{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BAYa class Assignment 2023\n",
    "\n",
    "In this assignment, your task will be to implement and analyze inference for the Probabilistic linear discriminant analysis (PLDA) model. This model was described in the corresponding [slides from BAYa class](http://www.fit.vutbr.cz/study/courses/BAYa/public/slides/2-Graphical%20Models.pdf). You will accomplish this task by completing this Jupyter Notebook, which already comes with a code generating the training data and some plotting functions for presenting the results. If you do not have any experience with Jupyter Notebook, the easiest way to start is to install Anaconda3, run Jupyter Notebook, and open this notebook downloaded from [BAYa_Assignment2023.ipynb](http://www.fit.vutbr.cz/study/courses/BAYa/public/notebooks/BAYa_Assignment2023.ipynb). You can also find some inspiration and pieces of code to reuse in the other [Jupyter Notebooks provided for this class](http://www.fit.vutbr.cz/study/courses/BAYa/public/notebooks).\n",
    "\n",
    "The Notebook is organized as follows:\n",
    "1. First comes a cell with a code of functions that will be later used for presenting the results and the learned models. You can skip this cell first as the use of the functions will be demonstrated later.\n",
    "2. Next comes a code that \"handcrafts\" some parameters of the PLDA model and implements the generative process assumed by the PLDA model. The code generates some artificial training data that you will use for PLDA model training. Please carefully read this code and the comments around it.\n",
    "3. Through this notebook, there are cells with instructions to fill in your implementations around the PLDA model. There are also fields with other tasks to accomplish and questions to answer. \n",
    "\n",
    "**Do not edit the code in the following cell for generating and presenting the training data!**\n",
    " $$\n",
    " \\DeclareMathOperator{\\E}{\\mathbb{E}}\n",
    "\\DeclareMathOperator{\\aalpha}{\\boldsymbol{\\alpha}}\n",
    "\\DeclareMathOperator{\\bbeta}{\\boldsymbol{\\beta}}\n",
    "\\DeclareMathOperator{\\NN}{\\mathbf{N}}\n",
    "\\DeclareMathOperator{\\ppi}{\\boldsymbol{\\pi}}\n",
    "\\DeclareMathOperator{\\mmu}{\\boldsymbol{\\mu}}\n",
    "\\DeclareMathOperator{\\SSigma}{\\boldsymbol{\\Sigma}}\n",
    "\\DeclareMathOperator{\\llambda}{\\boldsymbol{\\lambda}}\n",
    "\\DeclareMathOperator{\\diff}{\\mathop{}\\!\\mathrm{d}}\n",
    "\\DeclareMathOperator{\\zz}{\\mathbf{z}}\n",
    "\\DeclareMathOperator{\\ZZ}{\\mathbf{Z}}\n",
    "\\DeclareMathOperator{\\XX}{\\mathbf{X}}\n",
    "\\DeclareMathOperator{\\xx}{\\mathbf{x}}\n",
    "\\DeclareMathOperator{\\YY}{\\mathbf{Y}}\n",
    "\\DeclareMathOperator{\\NormalGamma}{\\mathcal{NG}}\n",
    "\\DeclareMathOperator{\\Tr}{Tr}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run this code! But there is no need to pay much attention to this cell at the first pass through the notebook\n",
    "\n",
    "%matplotlib inline \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as sps\n",
    "\n",
    "\n",
    "def rand_gauss(n, mu, cov):\n",
    "    \"\"\"\n",
    "    Sample n data points from multivariate Gaussian distribution with mean mu and covariance cov\n",
    "    \"\"\"\n",
    "    return np.atleast_2d(sps.multivariate_normal.rvs(mu, cov, n))\n",
    "\n",
    "def logpdf_gauss(x, mu, cov):\n",
    "    \"\"\"\n",
    "    Evaluation of the log probability density function for multivariate Gaussian with mean mu and covariance cov\n",
    "    \"\"\"\n",
    "    return sps.multivariate_normal.logpdf(x, mu, cov)\n",
    "   \n",
    "def gellipse(mu, cov, n=100, *args, **kwargs):\n",
    "    \"\"\"\n",
    "    Contour plot of 2D Multivariate Gaussian distribution.\n",
    "\n",
    "    gellipse(mu, cov, n) plots ellipse given by mean vector MU and\n",
    "    covariance matrix COV. Ellipse is plotted using N (default is 100)\n",
    "    points. Additional parameters can specify various line types and\n",
    "    properties. See description of matplotlib.pyplot.plot for more details.\n",
    "    \"\"\"\n",
    "    if mu.shape != (2,) or cov.shape != (2, 2):\n",
    "        raise RuntimeError('mu must be a two element vector and cov must be 2 x 2 matrix')\n",
    "\n",
    "    d, v = np.linalg.eigh(4 * cov)\n",
    "    d = np.diag(d)\n",
    "    t = np.linspace(0, 2 * np.pi, n)\n",
    "    x = v @ np.sign(d) @ np.sqrt(np.abs(d)) @ np.array([np.cos(t), np.sin(t)]) + mu[:,np.newaxis]\n",
    "    return plt.plot(x[0], x[1], *args, **kwargs)\n",
    "\n",
    "def probit(a):\n",
    "    from scipy.special import erfinv\n",
    "    return np.sqrt(2.0) * erfinv(2.0 * a - 1.0)\n",
    "\n",
    "def plot_det(tar, non, label=\"\",\n",
    "             axis = [0.2, 40, 0.2, 80],\n",
    "             xticks = [0.2, 0.5, 1, 2, 5, 10, 20, 35, 50, 65, 80],\n",
    "             yticks = [0.2, 0.5, 1, 2, 5, 10, 20, 35, 50, 65, 80],\n",
    "             **kwargs):\n",
    "        \"\"\"\n",
    "        plots DET curve \n",
    "        \"\"\"\n",
    "        tar = np.array(tar)\n",
    "        non = np.array(non)\n",
    "        ntrue=len(tar)\n",
    "        nfalse=len(non)\n",
    "        ntotal=ntrue+nfalse\n",
    "\n",
    "        Pmiss=np.zeros(ntotal+1,np.float32) # 1 more for the boundaries\n",
    "        Pfa=np.zeros_like(Pmiss)\n",
    "\n",
    "        scores=np.zeros((ntotal,2),np.float32)\n",
    "        scores[0:nfalse,0]=non\n",
    "        scores[0:nfalse,1]=0\n",
    "        scores[nfalse:ntotal,0]=tar\n",
    "        scores[nfalse:ntotal,1]=1\n",
    "        scores=scores[scores[:,0].argsort(),]\n",
    "\n",
    "        sumtrue=np.cumsum(scores[:,1])\n",
    "        sumfalse=nfalse - (np.arange(1,ntotal+1)-sumtrue)\n",
    "\n",
    "        Pmiss[0]=float(ntrue-ntrue) / ntrue\n",
    "        Pfa[0]=float(nfalse) / nfalse\n",
    "        Pmiss[1:]=(sumtrue+ntrue-ntrue) / ntrue\n",
    "        Pfa[1:]=sumfalse / nfalse\n",
    "        \n",
    "        idxeer=np.argmin(np.abs(Pfa-Pmiss))\n",
    "        EER = 0.5*(Pfa[idxeer]+Pmiss[idxeer])*100\n",
    "\n",
    "        plt.plot(probit(Pfa), probit(Pmiss), label=label + ' EER=%.2f%%' % EER, **kwargs)\n",
