Ex3_newer_version.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task A:**\n",
    "*Derive the probability density function $p(x|Θ) $(see Fig. 1B) for this model.*\n",
    "\n",
    "*Solution:*\n",
    "\n",
    "We can use the product rule in order to get p(x|Θ). This result was given in the lecture.\n",
    "\n",
    "\n",
    "$p(x|Θ) = \\sum_{c=1}^{2}p(x|c,Θ)·p(c|Θ)=p(x|c=1,Θ)·p(c=1|Θ)+p(x|c=2,Θ)·p(c=2|Θ)=$\n",
    "\n",
    "$$\\frac{1}{\\sqrt{2\\pi\\sigma_1}}exp(-\\frac{(x-\\mu_1)^2}{2\\sigma_1^2})*\\pi_1+\\frac{1}{\\sqrt{2\\pi\\sigma_2}}exp(-\\frac{(x-\\mu_2)^2}{2\\sigma_2^2})*(1-\\pi_1)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task B:**\n",
    "Using the values $π_1 = 0.4, π_2 = 0.6, μ_1 = −2, μ_2 = 4, σ_1^2 = 1, σ_2^2 = 10 $ for the parameters,\n",
    "plot the probability density function (pdf) obtained in Task A.\n",
    "\n",
    "*Solution:*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "\n",
    "from scipy.stats import norm\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Define the distributions to be plotted\n",
    "\n",
    "sigma_values = [1,np.sqrt(10)]\n",
    "\n",
    "mu = [-2,4]\n",
    "\n",
    "pi = 0.4\n",
    "\n",
    "N=1000\n",
    "\n",
    "x = np.linspace(-10, 20, N)\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Define the distributions to be plotted\n",
    "sigma_values = [1,np.sqrt(10)]\n",
    "\n",
    "mu = [-2,4]\n",
    "\n",
    "\n",
    "dist1 = norm(mu[0],sigma_values[0])\n",
    "\n",
    "dist2 = norm(mu[1],sigma_values[1])\n",
    "\n",
    "pdft= pi*dist1.pdf(x)+(1-pi)*dist2.pdf(x)\n",
    "\n",
    "\n",
    "plt.plot(x, pdft)\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "plt.title(r'Plot of the PDF $p(x|{\\theta})$')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task C:\n",
    "Generate 1000 data points using the generative model described above (equations 1 and\n",
    "2) and the parameters given in Task B). Plot the data points using a one-dimensional plot\n",
    "(scatter-plot)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 2880x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def generate_x(N, pi_1,sigma_sq_1,sigma_sq_2,mu_1,mu_2):\n",
    "    \n",
    "    N1=math.floor(N*pi)\n",
    "\n",
    "    N2=N-N1\n",
    "    \n",
    "    generated_x=np.append(np.random.normal(mu_1 , sigma_sq_1, N1), np.random.normal(mu_2, sigma_sq_2, N2))\n",
    "    \n",
    "    return generated_x\n",
    "\n",
    "generated_x=generate_x(N,pi,sigma_values[0],sigma_values[1],mu[0],mu[1])\n",
    "\n",
    "\n",
    "plt.figure(figsize=(40,10))\n",
    "\n",
    "plt.plot(generated_x, len(generated_x)*[0] , '+')\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.xlabel('$x$', fontsize=40)\n",
    "\n",
    "plt.title('Scatter plot of the generated data using generative model', fontsize=30)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task D:\n",
    "Using the data points generated in Task C), divide the x-dimension into \f",
    "fty equally sized\n",
    "bins and compute a histogram on the interval [-10; 20]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(generated_x, bins=50)  \n",
    "\n",
    "plt.title(\"Histogram with 50 bins\")\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel('$N$')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task E:\n",
    "Normalize the heights of the bars in Task D) such that they represent an approximation\n",
    "to the probability density in the interval [-10; 20]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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.hist(generated_x, bins=50, density=True)  \n",
