{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# BAYa class Assignment 2023\n", "\n", "In this assignment, your task will be to implement and analyze inference in the Probailistic 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. Specifically, it contains code for plotting 2 dimensional multivariate Gaussian distributions, and plotting 2-dimensional data points. 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 2D 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 Gaussian with mean mu and covariance cov\n", " \"\"\"\n", " return sps.multivariate_normal.logpdf(x, mu, cov)\n", "\n", "def plot2dfun(f, limits, resolution, ax=None):\n", " \"\"\"\n", " Greyscale plot of 2D Multivariate distributions.\n", " \n", " \"\"\"\n", " if ax is None:\n", " ax = plt\n", " xmin, xmax, ymin, ymax = limits\n", " xlim = np.arange(ymin, ymax, (ymax - ymin) / float(resolution))\n", " ylim = np.arange(xmin, xmax, (xmax - xmin) / float(resolution))\n", " a, b = np.meshgrid(ylim, xlim)\n", " img = f(np.vstack([np.ravel(a), np.ravel(b)[::-1]]).T)\n", " img = (img - img.min()) /(img.max() - img.min()) # normalize to range 0.0 - 1.0\n", " img = img.reshape(a.shape+img.shape[1:])\n", " return ax.imshow(img, cmap='gray', aspect='auto', extent=(xmin, xmax, ymin, ymax))\n", "\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" ] }, { "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 generative process for the embeddings (our observations):\n", "\n", "\n", "\n", "\\begin{align}\n", "{\\mathbf{z}_s} &\\sim \\mathcal{N}(\\mathbf{z}_s;\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}_{ac})&& \\text{for } s=1, \\dots, S\\\\\n", "{\\mathbf{x}_{sn}} &\\sim \\mathcal{N}(\\mathbf{x}_{sn};\\mathbf{z}_{s},\\boldsymbol{\\Sigma}_{wc})&& \\text{for } n=1, \\dots, N_s\\\\\n", "\\end{align}\n", "\n", "\n", "\n", "where $\\mathbf{z}$ is the continuous latent random variable related to the distribution of speaker means, $\\boldsymbol{\\mu}$ is the global speaker mean, $\\boldsymbol{\\Sigma}_{ac}$ is the across-class (across-speaker) covariance matrix, $\\mathbf{x}$ is the continuous random variable related to the distribution of per-speaker observations (per-speaker embeddings), $\\mathbf{z}_s$ is the speaker-specific 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": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "
" ] }, { "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: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$P(\\XX, \\ZZ) \n", "= \\prod_{s=1}^S p(\\XX_s,\\zz_s)\n", "= \\prod_{s=1}^S \\left( p(\\zz_s) \\prod_{n=1}^{N_s} p(\\xx_{sn}|\\zz_s) \\right)$$\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 $\\boldsymbol{\\Sigma}_{ac}^{GT}$ and the red elipse is the countour plot of $\\boldsymbol{\\Sigma}_{wc}^{GT}$.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "(-5.95685675343921, 7.954118920044291, -2.2998612816384827, 4.299970466102776)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "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", "plt.plot(mu_gt[0], mu_gt[1], '.', ms=10) #plotting the PLDA model\n", "gellipse(mu_gt, Sigma_ac_gt, 100, 'b', lw=2)\n", "gellipse(np.array([0,0]), Sigma_wc_gt, 100, 'r', lw=2) #for mere visualization purposes, we center the within-class covariance on the origin (0,0)\n", "plt.axis('equal')\n" ] }, { "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.\n", "\n", "Besides sampling the data, the code below plots the countour of $\\boldsymbol\\Sigma_{ac}^{GT}$, the sampled speaker means, the countour of the per-speaker $\\boldsymbol\\Sigma_{wc}^{GT}$ and the per-speaker sampled embeddings." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Do not edit this code!\n", "S = 10\n", "#N = (np.arange(S)+1)**2 # (somewhat cryptic way of) assigning different N_s to each speaker, ranging from 1 to 10^2 \n", "N = np.random.randint(1, 3, S) \n", "Z = rand_gauss(S, mu_gt, Sigma_ac_gt) # training speaker xvector 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_gt)\n", " X.append(X_s)\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", "gellipse(mu_gt, Sigma_ac_gt, 100, 'b', lw=2)" ] }, { "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", "$\\mmu = \\frac{1}{N} \\sum_{s=1}^S \\sum_{n=1}^{N_s} \\xx_{sn}$\n", "\n", "$\\mmu_s = \\frac{1}{N_s} \\sum_{n=1}^{N_s} \\xx_{sn}$\n", "\n", "$\\SSigma_{ac} = \\frac{1}{N} \\sum_{s=1}^S N_s \\left(\\mmu_s-\\mmu\\right)\\left(\\mmu_s-\\mmu\\right)^T$\n", "\n", "$\\SSigma_{wc} = \\frac{1}{N} \\sum_{s=1}^S N_s \\left(\\frac{1}{N_s} \\sum_{n=1}^{N_s} \\left(\\xx_{sn}-\\mmu_s\\right)\\left(\\xx_{sn}-\\mmu_s\\right)^T\\right)$\n", "\n", "### Task 1 \n", "\n", "Implement such updates for the PLDA parameters and plot the obtained result, together with the ground truth PLDA model (plot the ground truth model for the sampled speakers with dotted lines for a better visualization)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#Your implementation of the simple ML estimate of the parameters goes here\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PLDA Expectation Maximization training\n", "\n", "With EM, we can get better estimate of the parameters than 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-Lieber 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 such update, 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": [ "
Tip: 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", "$$\\ln \\mathcal{N}(\\mathbf{y};\\mmu_o,\\SSigma_o) = -\\frac{D}{2} \\ln (2\\pi)-\\frac{1}{2} \\ln|\\SSigma_o|-\\frac{1}{2} (\\mathbf{y}-\\mmu_o)^T\\SSigma_o^{-1}(\\mathbf{y}-\\mmu_o) = -\\frac{1}{2} \\mathbf{y}^T \\SSigma_o^{-1} \\mathbf{y} + \\mathbf{y}^T \\SSigma_o^{-1}\\mmu_o + const.$$\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", "
\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", "
Tip: \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", "
" ] }, { "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 $\\mathcal{Q}$ and set it equal to 0 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": [ "
Tip: \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", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Task 5\n", "Using the updates for the E and M step provided above, implement the EM algorithm for PLDA model training.\n", "\n", "The cell below provides some initialization for the PLDA parameters.\n", "Run the algorithm for 10 iterations and plot the obtained result, together with the ground truth PLDA model (plot the ground truth model for the sampled speakers with dotted lines for an better visualization).\n", "\n", "\n", "****Note that we might modify this task so that the algorithm fits some specific form or function*" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Make use of the following variables\n", "mu = np.array([0.0, 0.0]) #intial global mean\n", "Sigma_ac = np.array([[1.0, 0.0], #initial across-class covariance matrix\n", " [0.0, 1.0]])\n", "Sigma_wc = np.array([[1.0, 0.0], #initial within-class covariance matrix\n", " [0.0, 1.0]])\n", "\n", "\n", "#Your implementation of the EM algorithm goes here\n", "\n", "#E-step\n", "\n", "#M-step\n", "\n", "\n", "\n", "\n", "\n", "\n", "#Plotting instructions go here, reuse the function gellipse defined above\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.15" } }, "nbformat": 4, "nbformat_minor": 2 }