    "        plt.xticks(probit(np.array(xticks)/100), xticks)\n",
    "        plt.yticks(probit(np.array(yticks)/100), yticks)\n",
    "        plt.axis(probit(np.array(axis)/100))\n",
    "\n",
    "        plt.xlabel(\"FA [%]\", fontsize = 12)\n",
    "        plt.ylabel(\"Miss [%]\", fontsize = 12)\n",
    "        plt.grid(True)\n",
    "        plt.legend(loc='upper left', bbox_to_anchor=(1, 1))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PLDA generative process\n",
    "\n",
    "A PLDA model is often used to model speaker embeddings in the speaker verification context.\n",
    "Such embeddings are obtained by means of a neural network (i.e. ResNet, TDNN, etc.) which is trained for speaker classification.\n",
    "The neural network transforms variable-length input speech utterances into some fixed-length low-dimensional (i.e. 512, 1024) vector representations (e.g. the embeddings are the output of a hidden layer of the neural network).\n",
    "\n",
    "The PLDA model assumes the following two-step generative process for the embeddings (our observations):\n",
    "\n",
    "1.\n",
    "\\begin{equation}\n",
    "{\\mathbf{z}_s} \\sim \\mathcal{N}(\\mathbf{z}_s;\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}_{ac}) \\quad \\text{for } s=1, \\dots, S\n",
    "\\end{equation}\n",
    "\n",
    "where, $\\mathbf{z}_s$ is the continuous latent random variable representing the speaker-specific mean for speaker $s$, $\\boldsymbol{\\mu}$ is the global speaker mean, $\\boldsymbol{\\Sigma}_{ac}$ is the across-class (across-speaker) covariance matrix.\n",
    "\n",
    "\n",
    "2.\n",
    "\\begin{equation}\n",
    "{\\mathbf{x}_{sn}} \\sim \\mathcal{N}(\\mathbf{x}_{sn};\\mathbf{z}_{s},\\boldsymbol{\\Sigma}_{wc}) \\quad \\text{for } n=1, \\dots, N_s\n",
    "\\end{equation}\n",
    "\n",
    "where, $\\mathbf{x}_{sn}$ is the continuous random variable representing observations specific to speaker $s$ (per-speaker embeddings), $N_s$ is the number of observations (embeddings) for spearker $s$, $\\mathbf{z}_s$ is the mean for speaker $s$,  and $\\boldsymbol{\\Sigma}_{wc}$ is the within-class (within-speaker) covariance matrix, which is shared among (the same for) all speakers.\n",
    "\n",
    "\n",
    "Therefore, we assume that $S$ speaker means were generated from a Gaussian distribution $\\mathcal{N}(\\mathbf{z}_s;\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}_{ac})$, and then $N_s$ embeddings were generated for each of such speakers from the Gaussian distribution $\\mathcal{N}(\\mathbf{x}_{sn};\\mathbf{z}_{s},\\boldsymbol{\\Sigma}_{wc})$. This process can also be visulized in the Bayesian Network shown below.\n",
    "\n",
    "Obviously, this assumption is something we make up when defining our model, as the embeddings were generated by the neural network, and not by such PLDA model."
   ]
  },
  {
   "attachments": {
    "PLDA_BN_2.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<div>\n",
    "<img src=\"attachment:PLDA_BN_2.png\" width=\"500\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Joint probability:\n",
    "\n",
    "Given the definition of the PLDA model, we can now write the joint probability of all observed variables $\\XX$ and latent variables $\\ZZ$, where it should be straighforward to see that the joint probability factorizes per speaker (see the Bayesian network).\n",
    "\n",
    "Let $\\XX=[\\XX_1,\\XX_2,...,\\XX_S]$, where $\\XX_s = [\\xx_{s1}, \\xx_{s2}, \\dots, \\xx_{sN_s} ]$contain the set of training observations of speaker $s$. Similarly, $\\ZZ=[\\zz_1,\\zz_2,...,\\zz_S]$.\n",
    "\n",
    "Then, the joint probability is: \n",
    "\n",
    "$$P(\\XX, \\ZZ) \n",
    "= \\prod_{s=1}^S p(\\XX_s,\\zz_s)\n",
    "= \\prod_{s=1}^S \\left( p(\\zz_s) \\prod_{n=1}^{N_s} p(\\xx_{sn}|\\zz_s) \\right)$$\n",
    "\n",
    "$$\\ln P(\\XX, \\ZZ) \n",
    "= \\sum_{s=1}^S \\ln p(\\XX_s,\\zz_s)\n",
    "= \\sum_{s=1}^S \\ln p(\\zz_s) + \\sum_{n=1}^{N_s} \\ln p(\\xx_{sn}|\\zz_s)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Handcrafting the PLDA model\n",
    "\n",
    "In order to generate some artificial training data, we will handcraft a *ground truth* PLDA model.\n",
    "We will handcraft the global ground truth speaker mean $\\boldsymbol\\mu^{GT}$, and the covariance matrices $\\boldsymbol{\\Sigma}_{ac}^{GT}$ and $\\boldsymbol{\\Sigma}_{wc}^{GT}$. \n",
    "We will generate our training data using this PLDA model, and we hope to learn it back (or some close to it) during the PLDA model training. \n",
    "In order to be able to draw, visualize and interpret our models, we consider only a toy example with $D=2$ dimensional data.\n",
    "\n",
    "The cell below handcrafts the PLDA model and plots its parameters. In the plot, the dot corresponds to the global mean, the blue elipse is the coutour plot of $\\mathcal{N}(\\mathbf{z}_s;\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}_{ac}^{GT})$ and the red elipse is the countour plot of $\\mathcal{N}(\\mathbf{x}_{sn};\\mathbf{0},\\boldsymbol{\\Sigma}_{wc}^{GT})$. The contours correspond to twice the standard deviation of the data from the mean.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Do not edit this code!\n",
    "mu_gt =  np.array([1, 2]) #ground truth global mean\n",
    "Sigma_wc_gt = np.array([[1, 0.8], #ground truth within class covariance\n",
    "                     [0.8, 1]])\n",
    "\n",
    "Sigma_ac_gt = np.array([[10, -2], #ground truth across class covariance\n",
    "                     [-2, 1]])\n",
    "\n",
    "def plotPLDA(mu, Sigma_ac, Sigma_wc, marker_mu, line_style_Sigmas, name):\n",
    "    \"\"\"\n",
    "    plot of a PLDA model that shows: \n",
    "    the global mean mu in green,\n",
    "    the across-class covariance Sigma_ac in blue, \n",
    "    and the within-class covariance Sigma_wc centered around [0,0] in red.\n",
    "    Possible markers for mu are: '.','o','x' (see https://matplotlib.org/stable/api/markers_api.html)\n",
    "    Possible line_styles for the countours are: '--', ':', '-'\n",
    "    name refers to the name of the PLDA model to be displayed in the legend\n",
    "    \n",
    "    \"\"\"\n",
    "    assert marker_mu in {\".\" , \"o\" , \"x\"}\n",
    "    assert line_style_Sigmas in {\"--\" , \":\" , \"-\"}\n",
