Renye Transfer Entropy Calculation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a8e01d50",
   "metadata": {},
   "source": [
    "# Renye Transfer Entropy Calculation\n",
    "\n",
    "This notebook consist of following activity:\n",
    "\n",
    "1. Function: KNN nearest neighbour method to estimate the probabailty distribution\n",
    "2. Function: Calculation of kth nearest distance of any provided dataset\n",
    "3. Function: Calcuation of Reny Entropy\n",
    "4. Calcuation: RE of probability distributions: Normal Distribution\n",
    "5. Calcuation: RE of probability distributions: Cauchy Distribution\n",
    "5. Calcuation: RE of probability distributions: Student-t Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9f1afc8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import\n",
    "import numpy as np\n",
    "from scipy.special import gamma,psi\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(['science', 'notebook', 'grid'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc9f74a1",
   "metadata": {},
   "source": [
    "## 1 KNN nearest neighbour method to estimate the probabailty distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ab016c1",
   "metadata": {},
   "source": [
    "* Function to calculate the kth nearest neighbour distance by considering the Euclidian style distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5d330411",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Get the k nearest neighbors between points in a random variable/vector.\n",
    "# Uses Euclidean style distances.\n",
    "'''\n",
    "Arguments: \n",
    "X -> list of point[x1, x1,..] or points [[x1, x1], [x2, y2], ...]\n",
    "k -> integer, the nearest value desired\n",
    "D -> is the distance, can be used to make the threshold cut-off in distance\n",
    "\n",
    "Returns:\n",
    "knn -> A dictationary with place_value(points) as key and \n",
    "'''\n",
    "def k_nearest_neighbors(X, k=1, D=1):\n",
    "    #length\n",
    "    nX = len(X)\n",
    "    #initialize knn dict\n",
    "    knn = {key: [] for key in range(nX)}\n",
    "    #make sure X has the right shape for the cdist function\n",
    "    X = np.reshape(X, (nX,-1))\n",
    "    dists_arr = cdist(X, X)\n",
    "    distances = [[i,j,dists_arr[i,j]] for i in range(nX-1) for j in range(i+1,nX)]\n",
    "    #sort distances\n",
    "    distances.sort(key=lambda x: x[2])\n",
    "    #pick up the k nearest\n",
    "    for d in distances:\n",
    "        i = d[0]\n",
    "        j = d[1]\n",
    "        dist = d[2]\n",
    "        if dist < D:\n",
    "            if len(knn[i]) < k:\n",
    "                knn[i].append([j, dist])\n",
    "            if len(knn[j]) < k:\n",
    "                knn[j].append([i, dist])\n",
    "    return knn\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28addd12",
   "metadata": {},
   "source": [
    "## 2 KNN nearest neighbour distance calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08c6bf16",
   "metadata": {},
   "source": [
    "* Function to calculate the distance for the provided kth nearest neighbour "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9f65824f",
   "metadata": {},
   "outputs": [],
   "source": [
    " \"\"\"Returns the distance for the kth nearest neighbor of each point.\n",
    "\n",
    "   Args:\n",
    "        X (np.array): A random variable of form X = {x_1, x_2, x_3,...,x_N} or\n",
    "            a random vector of form X = {(x_1, y_1), (x_2, y_2),...,(x_N,\n",
    "            y_n)}.\n",
    "        k (Optional[int]): The number of nearest neighbors to check for each\n",
    "            point. Defaults to 1.\n",
    "    Returns:\n",
    "        list: A list in same order as X with the distance value to the kth\n",
    "        nearest neighbor of each point in X.\n",
    "\n",
    "    \"\"\"\n",
    " \n",
    "\n",
    "def kth_nearest_neighbor_distances(X, k=1):\n",
    "    nX = len(X)\n",
    "    # make sure X has the right shape for the cdist function\n",
    "    X = np.reshape(X, (nX,-1))\n",
