ;\n",
    "txt1 = '$\\mu_p = %1.1f$, $\\sigma_p = %1.0f$, $n_p= %1.0f$' % (mu_p, sigma_p, n_p)\n",
    "txt2 = '$\\mu_q = %1.1f$, $\\sigma_q = %1.0f$, $n_q= %1.0f$' % (mu_q, sigma_q, n_q)\n",
    "plt.legend([txt1, txt2]) ;\n",
    "plt.savefig('img/IPM_normal_histo_2.png', dpi=120) ; # to save the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_IPM_mu = []\n",
    "l_diff_mu = []\n",
    "\n",
    "mu_p = -5\n",
    "sigma_p = 2\n",
    "n_p = 30 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "\n",
    "sigma_q = 2\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 20+0.5, 0.5)\n",
    "for mu_q in l_abs:\n",
    "    np.random.seed(int(mu_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "    l_diff_mu.append([mu_q-mu_p])\n",
    "    l_IPM_mu.append([kantorovich_metric(X_p, X_q)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "txt = 'Comparison of two normal distributions $\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\mu_p = %1.0f$, $\\sigma_p = %1.0f, $' % (n_p, mu_p, sigma_p)\n",
    "txt = txt + '$n_q = %1.0f$, $\\sigma_q = %1.0f$' % (n_q, sigma_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of means $\\mu_q-\\mu_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_mu, l_IPM_mu, 'o') ;\n",
    "plt.savefig('img/IPM_normal_diff_mu.png', dpi=120) # to save the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we say that the dependency of $W(p,q)$ to $\\mu_q-\\mu_p$ is linear? Yes. Indeed, we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.997\n",
      "The regression coefficients are: \n",
      " [[0.987]]\n",
      "The regression intercept is: \n",
      " [0.379]\n"
     ]
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_mu), 1)\n",
    "y = np.asarray(l_IPM_mu)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We used the the linear regression function from [scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) and the [score method](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression.score) returns the coefficient of determination `R^2` of the prediction. The coefficient `R^2` is defined as `(1 - u/v)`, where $u$ is the residual sum of squares `((y_true - y_pred) ** 2).sum()` and `v` is the total sum of squares `((y_true - y_true.mean()) ** 2).sum()`. The best possible score is $1.0$ and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of `y`, disregarding the input features, would get a `R^2` score of `0.0`.\n",
    "\n",
    "Now we do the same as previously, but by changing the fixed values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.249\n",
      "The regression coefficients are: \n",
      " [[0.012]]\n",
      "The regression intercept is: \n",
      " [11.642]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_IPM_mu = []\n",
    "l_diff_mu = []\n",
    "\n",
    "mu_p = 3\n",
    "sigma_p = 4\n",
    "n_p = 30 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "\n",
    "sigma_q = 4\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 20+0.5, 0.5)\n",
    "for mu_q in l_abs:\n",
    "    np.random.seed(int(mu_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "    l_diff_mu.append([mu_q-mu_p])\n",
    "    l_IPM_mu.append([kantorovich_metric(X_p, X_q)])\n",
    "\n",
    "\n",
    "txt = 'Comparison of two normal distributions $\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\mu_p = %1.0f$, $\\sigma_p = %1.0f, $' % (n_p, mu_p, sigma_p)\n",
    "txt = txt + '$n_q = %1.0f$, $\\sigma_q = %1.0f$' % (n_q, sigma_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of means $\\mu_q-\\mu_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_mu, l_IPM_mu, 'o') ;\n",
    "plt.savefig('img/IPM_normal_diff_mu_2.png', dpi=120) # to save the figure\n",
    "\n",
    "\n",
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_mu), 2)\n",
    "y = np.asarray(l_IPM_mu)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influence of the difference of standard deviations $\\sigma_q-\\sigma_p$ on $W$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.856\n",
      "The regression coefficients are: \n",
      " [[0.573]]\n",
      "The regression intercept is: \n",
      " [6.891]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_IPM_sigma = []\n",
    "l_diff_sigma = []\n",
    "\n",
    "mu_p = 0\n",
    "sigma_p = 2\n",
    "n_p = 30 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "\n",