    "\n",
    "plt.title(\"Normalized Histogram with 50 bins\")\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task F:\n",
    "Re-plot the pdf used in Task B) together with the normalized histogram obtained in Task\n",
    "E) in the same figure. Try out different numbers of bins and data points. Does the density\n",
    "estimation in Task E) approximate the true underlying density p(xj\u0002) in Task B) equally\n",
    "well for all numbers of bins and data points? Why (not)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot of Histogram and PDF with 50 bins and 1000 data points\n",
    "plt.plot(x, pdft)\n",
    "\n",
    "plt.hist(generated_x, bins=50, density=True,orientation = u'vertical')\n",
    "\n",
    "plt.title(\"Normalized Histogram with 50 bins and PDF plotted against x (thousand datapoints)\")\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#Plot of Histogram and PDF with 50 bins and a million data points\n",
    "generated_x_million=generate_x(1000000,pi,sigma_values[0],sigma_values[1],mu[0],mu[1])\n",
    "\n",
    "plt.plot(x, pdft)\n",
    "\n",
    "plt.hist(generated_x_million, bins=50, density=True,orientation = u'vertical')\n",
    "\n",
    "plt.title(\"Normalized Histogram with 50 bins and PDF plotted against x (million datapoints)\")\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#Plot of Histogram and PDF with 500 bins and a million data points\n",
    "plt.plot(x, pdft)\n",
    "\n",
    "plt.hist(generated_x_million, bins=500, density=True,orientation = u'vertical')\n",
    "\n",
    "plt.title(\"Normalized Histogram with 500 bins and PDF plotted against x (million datapoints)\")\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "\n",
    "plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "plt.xlim(-10, 20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer Task F:\n",
    "As the interval window, it starts going from being a discrete value sum to a continous valued integral like situation. But if the bins equal to the datapoints number, there's not enough points to average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task G:\n",
    "Compute the log-likelihood for N data points under the generative model given in equa-\n",
    "tions 1 and 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'pi' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-c8c9d91db530>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     55\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     56\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 57\u001b[1;33m \u001b[0mplot_log_likelihood\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msigma_values\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msigma_values\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34mr'$(\\theta_i)$'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'pi' is not defined"
     ]
    }
   ],
   "source": [
    "def log_likelihood(generated_x, pi, mu1, sigma1, mu2, sigma2):\n",
    "    \n",
    "    sum_C=0 #Initialize sum over classes\n",
    "    sum_N=0\n",
    "    \n",
    "    N=len(generated_x)\n",
    "    \n",
    "    dist1 = norm(mu1,sigma1)\n",
    "\n",
    "    dist2 = norm(mu2,sigma2)\n",
    "\n",
    "    for i in range(N):\n",
    "\n",
    "        sum_C=pi*dist1.pdf(generated_x[i]) + (1-pi)*dist2.pdf(generated_x[i])\n",
    "\n",
    "        sum_C_log=np.log(sum_C)\n",
    "        \n",
    "        sum_N+=sum_C_log\n",
    "    \n",