    "    \n",
    "    plt.plot(mu[0], mu[1], 'g'+marker_mu, ms=10, label='Mean '+name) \n",
    "    gellipse(mu, Sigma_ac, 100, 'b'+line_style_Sigmas, lw=2, label='Sigma_ac '+name)\n",
    "    gellipse(np.array([0,0]), Sigma_wc, 100, 'r'+line_style_Sigmas, lw=2, label='Sigma_wc '+name) #for mere visualization purposes, we center the within-class covariance on the origin (0,0)\n",
    "    plt.axis('equal')\n",
    "    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))\n",
    "\n",
    "plotPLDA(mu_gt,Sigma_ac_gt,Sigma_wc_gt,'.','--','GT')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling training data\n",
    "Once we have the global mean and the matrices $\\boldsymbol\\Sigma_{ac}^{GT}$ and $\\boldsymbol\\Sigma_{wc}^{GT}$, we can sample speakers and their corresponding embeddings.\n",
    "We sample $S=10$ speaker means and then their corresponding embeddings, where we sample a different number of embeddings per speaker. For now, we consider a rather extreme case with only one or two samples per speaker.\n",
    "\n",
    "Besides sampling the data, the code below plots the countour of $\\mathcal{N}(\\mathbf{z}_s;\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}_{ac}^{GT})$, the sampled speaker means $\\zz_s$, the countour of the per-speaker embedding distribution $\\mathcal{N}(\\mathbf{x}_{sn};\\zz_s,\\boldsymbol{\\Sigma}_{wc}^{GT})$ and the per-speaker embeddings sampled from this distribution.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Do not edit this code!\n",
    "def sample_from_PLDA(mu, Sigma_ac, Sigma_wc, S, min_samples_per_speaker, max_samples_per_speaker):\n",
    "    \"\"\"\n",
    "    Generate samples from a PLDA distribution, where each speaker can have a different number of samples:\n",
    "    mu: global mean\n",
    "    Sigma_ac: across-class covariance matrix\n",
    "    Sigma_wc: within-class covariance matrix\n",
    "    S: Number of speakers to be sampled\n",
    "    min_samples_per_speaker: minimum number of observations to be sampled for a speaker\n",
    "    max_samples_per_speaker: maximum number of observations to be sampled for a speaker\n",
    "    \n",
    "    Returns:\n",
    "    Z: two dimensional array where each row is a sampled speaker mean\n",
    "    X: list of two dimensional arrays, where rows of each array are the individual observations per speaker\n",
    "    \"\"\"\n",
    "    N = np.random.randint(min_samples_per_speaker, max_samples_per_speaker+1, S) # Number of observations per speaker\n",
    "    Z =  rand_gauss(S, mu, Sigma_ac) # speaker means\n",
    "    X = [] # Collection of all the X_s\n",
    "\n",
    "    # For each speaker\n",
    "    for ns, z in zip(N, Z):\n",
    "        X_s = rand_gauss(ns, z, Sigma_wc)\n",
    "        X.append(X_s)\n",
    "    return X, Z   #Recall, that we do not return N, which can be easily derived from X\n",
    "\n",
    "#Sampled training data for 10 speakers with only one or two samples per speaker:\n",
    "X, Z = sample_from_PLDA(mu_gt, Sigma_ac_gt, Sigma_wc_gt, S=10, min_samples_per_speaker=1, max_samples_per_speaker=2)\n",
    "\n",
    "gellipse(mu_gt, Sigma_ac_gt, 100, 'b', lw=2)\n",
    "for X_s, z in zip(X, Z):\n",
    "    p = plt.plot(X_s[:,0], X_s[:,1], '.', ms=2)\n",
    "    c = p[0].get_color()\n",
    "    plt.plot(z[0], z[1], '.', c=c, ms=10)\n",
    "    gellipse(z, Sigma_wc_gt, 100, c=c)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple maximum-likelihood estimate of parameters\n",
    "\n",
    "We can estimate the parameters of the PLDA model using the following formulas (which are the same as the ones used in the linear distriminant analysis or linear Gaussian classifier from SUR classes).\n",
    "\n",
    "$N =  \\sum_{s=1}^S N_s$\n",
    "\n",
    "$\\overline{\\mmu} = \\frac{1}{N} \\sum_{s=1}^S \\sum_{n=1}^{N_s} \\xx_{sn}$\n",
    "\n",
    "$\\overline{\\mmu}_s = \\frac{1}{N_s} \\sum_{n=1}^{N_s} \\xx_{sn}$\n",
    "\n",
    "$\\overline{\\SSigma}_{ac} = \\frac{1}{N} \\sum_{s=1}^S N_s \\left(\\overline{\\mmu}_s-\\overline{\\mmu}\\right)\\left(\\overline{\\mmu}_s-\\overline{\\mmu}\\right)^T$\n",
    "\n",
    "$\\overline{\\SSigma}_{wc} = \\frac{1}{N} \\sum_{s=1}^S N_s \\underbrace{\\left(\\frac{1}{N_s} \\sum_{n=1}^{N_s} \\left(\\xx_{sn}-\\overline{\\mmu}_s\\right)\\left(\\xx_{sn}-\\overline{\\mmu}_s\\right)^T\\right)}_{\\overline{\\Sigma}_s}$\n",
    "\n",
    "\n",
    "\n",
    "### Task 1 \n",
    "\n",
    "- Implement these simple maximum-likelihood estimates for the PLDA parameters. To do so, complete the *simple_PLDA_estimate* function defined below.\n",
    "- Next, plot (in the same plot) the obtained PLDA parameters and the ground truth PLDA model parameters. Use the function *plotPLDA* defined above with different markers and line styles for a proper visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_PLDA_estimate(X):\n",
    "    \"\"\"\n",
    "    Estimates the PLDA parameters using the simple maximum-likelihood approach:\n",
    "    - X: whole set of training embeddings (for all speakers) as a list of two dimensional arrays, \n",
    "         where rows of each array are the individual observations per speaker\n",
    "    \n",
    "    Returns:\n",
    "    - mu: global mean\n",
    "    - Sigma_ac: across-class covariance matrix\n",
    "    - Sigma_wc: within-class covariance matrix\n",
    "    \"\"\"\n",
    "    \n",
    "    # your code goes here\n",
    "    \n",
    "    return mu, Sigma_wc, Sigma_ac\n",
    "\n",
    "#Make use of the following variable names\n",
    "#mu_simple1, Sigma_wc_simple1, Sigma_ac_simple1 = simple_PLDA_estimate(X)\n",
    "\n",
    "\n",
    "\n",
    "#code for plots goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PLDA Expectation Maximization training\n",
    "\n",
    "With EM, we can get better estimate of the parameters than with the *naive* simple maximum-likelihood estimates.\n",
    "\n",
    "Your first task here will be to derive some of the math related to the expectation-maximization updates for PLDA model training.\n",
    "Below we provide the framework for such derivations.\n",
    "\n",
    "\n",
    "## Summary of the EM algorithm\n",
    "\n",