    "mu_q = 0\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 10, 0.25)\n",
    "for sigma_q in l_abs:\n",
    "    np.random.seed(int(sigma_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "    l_diff_sigma.append([sigma_q-sigma_p])\n",
    "    l_IPM_sigma.append([kantorovich_metric(X_p, X_q)])\n",
    "\n",
    "txt = 'Comparison of two normal distributions $\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\mu_p = %1.0f$, $\\sigma_p = %1.0f, $' % (n_p, mu_p, sigma_p)\n",
    "txt = txt + '$n_q = %1.0f$, $\\mu_q = %1.0f$' % (n_q, mu_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of standard deviations $\\sigma_q-\\sigma_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_sigma, l_IPM_sigma, 'o') ;\n",
    "plt.savefig('img/IPM_normal_diff_sigma.png', dpi=120) # to save the figure\n",
    "\n",
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_sigma), 1)\n",
    "y = np.asarray(l_IPM_sigma)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influence of the number of samples on $W$\n",
    "\n",
    "For $n_p=n_q=10$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.991\n",
      "The regression coefficients are: \n",
      " [[1.021]]\n",
      "The regression intercept is: \n",
      " [-0.048]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_IPM_mu = []\n",
    "l_diff_mu = []\n",
    "\n",
    "mu_p = -5\n",
    "sigma_p = 2\n",
    "n_p = 10 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "\n",
    "sigma_q = 2\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 20+0.5, 0.5)\n",
    "for mu_q in l_abs:\n",
    "    np.random.seed(int(mu_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "    l_diff_mu.append([mu_q-mu_p])\n",
    "    l_IPM_mu.append([kantorovich_metric(X_p, X_q)])\n",
    "\n",
    "\n",
    "txt = 'Comparison of two normal distributions $\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\mu_p = %1.0f$, $\\sigma_p = %1.0f, $' % (n_p, mu_p, sigma_p)\n",
    "txt = txt + '$n_q = %1.0f$, $\\sigma_q = %1.0f$' % (n_q, sigma_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of means $\\mu_q-\\mu_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_mu, l_IPM_mu, 'o') ;\n",
    "plt.savefig('img/IPM_normal_diff_n.png', dpi=120) # to save the figure\n",
    "\n",
    "\n",
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_mu), 1)\n",
    "y = np.asarray(l_IPM_mu)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $n_p=n_q=50$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.998\n",
      "The regression coefficients are: \n",
      " [[0.994]]\n",
      "The regression intercept is: \n",
      " [0.228]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_IPM_mu = []\n",
    "l_diff_mu = []\n",
    "\n",
    "mu_p = -5\n",
    "sigma_p = 2\n",
    "n_p = 50 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.normal(mu_p, sigma_p, n_p)\n",
    "\n",
    "sigma_q = 2\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 20+0.5, 0.5)\n",
    "for mu_q in l_abs:\n",
    "    np.random.seed(int(mu_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.normal(mu_q, sigma_q, n_q)\n",
    "    l_diff_mu.append([mu_q-mu_p])\n",
    "    l_IPM_mu.append([kantorovich_metric(X_p, X_q)])\n",
    "\n",
    "\n",
    "txt = 'Comparison of two normal distributions $\\mathcal{N}(\\mu_p, \\sigma_p)$ and $\\mathcal{N}(\\mu_q, \\sigma_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\mu_p = %1.0f$, $\\sigma_p = %1.0f, $' % (n_p, mu_p, sigma_p)\n",
    "txt = txt + '$n_q = %1.0f$, $\\sigma_q = %1.0f$' % (n_q, sigma_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of means $\\mu_q-\\mu_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_mu, l_IPM_mu, 'o') ;\n",
    "plt.savefig('img/IPM_normal_diff_n_2.png', dpi=120) # to save the figure\n",
    "\n",
    "\n",
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_mu), 1)\n",
    "y = np.asarray(l_IPM_mu)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of two exponential distributions\n",
    "\n",
    "\n",
    "Here we consider two exponential distributions $\\mathbb{P} = \\mathcal{E}(\\lambda_p)$ and $\\mathbb{Q} = \\mathcal{E}(\\lambda_q)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_IPM_lambda = []\n",
    "l_diff_lambda = []\n",
    "\n",
    "lambda_p = 1\n",
    "n_p = 30 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.exponential(lambda_p, n_p)\n",
    "\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(1, 20, 0.5)\n",