    "    return sum_N\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def plot_log_likelihood(pi,sigma1,sigma2,mu1,mu2,parameter_no):\n",
    "    step=11\n",
    "\n",
    "    N_int=np.arange(0, step)\n",
    "\n",
    "    log_likelihood_values=np.zeros(step)\n",
    "\n",
    "    for i in range(step):\n",
    "\n",
    "        x=np.linspace(0, step-1, step)\n",
    "\n",
    "        N_float=2**x[i]\n",
    "\n",
    "        N_int[i]=math.floor(N_float)\n",
    "\n",
    "\n",
    "        generated_x_values=generate_x(N_int[i],pi,sigma1,sigma2,mu1,mu2)\n",
    "\n",
    "        log_likelihood_values[i]=log_likelihood(generated_x_values, pi, mu1, sigma1, mu2, sigma2)\n",
    "        \n",
    "    plt.figure(figsize=(10,5))\n",
    "\n",
    "    plt.plot(N_int, log_likelihood_values)\n",
    "\n",
    "    plt.xlabel('$N$')\n",
    "\n",
    "    plt.ylabel(r'$\\mathcal{L}(\\theta)$')\n",
    "\n",
    "    plt.title(r'Log-likelihood $\\mathcal{L}(\\theta)$ for N datapoints using paramters' + parameter_no, fontsize=15)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "plot_log_likelihood(pi,sigma_values[0],sigma_values[1],mu[0],mu[1], r'$(\\theta_i)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task H:\n",
    "Evaluate the log-likelihood computed in Task G) using the 1000 data points you have generated in Task C). What is the log-likelihood for other parameters? What do you observe\n",
    "for more and for less data points?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihood using the 1000 datapoints with intial parameters generated is -2596.7417737667565\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihood using the 1000 datapoints generated with different paramters:\n",
      "pi = 0.5\n",
      "µ_1 = 5\n",
      "µ_2 = 15\n",
      "σ_1 =  3.1622776601683795\n",
      "σ_2 =  2.0\n",
      "Log-likehood: -2929.5584798934974\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihood using the 1000 datapoints generated with different paramters:\n",
      "pi = 0.2\n",
      "µ_1 = 4\n",
      "µ_2 = 10\n",
      "σ_1 =  1.4142135623730951\n",
      "σ_2 =  1.4142135623730951\n",
      "Log-likehood: -2497.682397938462\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihood using the 1000 datapoints generated with different paramters:\n",
      "pi = 0.7\n",
      "µ_1 = 8\n",
      "µ_2 = 1\n",
      "σ_1 =  2.8284271247461903\n",
      "σ_2 =  2.6457513110645907\n",
      "Log-likehood: -3019.53950252573\n"
     ]
    }
   ],
   "source": [
    "print('Log-likelihood using the 1000 datapoints with intial parameters generated is', log_likelihood(generated_x, pi, mu[0], sigma_values[0], mu[1], sigma_values[1]))\n",
    "\n",
    "#Change parameters in Distribution 1 and 2\n",
    "def diff_param(pi, mu1, sigma1, mu2, sigma2):\n",
    "\n",
    "    dist1 = norm(mu1,sigma1)\n",
    "\n",
    "    dist2 = norm(mu2,sigma2)\n",
    "\n",
    "    pdft= pi*dist1.pdf(x)+(1-pi)*dist2.pdf(x)\n",
    "\n",
    "    plt.plot(x, pdft)\n",
    "\n",
    "    plt.xlim(-10, 20)\n",
    "\n",
    "    plt.xlabel('$x$')\n",
    "\n",
    "    plt.ylabel(r'$p(x|\\theta)$')\n",
    "\n",
    "    plt.title(r'Plot of the PDF $p(x|{\\theta_1})$')\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "    new_generated_x=generate_x(N,pi,sigma1,sigma2,mu1,mu2)\n",
    "    \n",
    "    print('Log-likelihood using the 1000 datapoints generated with different paramters:')\n",
    "    print('pi =', pi)\n",
    "    print('µ_1 =', mu1)\n",
    "    print('µ_2 =', mu2)\n",
    "    print('σ_1 = ', sigma1)\n",
    "    print('σ_2 = ', sigma2)\n",