    "    dists_arr = cdist(X, X) # creates a distance matrix with all the distances between every points as elements\n",
    "    dists_arr.sort() #sort the distances (rows) in ascending order\n",
    "    return [dists_arr[i][k] for i in range(nX)] #call for the required distance(value) in the distance matrix \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc18894d",
   "metadata": {},
   "source": [
    "## 3 Calculation of Renyi Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdc39574",
   "metadata": {},
   "source": [
    "*Python Function to calculate the Renyi Entropy for the provided kth nearest neighbour *\n",
    "\n",
    "The estimator has been adopted from following article (section 3.1) (https://arxiv.org/abs/0810.5302#:~:text=A%20class%20of%20R%C3%A9nyi%20information%20estimators%20for%20multidimensional%20densities,-Nikolai%20Leonenko%2C%20Luc&text=A%20class%20of%20estimators%20of,i.i.d.%20vectors%20with%20distribution%20f.)\n",
    "\n",
    "1. Firstly calculate: $ \\zeta_{(N, i, k)}$ as follows:\n",
    "\n",
    "$$\\zeta_{(n, i, k)} =  (n-1) C_{k} V_{d} (\\rho_{k}^{(i)}, _{(n-1)})^{d} $$\n",
    "\n",
    "where: \n",
    "\n",
    "$$V_{d}  = \\frac {\\pi^{d/2}}  {\\Gamma{(d/2 + 1)}}$$\n",
    "\n",
    "is the volume of the unit ball $B(0, 1)$ in $R^{d}$\n",
    "\n",
    "$$ C_{k} = \\left[ \\frac {\\Gamma{(k)}} {\\Gamma {(k + 1 - alpha)}} \\right] $$\n",
    "\n",
    "\n",
    "2. Secondly calculate $I_{(n, k, alpha)}$ as follows:\n",
    "\n",
    "$$ I_{(n, k, alpha)} = \\frac {1}{n} \\sum_{i = 1}^{n} \\zeta_{(n, i, k)} $$\n",
    "\n",
    "\n",
    "3. Thirdly estimate the Renyi Tallis Entropy as follows:\n",
    "\n",
    "$$ H_{(n, k, alpha)} = \\frac {1}{1-alpha}  log(I_{(n, k, alpha)} )$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "293dea8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimation of Renyi Entropy by using above formula\n",
    "\n",
    "\"\"\"\n",
    "   Args:\n",
    "        X (np.array): A random variable of form X = {x_1, x_2, x_3,...,x_N} or\n",
    "            a random vector of form X = {(x_1, y_1), (x_2, y_2),...,(x_N,\n",
    "            y_n)}.\n",
    "       alpha [int] : the alpha parameter of RE\n",
    "        k (Optional[int]): The number of nearest neighbors to check for each\n",
    "            point. Defaults to 1.\n",
    "        \n",
    "    Returns:\n",
    "        array: Aa array of thus calculated Renyi Entropy.\n",
    "\"\"\"\n",
    "def RE_estimate(X, alpha, k, kth_dists=None): #output an array for all the values of i in X\n",
    "    r_k = kth_dists # the kth nearest neighbor distances\n",
    "    if kth_dists is None:\n",
    "        r_k = kth_nearest_neighbor_distances(X, k=k)\n",
    "        \n",
    "    n = len(X) # length\n",
    "    #a = 1.0-alpha #dummy a\n",
    "    d = 1 #dimension\n",
    "    if len(X.shape) == 2:\n",
    "        d = X.shape[1]\n",
    "    # volume of unit ball in R^d\n",
    "    V_d = np.pi**(0.5*d)/gamma(0.5*d + 1.0) # output numpy.float64\n",
    "    #Ck\n",
    "    C_k = (gamma(k)/gamma(k + 1-alpha))**(1/(1-alpha)) # output list\n",
    "    #zeta\n",
    "    zeta_n_i_k = (n-1) * np.array(C_k) * V_d * np.array(r_k)**d\n",
    "    #I\n",
    "    I_n_k_alpha = (1/n) * np.sum(np.array(zeta_n_i_k)**(1-alpha))\n",
    "    #RE estimate\n",
    "    RE = np.log2(I_n_k_alpha)/(1-alpha) \n",
    "    return RE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc95d7a",
   "metadata": {},
   "source": [
    "## 4: Renye Entropy: Normal Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88974e8f",
   "metadata": {},
   "source": [
    "1. RE Estimates for Univariate Normal Distribtuon\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01184ac3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the dataset for Univariate normal distibution\n",
    "N = np.random.normal(0,1,10000) # numpy.ndarray\n",
    "N = np.reshape(N, (len(N), -1))\n",
    "#n = len(N)\n",
    "#calculate the RE estimates\n",
    "alphas = np.arange(0.1,4,0.04) #defining alphas upto  alpha< k + 1\n",