    "for lambda_q in l_abs:\n",
    "    np.random.seed(int(lambda_q*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.exponential(lambda_q, n_q)\n",
    "    l_diff_lambda.append([lambda_q-lambda_p])\n",
    "    l_IPM_lambda.append([kantorovich_metric(X_p, X_q)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "txt = 'Comparison of two exponential distributions $\\mathcal{E}(\\lambda_p)$ and $\\mathcal{E}(\\lambda_q)$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $\\lambda_p = %1.0f$, ' % (n_p, lambda_p)\n",
    "txt = txt + '$n_q = %1.0f$' % (n_q)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of parameters $\\lambda_q-\\lambda_p$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_lambda, l_IPM_lambda, 'o') ;\n",
    "plt.savefig('img/IPM_exponential_diff.png', dpi=120) # to save the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 0.865\n",
      "The regression coefficients are: \n",
      " [[0.957]]\n",
      "The regression intercept is: \n",
      " [1.402]\n"
     ]
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_lambda), 1)\n",
    "y = np.asarray(l_IPM_lambda)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of two uniform distributions\n",
    "\n",
    "Here we consider two normal distributions $\\mathbb{P} = \\mathbb{U}\\left([a, a+h]\\right)$ and $\\mathbb{Q} = \\mathbb{U}\\left([r, r+h]\\right)$ where $h$ is the length of the intervals.\n",
    "\n",
    "Note: $a$ is called the **interval start** of $[a, a+h]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_IPM_unif = []\n",
    "l_diff_unif = []\n",
    "\n",
    "h = 2 # length of the intervals\n",
    "a = 0\n",
    "b = a+h\n",
    "n_p = 30 # after several simulations, 30 seems enough\n",
    "np.random.seed(1) # random seed for reproducability\n",
    "X_p = np.random.uniform(a, b, n_p)\n",
    "\n",
    "n_q = n_p\n",
    "\n",
    "l_abs = np.arange(0, 20, 0.5)\n",
    "for r in l_abs:\n",
    "    np.random.seed(int(r*10)) # random seed for reproducability, different each time\n",
    "    X_q = np.random.uniform(r, r+h, n_q)\n",
    "    l_diff_unif.append([r-a])\n",
    "    l_IPM_unif.append([kantorovich_metric(X_p, X_q)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "txt = 'Comparison of two uniform distributions $\\mathbb{U}([a, a+h])$ and $\\mathbb{U}([r, r+h])$ \\n'\n",
    "txt = txt + 'with $n_p = %1.0f$, $a = %1.0f$, $h = %1.0f, $' % (n_p, a, h)\n",
    "txt = txt + '$n_q = %1.0f$, $h = %1.0f$' % (n_q, h)\n",
    "plt.title(txt)\n",
    "plt.xlabel('Difference of interval starts $r-a$')\n",
    "plt.ylabel('Empirical Kantorovich metric $W(p, q)$')\n",
    "plt.plot(l_diff_unif, l_IPM_unif, 'o') ;\n",
    "plt.savefig('img/IPM_uniform_diff.png', dpi=120) # to save the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression score is: \n",
      " 1.0\n",
      "The regression coefficients are: \n",
      " [[0.998]]\n",
      "The regression intercept is: \n",
      " [0.693]\n"
     ]
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "X = np.power(np.asarray(l_diff_unif), 1)\n",
    "y = np.asarray(l_IPM_unif)\n",
    "\n",
    "reg.fit(X, y)\n",
    "print('The regression score is: \\n', round(reg.score(X, y), 3))\n",
    "print('The regression coefficients are: \\n', np.round(reg.coef_, 3))\n",
    "print('The regression intercept is: \\n', np.round(reg.intercept_, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Application of the Kantorovich metric to the data generated from two methods for computing the Choquet integral\n",
    "\n",
    "## For the Choquet integral of normal distributions\n",
    "\n",
    "### Presenting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xp_df = pd.read_csv('data/X1_normal.csv', sep=',', header=None)\n",
    "Xq_df = pd.read_csv('data/X2_normal.csv', sep=',', header=None)\n",
    "\n",
    "Xp_list = Xp_df.values.tolist()\n",
    "Xq_list = Xq_df.values.tolist()\n",
    "\n",
    "sns.distplot(Xp_list) ;\n",
    "sns.distplot(Xq_list) ;\n",
    "plt.title('Histogram of the samples from two Choquet integrals \\n of normal distributions') ;\n",
    "plt.legend(['with the direct method', 'with the new formula']) ;\n",
    "plt.savefig('img/choquet_normal_X.png', dpi=120) # to save the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are `Xp` and `Xq` from normal distributions? We use the `scipy.stats.normaltest` function [SciPy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html) which tests the null hypothesis that a sample comes from a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pvalue is: \n",