    "    print('Log-likehood:', log_likelihood(new_generated_x,pi, mu1, sigma1, mu2, sigma2))\n",
    "    \n",
    "diff_param(0.5, 5, np.sqrt(10), 15, np.sqrt(4))\n",
    "\n",
    "diff_param(0.2, 4, np.sqrt(2), 10, np.sqrt(2))\n",
    "\n",
    "diff_param(0.7, 8, np.sqrt(8), 1, np.sqrt(7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer Task H:\n",
    "Log-likelihood using the 1000 datapoints with intial parameters generated is -2596.7417737667565\n",
    "With more datapoints N, the log likelihood decreases linearly. \n",
    "By changing the paramters, there is a different in log likelihood but not as major as with changing the number of datapoints. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercise 2\n",
    "\n",
    "Consider the general form of a Mixture of Gaussians Model (MoG):\n",
    "\n",
    "$p(c|\\theta)=\\pi_c$ with $(c=1,...,C);  \\quad \\Sigma_{c=1}^{C} \\pi_c=1$\n",
    "$\\quad p(\\vec{x}|c,\\theta)=\\mathcal{N}(\\vec{x},\\vec{\\mu_c},\\theta)$\n",
    "\n",
    "Use the equations for the E-step and M-step of the Expectation Maximization approach,\n",
    "which were given in the lecture, to derive the update rules for:\n",
    "\n",
    "**Task A**\n",
    "\n",
    "$ \\vec{\\mu_c}$ with $c=1,...,C.$\n",
    "\n",
    "Solution:\n",
    "\n",
    "From our lecture we already know the form of the free energy. The algorithm of EM was already given in class but now we need to extend it in a linear algebra form. We are not going to write the hole algorithm because it's consistenly the same rather than focus on the E-Step and M-Step which are going to be slightly different.\n",
    "\n",
    "*E-Step*\n",
    "\n",
    "This is E-Step it's not so different. Just we need to adjust our denominator for all posible clases\n",
    "\n",
    "$$\\vec{q}(c;\\theta^{old})=p(\\vec{x}|c,\\theta^{old})p(c|\\theta^{old}) =\\frac{ \\pi_c·exp(-\\frac{1}{2}(\\vec{x}-\\vec{\\mu_c})^t\\Sigma_c^{-1}(\\vec{x}-\\vec{\\mu_c}))}{\\Sigma_{c=1}^{C} \\pi_c·exp(-\\frac{1}{2}(\\vec{x}-\\vec{\\mu_c})^t\\Sigma_c^{-1}(\\vec{x}-\\vec{\\mu_c}))}$$\n",
    "\n",
    "\n",
    "*M-Step*\n",
    "\n",
    "Now our $\\vec{q}$ is going to be fixed after our last computation.\n",
    "\n",
    "$$\\frac{d}{d\\theta}\\xi(\\vec{q}(c;\\theta^{old}),\\theta)=0$$\n",
    "\n",
    "That means we need to maximaze the free energy for the $\\vec{\\mu_c}$ and for $\\vec{\\sigma_c}$\n",
    "\n",
    "Let's do the first one:\n",
    "\n",
    "\n",
    "$$\\frac{d}{d\\vec{\\mu_c}}\\xi(...)=0$$\n",
    "$$0=\\Sigma_n\\Sigma_c\\vec{q}(c,\\theta^{old})\\frac{d}{d\\vec{\\mu_{c'}}}(log(\\mathcal{N}))=0=\\Sigma_n\\Sigma_c\\vec{q}(c,\\theta^{old})·(0+0+\\frac{-1}{2}[\\frac{d}{d\\mu_{c'}}(\\vec{x}-\\vec{\\mu_c})^t\\Sigma_c^{-1}(\\vec{x}-\\vec{\\mu_c})])$$\n",
    "\n",
    "We stress the fact that the n indices are the indices of the $\\vec{q}$ vector.\n",
    "\n",
    "Now using the second equation of our exercise sheet so this derivate becomes\n",
    "\n",
    "$$-2\\Sigma_{c'}^{-1}(\\vec{x}-\\vec{\\mu_{c'}})$$\n",
    "and isolating the $\\vec{\\mu_c}$ vector then we have \n",
    "$$\\vec{\\mu_{c}}=\\frac{\\Sigma_n\\vec{q}(c;\\theta^{old})\\vec{x}}{\\Sigma_n\\vec{q}(c;\\theta^{old})}$$\n",
    "\n",
    "\n",
    "\n",
    "The second one:\n",
    "\n",
    "$0=\\frac{d}{d\\Sigma_c}\\xi(q,\\theta)$\n",
    "\n",
    "$$\\bullet \\quad-\\frac{1}{2}\\frac{d}{d\\Sigma_{c'}}log(det[2\\pi\\Sigma_c])=Tr((2\\pi\\Sigma_c)^{-1}\\frac{d(2\\pi\\Sigma_c)}{d\\Sigma_{c'}}$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}