    "RE_est = [ RE_estimate(N, alpha, k=5, kth_dists=None) for alpha in alphas]   \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bfa9fc1",
   "metadata": {},
   "source": [
    "2. RE analytically calculated for Normal Distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a0dabbdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "# In order to analytically calculate the RE for Gaussian distribution, the equation is adopted from the \n",
    "master thesis (Tabochavo et. al) (Section: 2.1.5) \n",
    "\"\"\"\n",
    "\n",
    "#cov = [[1, 0], [0, 1]]  # diagonal covariance\n",
    "cov = [[1]]\n",
    "def RE_analytical(N, alpha):\n",
    "    RE = np.log2((2*np.pi)**(N/2)* (np.linalg.det(cov))**0.5) + (1/(1-alpha))*np.log2(alpha**(-N/2))\n",
    "    return RE\n",
    "\n",
    "alphas = np.arange(0.1,4,0.04) #defining alphas\n",
    "RE_analy = [RE_analytical(1,alpha) for alpha in alphas] #calculating RE for all alphas and assigning it to a object\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cad769b4",
   "metadata": {},
   "source": [
    "plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b31ab06b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d93169db20>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot RE estimates\n",
    "plt.plot(alphas, RE_est, '--', label = 'RE estimated')\n",
    "\n",
    "#plot RE analytical\n",
    "plt.plot(alphas, RE_analy, label = 'RE Analytical')\n",
    "\n",
    "plt.xlabel('alphas')\n",
    "plt.ylabel('Renye Entropy')\n",
    "plt.legend(loc = 'upper right', fontsize = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5096b91",
   "metadata": {},
   "source": [
    "## 5: Renye Entropy: Cauchy Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "12eec6d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d9317b44c0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# RE Estimates for Cauchy distribution\n",
    "N = np.random.standard_cauchy(2000) \n",
    "N = np.reshape(N, (len(N), -1))\n",
    "alphas = np.arange(0.6,4,0.03) #defining alphas as alpha<k + 1 and above 0.5\n",
    "\n",
    "RE_est_cauchy = [ RE_estimate(N, alpha, k=5, kth_dists=None) for alpha in alphas]   \n",
    "\n",
    "# Analytical solution for cauchy distribution\n",
    "def RE_analytical_cauchy(alpha):\n",
    "    RE = np.log2((1/np.pi ** (alpha-0.5)) * gamma(alpha-0.5)/gamma(alpha)) * (1/(1-alpha))\n",
    "    return RE\n",
    "\n",
    "RE_analy_cauchy = [RE_analytical_cauchy(alpha) for alpha in alphas]\n",
    "\n",
    "#plot\n",
    "plt.plot(alphas, RE_est_cauchy, '--', label = 'RE estimated cauchy')\n",
    "plt.plot(alphas, RE_analy_cauchy, label = 'RE Analytical Cauchy')\n",
    "plt.xlabel('alphas')\n",
    "plt.ylabel('Renye Entropy')\n",
    "plt.legend(loc = 'upper right', fontsize = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abaeb63e",
   "metadata": {},
   "source": [
    "## 6: Renye Entropy : Student -t Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd976ce3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# RE Estimates for student t distribution\n",
    "N = np.random.standard_t(10, size=1000) #with 10 degree of freedom\n",
    "N = np.reshape(N, (len(N), -1))\n",
    "alphas = np.arange(0.6,4,0.03) #defining alphas as alpha<k + 1 and above 0.5\n",
    "\n",
    "RE_est_cauchy = [ RE_estimate(N, alpha, k=5, kth_dists=None) for alpha in alphas]   \n",
    "\n",
    "# Analytical solution for cauchy distribution\n",
    "def RE_analytical_cauchy(alpha):\n",
    "    RE = np.log2((1/np.pi ** (alpha-0.5)) * gamma(alpha-0.5)/gamma(alpha)) * (1/(1-alpha))\n",
    "    return RE\n",
    "\n",
    "RE_analy_cauchy = [RE_analytical_cauchy(alpha) for alpha in alphas]\n",
    "\n",
    "#plot\n",
    "plt.plot(alphas, RE_est_cauchy, '--', label = 'RE estimated cauchy')\n",
    "plt.plot(alphas, RE_analy_cauchy, label = 'RE Analytical Cauchy')\n",
    "plt.xlabel('alphas')\n",
    "plt.ylabel('Renye Entropy')\n",
    "plt.legend(loc = 'upper right', fontsize = 10)"
   ]
  }
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