      " [1.158583e-26]\n",
      "Null hypothesis: Xp comes from a normal distribution: Xp does not come from a normal distribution.\n",
      "The null hypothesis can be rejected.\n"
     ]
    }
   ],
   "source": [
    "alpha = 1e-3\n",
    "\n",
    "k2, p = stats.normaltest(Xp_list)\n",
    "print('The pvalue is: \\n', p)\n",
    "\n",
    "print('Null hypothesis: Xp comes from a normal distribution: Xp does not come from a normal distribution.')\n",
    "if p < alpha:  \n",
    "    print(\"The null hypothesis can be rejected.\")\n",
    "else:\n",
    "    print(\"The null hypothesis cannot be rejected.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pvalue is: \n",
      " [9.25336667e-29]\n",
      "Null hypothesis: Xq comes from a normal distribution.\n",
      "The null hypothesis can be rejected: q does not come from a normal distribution.\n"
     ]
    }
   ],
   "source": [
    "alpha = 1e-3\n",
    "\n",
    "k2, p = stats.normaltest(Xq_list)\n",
    "print('The pvalue is: \\n', p)\n",
    "\n",
    "print('Null hypothesis: Xq comes from a normal distribution.')\n",
    "if p < alpha:  \n",
    "    print(\"The null hypothesis can be rejected: q does not come from a normal distribution.\")\n",
    "else:\n",
    "    print(\"The null hypothesis cannot be rejected.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the Kantorovich metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the Kantorovich metrics is: \n",
      " 0.894\n",
      "The standard deviation of the Kantorovich metrics is: \n",
      " 0.033\n",
      "The total processing time is: \n",
      " 0:00:35.699360\n"
     ]
    }
   ],
   "source": [
    "t_start = process_time()\n",
    "l_IPM_choquet_normal = []\n",
    "\n",
    "random.seed(1)\n",
    "Xp = random.sample(Xp_list, 100)\n",
    "\n",
    "for i in range(10, 20):\n",
    "    random.seed(i)\n",
    "    Xq = random.sample(Xq_list, 100)\n",
    "    W = kantorovich_metric(Xp, Xq)\n",
    "    l_IPM_choquet_normal.append(W)\n",
    "t_stop = process_time()\n",
    "\n",
    "print('The mean of the Kantorovich metrics is: \\n', np.round(np.mean(l_IPM_choquet_normal), 3))\n",
    "print('The standard deviation of the Kantorovich metrics is: \\n', np.round(np.std(l_IPM_choquet_normal), 3))\n",
    "print('The total processing time is: \\n', datetime.timedelta(seconds=t_stop-t_start))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For the Choquet integral of exponential distributions\n",
    "\n",
    "### Presenting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xp_df = pd.read_csv('data/X1_exp.csv', sep=',', header=None)\n",
    "Xq_df = pd.read_csv('data/X2_exp.csv', sep=',', header=None)\n",
    "\n",
    "Xp_list = Xp_df.values.tolist()\n",
    "Xq_list = Xq_df.values.tolist()\n",
    "\n",
    "sns.distplot(Xp_list) ;\n",
    "sns.distplot(Xq_list) ;\n",
    "plt.title('Histogram of the samples from two Choquet integrals \\n of exponential distributions') ;\n",
    "plt.legend(['with the direct method', 'with the new formula']) ;\n",
    "plt.savefig('img/choquet_exp_X.png', dpi=120) # to save the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the Kantorovich metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the Kantorovich metrics is: \n",
      " 0.776\n",
      "The standard deviation of the Kantorovich metrics is: \n",
      " 0.051\n",
      "The total processing time is: \n",
      " 0:00:35.550855\n"
     ]
    }
   ],
   "source": [
    "t_start = process_time()\n",
    "l_IPM_choquet_exp = []\n",
    "\n",
    "random.seed(1)\n",
    "Xp = random.sample(Xp_list, 100)\n",
    "\n",
    "for i in range(10, 20):\n",
    "    random.seed(i)\n",
    "    Xq = random.sample(Xq_list, 100)\n",
    "    W = kantorovich_metric(Xp, Xq)\n",
    "    l_IPM_choquet_exp.append(W)\n",
    "t_stop = process_time()\n",
    "\n",
    "print('The mean of the Kantorovich metrics is: \\n', np.round(np.mean(l_IPM_choquet_exp), 3))\n",
    "print('The standard deviation of the Kantorovich metrics is: \\n', np.round(np.std(l_IPM_choquet_exp), 3))\n",
    "print('The total processing time is: \\n', datetime.timedelta(seconds=t_stop-t_start))"
   ]
  }
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