    "The EM algorithm makes use of the following formula to find the parameters that maximize the likelihood of the data:\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$\\ln p(\\mathbf{\\XX}|\\boldsymbol{\\eta}) = \n",
    "\\underbrace{\\sum_{\\ZZ}q(\\ZZ) \\ln p(\\XX,\\ZZ)|\\boldsymbol{\\eta})}_{\\mathcal{Q}(q(\\ZZ),\\eta)}\n",
    "\\underbrace{-\\sum_{\\ZZ}q(\\ZZ) \\ln q(\\ZZ)}_{H(q(\\ZZ))}\n",
    "\\underbrace{-\\sum_{\\ZZ} q(\\ZZ) \\ln \\frac{p(\\ZZ | \\XX,\\boldsymbol{\\eta})}{q(\\ZZ)}}_{D_{KL}(q(\\ZZ)||p(\\ZZ|\\XX,\\eta)}$\n",
    "\n",
    "The steps for the EM algorithm are:\n",
    "1. Initialize parameters of the model (e.g. randomly or to constant values).\n",
    "2. E-step, set $q(\\ZZ):=p(\\ZZ|\\XX,\\eta)$, to make the Kullback-Liebler divergence 0\n",
    "3. M-step, having fixed $q(\\ZZ)$, optimize the parameters of the PLDA model to maximize the auxiliary function $\\mathcal{Q}$ (and maximize therefore the likelihood of the data)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## E-step\n",
    "In the E-step, we need to set $q(\\ZZ):=p(\\ZZ|\\XX,\\eta)$. \n",
    "By looking at the Bayesian network we can see that the posterior distribution of the latent variable  factorizes as $p(\\ZZ|\\XX,\\eta)= \\prod_s p(\\mathbf{z}_s|\\mathbf{X}_s,\\eta)$.  Therefore $q(\\ZZ)=\\prod_s q(\\zz_s)$ where we set $ q(\\zz_s):=  p(\\mathbf{z}_s|\\mathbf{X}_s,\\eta)$, which can be calculated as:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$$ p(\\zz_s | \\XX_s, \\eta) \n",
    "=  \\mathcal{N}(\\zz_s;\\mmu_s,\\SSigma_s)$$ \n",
    "\n",
    "$$ \\mmu_s = \\SSigma_s \\left(\\SSigma_{ac}^{-1}\\mmu + \\SSigma_{wc}^{-1} \\sum_{n=1}^{N_s}\\xx_{sn}\\right)  \\hspace{2cm} \\SSigma_s = \\left(\\SSigma_{ac}^{-1} + N_s \\SSigma_{wc}^{-1} \\right)^{-1}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2: \n",
    "Complete the derivations of the E-step to obtain the formulas above. Start from the expression given below (but check the tips given after it)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "\\ln p(\\zz_s | \\XX_s, \\eta) \n",
    "&= \\ln p(\\XX_s,\\zz_s) + const. \\\\\n",
    "&= \\ln \\left[ p(\\zz_s) \\prod_{n=1}^{N_s} p(\\xx_{sn}|\\zz_s) \\right] + const. \\\\\n",
    "&... \\color{red}{write\\ your\\ derivations\\ here}\\\\\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Tip: </b> To complete the derivation, it might be useful to understand what is the \"completion of squares\" method:\n",
    "\n",
    "\n",
    "For any Gaussian distribution $\\mathcal{N}(\\mathbf{y};\\mmu_o,\\SSigma_o)$, the following holds: \n",
    "\n",
    "$$\\ln \\mathcal{N}(\\mathbf{y};\\mmu_o,\\SSigma_o) = -\\frac{D}{2} \\ln (2\\pi)-\\frac{1}{2} \\ln|\\SSigma_o|-\\frac{1}{2} (\\mathbf{y}-\\mmu_o)^T\\SSigma_o^{-1}(\\mathbf{y}-\\mmu_o) $$\n",
    "\n",
    "Given that it is a function of the random variable $\\mathbf{y}$, we can consider:\n",
    "    \n",
    "$$= -\\frac{1}{2} \\mathbf{y}^T \\SSigma_o^{-1} \\mathbf{y} + \\mathbf{y}^T \\SSigma_o^{-1}\\mmu_o + const.$$\n",
    "    \n",
    "where $const$ is a constant encompassing all terms independent of $\\mathbf{y}$.\n",
    "    \n",
    "Therefore, if you obtain an expression in the form:\n",
    "\n",
    "$$-\\frac{1}{2} \\mathbf{y}^T A \\mathbf{y} + \\mathbf{y}^T B$$\n",
    "\n",
    "and you know that it corresponds to a valid probability distribution (up to the missing constant term) then it corresponds to the log of a (unnormalized) Gaussian distribution where $A$ and $B$ will be the terms $A=\\SSigma_o^{-1}$ and $B=\\SSigma_o^{-1}\\mmu_o$. \n",
    "That is, it corresponds to $\\ln \\mathcal{N}(\\mathbf{y};A^{-1}B, A^{-1})$.\n",
    "</div>\n",
    "    \n",
    "\n",
    "    \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## M-step\n",
    "In the M-step, we keep $q(\\mathbf{z}_s)$ fixed and we optimize the parameters of the model to maximize the auxliliary function.\n",
    "\n",
    "### Task 3: \n",
    "Complete the derivation for the M-step.\n",
    "**Explain** the different steps taken.\n",
    "Start from the expression below, where the first steps are given, as well as the final solution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\small\n",
    "\\begin{align}\n",
    "\\mathcal{Q} \n",
    "&= \\int q(\\ZZ) \\ln p(\\XX,\\ZZ) \\diff \\ZZ \\\\\n",
    "&= \\int \\dots \\int \\left(\\prod_{s=1}^S q(\\zz_s)\\right) \\sum_{s=1}^S \\left(\\ln p(\\zz_s) + \\sum_{n=1}^{N_s} \\ln p(\\xx_{sn}|\\zz_s)\\right) \\diff\\zz_1 \\dots \\diff \\zz_S \\\\\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "Given the factorization over components (see slide 28 from [EM algorithm](https://www.fit.vutbr.cz/study/courses/BAYa/public/slides/3-EM%20algorithm.pdf)):\n",
    "\n",
    "$\n",
    "\\small\n",
    "\\begin{align}\n",
    "\\mathcal{Q}&= \\sum_{s=1}^S \\int q(\\zz_s) \\left(\\ln p(\\zz_s) + \\sum_{n=1}^{N_s} \\ln p(\\xx_{sn}|\\zz_s)\\right) \\diff\\zz_s\\\\\n",
    "& ... \\color{red}{write\\ your\\ derivations\\ here\\ to\\ obtain:}\\\\\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "$\n",
    "\\scriptsize\n",
    "\\begin{align}\n",
    "&\\mathcal{Q} = -\\frac{1}{2} \\sum_{s=1}^S \\left(\n",
    "-\\ln |\\SSigma_{ac}^{-1}| + \\Tr\\left(\\SSigma_s \\SSigma_{ac}^{-1}\\right) +\\left(\\mmu_s-\\mmu\\right)^T\\SSigma_{ac}^{-1}\\left(\\mmu_s-\\mmu\\right) \n",
    "+ \\sum_{n=1}^{N_s}\\left(-\\ln |\\SSigma_{wc}^{-1}| + \\Tr\\left(\\SSigma_s\\SSigma_{wc}^{-1}\\right) +\\left(\\xx_{sn}-\\mmu_s\\right)^T\\SSigma_{wc}^{-1}\\left(\\xx_{sn}-\\mmu_s\\right)\\right)\\right) + const. \\\\\n",
    "\\end{align}\n",
    "$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-info\"><b>Tip: </b> \n",
    "Given a probability density function $q(\\mathbf{y})$, we define the expected values as:\n",
    "\n",
    "$$ \\E[\\mathbf{y}] = \\int q(\\mathbf{y}) \\mathbf{y} d\\mathbf{y} $$\n",
    "\n",
    "$$ \\E[f(\\mathbf{y})] = \\int q(\\mathbf{y}) f(\\mathbf{y}) d\\mathbf{y} $$\n",
    "\n",
    "The expected values have (among others) the following properties:\n",
    "   \n",
    "$\\E[X+Y]=\\E[X]+\\E[Y]$\n",
    "    \n",
    "$\\E[aX]=a\\E[X]$\n",
    "    \n",
    "For a Gaussian distribution $q(\\mathbf{y})=\\mathcal{N}(\\mathbf{y};\\mmu_o,\\SSigma_o)$, it holds:\n",
    "\n",
    "(1) $\\E[\\mathbf{y}] = \\mmu_o$\n",
    "\n",
    "(2) $\\E[\\mathbf{y}\\mathbf{y}^T]=\\SSigma_o+\\mmu_o\\mmu_o^T$\n",
    "\n",
    "(3) $\\E[\\mathbf{y}^TA\\mathbf{y}]=Tr(A\\SSigma_o)+\\mmu_o^TA\\mmu_o$\n",
    "\n",
    "where the operator $\\Tr$ refers to $trace$, the sum of elements on the main diagonal of a matrix, which has the following properties:\n",
    "\n",
    "$\\Tr(A+B)=\\Tr(A)+\\Tr(B)$\n",
    "\n",
    "$\\Tr(ABC)=\\Tr(CAB)=\\Tr(BCA)$\n",
    "\n",
    "In the derivations, you can make use of the results and properties defined above. If used, reference them in the explanations of the derivation.\n",
    "    \n",
    "Most of these $tricks$ and many others can be found in [The matrix cookbook]( https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf). If you use this book for any step of the derivations, reference the corresponding formula in the text. \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4\n",
    "Now, using the expression of the auxiliary function $\\mathcal{Q}$ provided above, derive the updates of $\\mmu$ and $\\SSigma_{ac}$ and $\\SSigma_{wc}$.\n",
    "Again, we provide the solution for these updates and you need to take the derivative of $\\mathcal{Q}$ with respect to each of the PLDA parameters, set it equal to 0 and solve for the corresponding parameters to get to such solutions.\n",
    "\n",
    "Recall, that even if you failed to complete the previous derivations you can proceed with this one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$\n",
    "\\begin{align}\n",
    "&\\frac{\\partial \\mathcal{Q}}{\\partial \\mmu}\n",
    "= \\color{red}{write\\ your\\ derivations\\ here}\\\\\n",
    "&\\implies \\mmu := \\frac{1}{S} \\sum_{s=1}^S \\mmu_s\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "&\\frac{\\partial \\mathcal{Q}}{\\partial \\SSigma_{ac}^{-1}}\n",
    "=\\color{red}{write\\ your\\ derivations\\ here}\\\\\n",
    "&\\implies \\SSigma_{ac} := \\frac{1}{S} \\sum_{s=1}^S \\SSigma_s + \\frac{1}{S} \\sum_{s=1}^S \\left(\\mmu_s-\\mmu\\right)\\left(\\mmu_s-\\mmu\\right)^T\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "&\\frac{\\partial \\mathcal{Q}}{\\partial \\SSigma_{wc}^{-1}}\n",
    "= \\color{red}{write\\ your\\ derivations\\ here}\\\\\n",
    "&\\implies \\SSigma_{wc} := \\frac{1}{\\sum_{s=1}^S N_s} \\sum_{s=1}^S N_s \\left(\\SSigma_s + \\frac{1}{N_s} \\sum_{n=1}^{N_s} \\left(\\xx_{sn}-\\mmu_s\\right)\\left(\\xx_{sn}-\\mmu_s\\right)^T\\right)\n",
    "\\end{align}\n",
    "$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Tip: </b> \n",
    "Note, that to obtain the updates of the covance matrices we are suggesting to take the derivative the auxiliary function $\\mathcal{Q}$ with respect to the inverse of the covariance matrices. This results in somewhat simpler derivation of the updates. \n",
    "But (if you want to show off), you can start with the derivative with respect to the (non-inverse) covariance matrices, which leads to the same result.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 5\n",
    "Using the formulas for the updates of the E and M step provided above, implement the EM algorithm for PLDA model training.\n",
    "\n",
    "- Initialize the PLDA parameters using the simple ML estimates you obtained above.\n",
    "- Fill in your implementation for the function *p_z_given_X*, which calculates the parameters $\\mmu_s$, $\\SSigma_s$ of the posterior distribution $p(\\zz_s|\\XX_s) = \\mathcal{N}(\\zz_s;\\mmu_s,\\SSigma_s)$ (E-step). Read carefully the information about the format of the input and output data.\n",
    "- Implement the EM algorithm as the function *EM_PLDA_estimate*. Again, check the template of such function and the format for the inputs and outputs.\n",
    "- Run the algorithm for 100 iterations. \n",
    "- Plot (in the same plot) using again the function *plotPLDA*:\n",
    "    - The parameters of the PLDA model trained with EM\n",
    "    - The parameters of the PLDA model obtained with simple ML\n",
    "    - The parameters of the ground truth PLDA model \n",
    "\n",
    "Answer the following questions:\n",
    "1. Is there something that the simple ML algorithm fails to do well as compared to the EM algorithm?\n",
    "2. How can you draw such conclusion from the plot? \n",
    "3. How do you explain the different behaviour of the two training algorithms?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def p_z_given_X(X, mu, Sigma_ac, Sigma_wc):\n",
    "    \"\"\"\n",
    "    For each speaker 's' in the input data X, it calculates the parameters of the posterior distribution \n",
    "    p(z_s|X_s)= N(z_s|mu_s,Sigma_s). For each speaker such parameters are mean (mu_s) \n",
    "    and covariance matrix (Sigma_s). The function returns the list of such means (one per speaker) \n",
    "    and the list of such covariance matrices (one per speaker).\n",
    "    \n",
    "    Inputs:\n",
    "    - X: whole set of embeddings (for all speakers) \n",
    "    - mu: global mean\n",
    "    - Sigma_ac: across-class covariance matrix\n",
    "    - Sigma_wc: within-class covariance matrix   \n",
    "    \n",
    "    Returns:\n",
    "    - mu_s: list of per-speaker posterior distribution means \n",
    "    - Sigma_s: list of per-speaker posterior distribution means covariance matrices\n",
    "    \"\"\"\n",
    "    \n",
    "    # Your code goes here\n",
    "    \n",
    "    return mu_s, Sigma_s\n",
    "    \n",
    "    \n",
    "    \n",
    "def EM_PLDA_estimate(X, mu_init, Sigma_ac_init, Sigma_wc_init, niters):\n",
    "    \"\"\"\n",
    "    Runs expectation-maximization algorithm for PLDA parameter estimation, where the input parameters are:\n",
    "    - X: whole set of embeddings (for all speakers)\n",
    "    - mu_init: initialization for the global mean\n",
    "    - Sigma_ac_init: initialization for the across-class covariance\n",
    "    - Sigma_wc_init: initialization for the within-class covariance\n",
    "    - niters: number of EM iterations \n",
    "    \n",
    "    Returns the EM estimates of:\n",
    "    - mu: global mean\n",
    "    - Sigma_ac: across-class covariance matrix\n",
    "    - Sigma_wc: within-class covariance matrix\n",
    "    \"\"\"\n",
    "\n",
    "    # Your code goes here\n",
    "\n",
    "    return mu, Sigma_wc, Sigma_ac\n",
    "\n",
    "\n",
    "# Use the following variable names for storing the PLDA model trained with EM in this task:\n",
    "# mu_EM1, Sigma_wc_EM1, Sigma_ac_EM1 = EM_PLDA_estimate()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#code for plots goes here\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 6\n",
    "\n",
    "Using the function *sample_from_PLDA*, generate a new training set from the ground truth PLDA, where you sample **1000** speakers, with 1 to 2 samples per speaker. Using the new training set:\n",
    "\n",
    "- Re-estimate the parameters of the PLDA using both approaches, the Simple-ML and the EM algorithm. \n",
    "- Plot the parameters obtained with both methods, together with the ground truth PLDA parameters (as done before, using plotPLDA).\n",
    "\n",
    "Questions:\n",
    "1. How do the new parameter estimations compare to the previous exercise? Are parameters better estimated? If so, which ones, for which method and why? (answering only \"because we have more data\" is not enough)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "#X, Z = #sample_from_PLDA() 1000 speakers, with 1 to 2 samples per speaker\n",
    "\n",
    "# Use the following variable names for storing the PLDA model trained with simple ML in this task:\n",
    "# mu_simple2, Sigma_wc_simple2, Sigma_ac_simple2\n",
    "\n",
    "# Use the following variable names for storing the PLDA model trained with EM in this task:\n",
    "# mu_EM2, Sigma_wc_EM2, Sigma_ac_EM2\n",
    "\n",
    "#code for plots goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 7\n",
    "Now, repeat the same exercise with a training set where you sample 1000 speakers, with **1 to 100** samples per speaker. Show the coresponding plots and answer the same questions for this new scenario.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#X, Z = #sample_from_PLDA() 1000 speakers, with 1 to 100 samples per speaker\n",
    "\n",
    "\n",
    "# Use the following variable names for storing the PLDA model trained with simple ML in this task:\n",
    "# mu_simple3, Sigma_wc_simple3, Sigma_ac_simple3\n",
    "\n",
    "# Use the following variable names for storing the PLDA model trained with EM in this task:\n",
    "# mu_EM3, Sigma_wc_EM3, Sigma_ac_EM3\n",
    "\n",
    "\n",
    "#code for plots goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PLDA Scoring\n",
    "\n",
    "Now we will perform (simulate) speaker verification experiments, where the PLDA model will be used to evaluate speaker verification scores.\n",
    "\n",
    "In each speaker verification experiment, we will consider independent *trials*. Each trial will consist of (one or) several enrollment embeddings $\\XX_e=[\\xx_1,\\xx_2,...,\\xx_{N_{e}}]$  generated from the same speaker and one test embedding $\\xx_t$. Our task will be to answer the question of whether the test and enrollment embeddings come from the same speaker (so called *target trial*) or different speakers (*non-target trial*).\n",
    "\n",
    "\n",
    "More formally, let $\\mathcal{H}_s$ correspond to the hypothesis that all embeddings $\\XX_e$ and $\\xx_t$ are generated by the *same speaker*. \n",
    "Let $\\mathcal{H}_d$ correspond to the hypothesis that the test embedding $\\xx_t$ was generated by a *different speaker* than $\\XX_e$.\n",
    "The Bayesian networks below describe the generative process corresponding to the two hypotesis, if we assume that the embeddings were generated according to the PLDA model.\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "BN_PLDA_Hd_Xe3.png": {
     "image/png": 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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table><tr>\n",
    "<td> \n",
    "  <p align=\"center\" style=\"padding: 10px\">\n",
    "    <img src=\"attachment:Hs_z.png\" width=\"400\">\n",
    "    <br>\n",
    "    <em style=\"color: grey\">Same speaker Hypothesis</em>\n",
    "  </p> \n",
    "</td>\n",
    "<td> \n",
    "  <p align=\"center\">\n",
    "    <img src=\"attachment:BN_PLDA_Hd_Xe3.png\" width=\"400\">\n",
    "    <br>\n",
    "    <em style=\"color: grey\">Different speaker Hypothesis</em>\n",
    "  </p> \n",
    "</td>\n",
    "</tr></table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Bayesian networks, we can easily see that the joint likelihood of the embeddings $\\xx_t,\\XX_e$ for the two the hypothesis can be evaluated as: \n",
    "\n",
    "$$p(\\xx_t, \\XX_e|\\mathcal{H}_s)=\\int p(\\xx_t|\\zz)p(\\XX_e|\\zz)p(\\zz)\\diff\\zz$$\n",
    "$$p(\\xx_t, \\XX_e|\\mathcal{H}_d)= p(\\xx_t)p(\\XX_e) = \\int p(\\xx_t|\\zz_t)p(\\zz_t)\\diff\\zz_t\\int p(\\XX_e|\\zz_e)p(\\zz_e)\\diff\\zz_e$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intuitively, we could see the task of deciding whether the trial is a *target trial* or *non-target trial* as a binary classification task, where the two classes are the two hypothesis $\\mathcal{H}_s, \\mathcal{H}_d$.\n",
    "\n",
    "Using Bayes rule, the posterior probability of the same-speaker hypothesis is:\n",
    "\n",
    "$$P(\\mathcal{H}_s|\\xx_t, \\XX_e) = \\frac{p(\\xx_t, \\XX_e|\\mathcal{H}_s) P(\\mathcal{H}_s)}{p(\\xx_t, \\XX_e|\\mathcal{H}_s) P(\\mathcal{H}_s) + p(\\xx_t, \\XX_e|\\mathcal{H}_d) P(\\mathcal{H}_d)} = \\sigma\\left(LLR(\\xx_t, \\XX_e)+\\ln\\frac{P(\\mathcal{H}_s)}{P(\\mathcal{H}_d)}  \\right),$$\n",
    "\n",
    "where $P(\\mathcal{H}_s)$ and $P(\\mathcal{H}_d)=1-P(\\mathcal{H}_s)$ are the prior probabilities of the two hypothesis (classes), $\\sigma$ is the logistic sigmoid function and $LLR$ stands for log-likelihood ratio:\n",
    "\n",
    "$$LLR(\\xx_t, \\XX_e) = \\ln\\frac{p(\\xx_t, \\XX_e|\\mathcal{H}_s)}{p(\\xx_t, \\XX_e|\\mathcal{H}_d)}.$$\n",
    "\n",
    "However, we are not going to treat the verification task as a binary classification task considering specific priors for the two hypotheses. Instead, we will evaluate the verification performance in terms of equal error rate (EER) and using detection error tradeoff (DET) curves, as is usual in the case of verification (detection) tasks. \n",
    "For this purpose we will only need to evaluate the $LLR$ score. This score is higher (positive) when $\\mathcal{H}_s$ is more likely and lower (negative) when $\\mathcal{H}_d$ is more likely.\n",
    "\n",
    "It is not easy to directly evaluate the likelihoods $p(\\xx_t, \\XX_e|\\mathcal{H}_s)$ and $p(\\xx_t, \\XX_e|\\mathcal{H}_d)$ from the numerator and denominator of the $LLR$, but the $LLR$ can be reformulated in terms of quantities that we already know how to evaluate:\n",
    "$\n",
    "\\begin{align}\n",
    "LLR(\\xx_t, \\XX_e) \n",
    "&= \\ln\\frac{p(\\xx_t, \\XX_e|\\mathcal{H}_s)}{p(\\xx_t, \\XX_e|\\mathcal{H}_d)}\n",
    "= \\ln\\frac{\\int p(\\xx_t|\\zz)p(\\XX_e|\\zz)p(\\zz)\\diff\\zz}{p(\\xx_t)p(\\XX_e)}\n",
    "= \\ln\\frac{\\int p(\\xx_t|\\zz)\\frac{p(\\zz|\\XX_e)p(\\XX_e)}{p(\\zz)}p(\\zz)\\diff\\zz}{p(\\xx_t)p(\\XX_e)}\n",
    "= \\ln\\frac{\\int p(\\xx_t|\\zz)p(\\zz|\\XX_e)\\diff\\zz}{\\int p(\\xx_t|\\zz)p(\\zz)\\diff\\zz}\n",
    "\\color{grey}{= \\ln\\frac{p(\\xx_t|\\XX_e)}{p(\\xx_t)}} \\\\\n",
    "&= \\ln\\frac{\\int \\mathcal{N}(\\xx_t;\\zz,\\SSigma_{wc})\\mathcal{N}(\\zz;\\mu_e,\\SSigma_e)\\diff\\zz}{\\int \\mathcal{N}(\\xx_t;\\zz,\\SSigma_{wc})\\mathcal{N}(\\zz;\\mmu,\\SSigma_{ac})\\diff\\zz}\n",
    "= \\ln\\frac{\\mathcal{N}(\\xx_t;\\mmu_e,\\SSigma_{wc}+\\SSigma_e)}{\\mathcal{N}(\\xx_t;\\mmu,\\SSigma_{wc}+\\SSigma_{ac})}\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "where the $p(\\zz|\\XX_e)=\\mathcal{N}(\\zz;\\mu_e,\\SSigma_e)$ is the posterior distribution of latent variable given the enrollment embeddings, which is estimated by the formula given in the E-step. \n",
    "Note that $p(\\xx_t|\\XX_e)$ is the posterior predictive distribution of the test embedding $\\xx_t$ given that is comes from the same speaker as the enrollment embeddings $\\XX_e$ and $p(\\xx_t)$ is the distribution of $\\xx_t$  independently generated from a random speaker.\n",
    "In other words, the $LLR$ tells us whether it is more likely that the test embedding comes from the same speaker as the enrollment embeddings $\\XX_e$ or from a random speaker.\n",
    "\n",
    "\n",
    "To analyze and compare the performance of different systems, we use the DET curve. This curve plots miss rate in the y-axis and false alarm raten in the x-axis (using probit scales).\n",
    "The point in the DER curve where miss and false alarm rate are the same is called the EER.\n",
    "The function to produce such plots is provided in the first (code) cell of this BAYa project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 8\n",
    "\n",
    "Your task now will be to implement such LLR scoring function, which we will later use it to evaluate speaker verification trials. \n",
    "\n",
    "- Implement the function evaluating the log-likelihood ratio scores. To do so, use the template of the function LLRs defined below and pay attention to the definition of its inputs and outputs.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LLRs(x_test, X_enrol, mu, Sigma_ac, Sigma_wc):\n",
    "    \"\"\"Given a PLDA model, evaluates log-likelihood ratio scores for a set of N verification trials.\n",
    "    Each trial consists of one test embedding and set of enrollment embeddings.\n",
    "    - x_test: two dimensional array with N rows, where each row contains a test embedding from one trial \n",
    "    - X_enrol: list of N two dimensional numpy arrays. Each element in the list contains a set \n",
    "        of enrollment embeddings from one trial. Embeddings from each enrollment set are stored\n",
    "        in rows of a two dimensional numpy array. \n",
    "    - mu: PLDA global mean\n",
    "    - Sigma_ac: PLDA across-class covariance matrix\n",
    "    - Sigma_wc: PLDA within-class covariance matrix  \n",
    "    \n",
    "    Returns: \n",
    "    - one dimensional numpy array containing N log-likelihood ratios.\n",
    "    \"\"\"\n",
    "    #Your code goes here\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 9\n",
    "\n",
    "Now you will generate (artificial) trials by sampling enrollment and test embeddings from the ground truth PLDA model and you will evaluate the speaker verification scores for these trials.\n",
    "\n",
    "Your tasks are:\n",
    "- Generate 20 enrollment embeddings for one random speaker.\n",
    "- Generate one test embedding from the same speaker and one test embedding from a different random speaker.\n",
    "- Using these generated embeddings, create now four trials:\n",
    "    - Single-enrollment, target trial\n",
    "    - Single-enrollment, non-target trial\n",
    "    - Multi-enrollment, target trial\n",
    "    - Multi-enrollment, non-target trial\n",
    "\n",
    "    where single-enrollment refers to the case when $\\XX_e$ contains a single embedding (selected from the 20 generated enrollment embeddings) and multi-enrollment refers to the case when $\\XX_e$ contains all 20 generated enrollment embeddings.\n",
    "- Evaluate the $LLR$ score for each such trial using the function you defined above and the *EM3* PLDA model (the PLDA model trained with EM using 1000 speakers and 1 to 100 samples per speakers). \n",
    "\n",
    "Questions:\n",
    "1. Comment on the obtained $LLR$ values, what values did you expect and why? \n",
    "2. Are the values that you obtained in agreement with those expectations? Why?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code for task 9 goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 10\n",
    "\n",
    "- Plot (into a single plot):\n",
    "    - Embeddings:\n",
    "        - All of the enrollment embeddings using black marker \".\"\n",
    "        - The single enrollment embedding using black marker \"x\"\n",
    "        - The target speaker test embedding as a green \"*\"\n",
    "        - The non-target speaker test embedding as a red \"*\"\n",
    "    - The contour of the marginal distribution $p(\\xx_t)$ in black color (use gellipse function)\n",
    "    - The contour of posterior distribution of the latent variable $p(\\zz|\\XX_e)$ for:\n",
    "        - Single-enrollment $\\XX_e$, blue color, dotted line\n",
    "        - Multi-enrollment $\\XX_e$, magenta color, dotted line  \n",
    "    - The contour of the posterior predictive distribution $p(\\xx_t|\\XX_e)$ for:\n",
    "        - Single-enrollment $\\XX_e$, blue color\n",
    "        - Multi-enrollment $\\XX_e$, magenta color\n",
    "        \n",
    "Questions:\n",
    "1. How do the posterior distributions $p(\\zz|\\XX_e)$ differ for the single and multi enrollment cases? Why?\n",
    "2. How do the posterior predictive distributions $p(\\xx_t|\\XX_e)$ differ for the single and multi enrollment cases? Why?\n",
    "3. For each of the trials from the previous tasks, look at the evaluated $LLR$ scores. Comment on how do these scores relate to what you see in this plot. Consider how the different embeddings fit different distributions in the plot. Can you see on the plot why different $LLRs$ have higher or lower values? \n",
    "\n",
    "<div class=\"alert alert-block alert-info\"><b>Tip: </b> \n",
    "Note that the trials you generated in task 9 were randomly generated, and you can get unlucky and get unintuitive results. \n",
    "You might want to re-generate the trials several times (and re-run related tasks 9 and 10) to assure that you get propper understanding.\n",
    "If you want, you can include outcomes of multiple such runs into the notebook and comment on the different outcomes.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Your code for the plot goes here\n",
    "\n",
    "#recall, that the contours can be plotted using: \n",
    "#gellipse(mu, Sigma, 100, ':', c='b', label='Sigma')\n",
    "# where ':' stands for for dotted line and 'b' for blue\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Speaker verification experiments\n",
    "\n",
    "Now, we will simulate speaker verification experiments involving 1000 target and 1000 non-target trials. \n",
    "In the cell below, we generate:\n",
    "- 10 enrollment embeddings per-speaker for 1000 different speakers. \n",
    "    - All 10 embeddings will be used for the multi-enrollment trials (variable x_enroll10)\n",
    "    - We select only one of these embeddings per-speaker to create the single-enrollment trials (x_enroll1)\n",
    "- 1000 target test embeddings, each corresponding to one of the enrollment speakers to form the target trials (x_test_target) \n",
    "- 1000 non-target test embeddings from 1000 random speakers to form the non-target trials (x_test_nontar)\n",
    "\n",
    "Note that each of the target/non-target test embedding is paired with only one enrollment speaker to generate a single trial.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Enrollment embedding and trial set generation. Do not edit this field!\n",
    "\n",
    "# Note, that all generated embeddings are stored in a form compatible with the definition \n",
    "# of the LLR given above: the test embeddings are stored in rows of two dimensional arrays \n",
    "# and the enrollment embeddings (even the single-enrollment ones) are stored in a list of \n",
    "# two dimensional numpy arrays, where each element in the list contains a set of enrollment \n",
    "# embeddings.\n",
    "\n",
    "# we sample 11 observations for 1000 speakers:\n",
    "X_tar = sample_from_PLDA(mu_gt, Sigma_ac_gt, Sigma_wc_gt, S=1000, min_samples_per_speaker=11, max_samples_per_speaker=11)[0] \n",
    "\n",
    "# for multi-enrollment, we use the first 10 embeddings per-speaker:\n",
    "x_enroll10    = [xs[:10] for xs in X_tar] \n",
    "# for single-enrollment, we use the first embedding per-speaker:\n",
    "x_enroll1     = [xs[:1] for xs in X_tar] \n",
    "\n",
    "# the last embedding per-speaker is used as the target test embedding:\n",
    "x_test_target = np.array([xs[-1] for xs in X_tar]) \n",
    "\n",
    "# we generate a non-target embeddings from different random speakers:\n",
    "x_test_nontar = np.vstack(sample_from_PLDA(mu_gt, Sigma_ac_gt, Sigma_wc_gt, 1000, 1, 1)[0]) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 11\n",
    "\n",
    "Let's first consider the single-enrollment trials. Your task is:\n",
    "- Evaluate the $LLRs$ for target trials (target scores) by scoring the test embeddings (x_test_target) against the corresponding enrollment embedding set x_enroll1.\n",
    "- Evaluate the $LLRs$ for non-target trials (non-target scores) by scoring the test embeddings (x_test_nontar) against the corresponding enrollment embedding set x_enroll1.\n",
    "- Plot the histogram of such scores\n",
    "\n",
    "Questions:\n",
    "1. What can you see in the histograms? Are the verification scores useful to discriminate between target and non-target trials?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 12\n",
    "\n",
    "- Repeat task 11, using for multi-enrollment trials (i.e. using x_enroll10 instead of x_enroll1)\n",
    "\n",
    "- Plot the DET curves for both scenarios in a single plot using the plot_det function defined above (which also reports the EER)\n",
    "\n",
    "Questions:\n",
    "1. Compare the histograms of tasks 11 and 12. How are they different and why?\n",
    "2. Looking now at the DET curves, how do scores of single and multi enrollment trials compare? Is this according to your intuition? Why?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code goes here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 13\n",
    "\n",
    "From now on, we will consider only the multi-enrollment trials.\n",
    "\n",
    "Your tasks are: \n",
    "- Plot, in a single plot, the DET curves for the $LLRs$ obtained with the three simple ML PLDA models (*simple1*, *simple2*, *simple3*, trained with different number of speakers and number of embeddings per-speaker in tasks 1, 6 and 7) as well as the GT PLDA model. \n",
    "\n",
    "- Plot, in a single plot, the DET curves for the $LLRs$ obtained with the three EM PLDA models trained above (*EM1*, *EM2*, *EM3*, trained with different number of speakers and number of embeddings per-speaker in tasks 5, 6 and 7) as well as the GT PLDA model. \n",
    "\n",
    "Questions:\n",
    "1. How does the performance of the three simple-trained PLDA models compare? What impact do the different training sets have on model's performance?\n",
    "2. How does the performance of the three EM-trained PLDA models compare? What impact do the different training sets have on model's performance?\n",
    "3. Does the EM algorithm have any advantage as compared to the simple ML in terms of performance? When and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code goes here \n",
    "\n"
   ]
  }
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