{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Working with Gaussians\n", "=======" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Preliminaries\n", "\n", "- Goal \n", " - Review of processing of Gaussian distributions in linear systems\n", "- Materials \n", " - Mandatory\n", " - These lecture notes\n", " - Optional\n", " - Bishop pp. 85-93 \n", " - [MacKay - 2006 - The Humble Gaussian Distribution](./files/Mackay-2006-The-humble-Gaussian-distribution.pdf) (highly recommended!)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Sums and Transformations of Gaussian Variables\n", "\n", "- The Gaussian distribution\n", "$$\n", "\\mathcal{N}(x|\\mu,\\Sigma) = |2 \\pi \\Sigma |^{-\\frac{1}{2}} \\,\\mathrm{exp}\\left\\{-\\frac{1}{2}(x-\\mu)^T \\Sigma^{-1} (x-\\mu) \\right\\}\n", "$$\n", "for variable $x$ is completely specified by its mean $\\mu$ and variance $\\Sigma$. \n", " - $\\Lambda = \\Sigma^{-1}$ is called the **precision matrix**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- A **linear transformation** $z=Ax+b$ of a Gaussian variable $\\mathcal{N}(x|\\mu,\\Sigma)$ is Gaussian distributed as\n", "\n", "$$\n", "p(z) = \\mathcal{N} \\left(z \\,|\\, A\\mu+b, A\\Sigma A^T \\right) \\tag{SRG-4a}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The **sum of two independent Gaussian variables** is also Gaussian distributed. Specifically, if $x \\sim \\mathcal{N} \\left(x|\\mu_x, \\Sigma_x \\right)$ and $y \\sim \\mathcal{N} \\left(y|\\mu_y, \\Sigma_y \\right)$, then the PDF for $z=x+y$ is given by\n", "\\begin{align}\n", "p(z) &= \\mathcal{N}(x\\,|\\,\\mu_x,\\Sigma_x) \\ast \\mathcal{N}(y\\,|\\,\\mu_y,\\Sigma_y) \\notag\\\\\n", " &= \\mathcal{N} \\left(z\\,|\\,\\mu_x+\\mu_y, \\Sigma_x +\\Sigma_y \\right) \\tag{SRG-8}\n", "\\end{align}\n", " - [Exercise]: Show that Eq.SRG-8 is really a special case of Eq.SRG-4a. \n", " - The sum of two Gaussian _distributions_ is NOT a Gaussian distribution. Why not?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: Gaussian Signals in a Linear System\n", "\n", "\n", "\n", "- [Q.]: Given independent variables\n", "$x \\sim \\mathcal{N}(\\mu_x,\\sigma_y)$ and $y \\sim \\mathcal{N}(\\mu_y,\\sigma_y)$, what is the PDF for $z = A\\cdot(x -y) + b$ ?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- [A.]: $z$ is also Gaussian with \n", "$$\n", "p_z(z) = \\mathcal{N}(z|A(\\mu_x-\\mu_y)+b, \\, A(\\sigma_x \\mathbf{+} \\sigma_y)A^T)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Think about the role of the Gaussian distribution for stochastic linear systems in relation to what sinusoidals mean for deterministic linear system analysis." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: Bayesian Estimation of a Constant\n", "\n", "\n", "- [Question] Estimate a constant $\\theta$ from one 'noisy' measurement $x$ about that constant. Assume the following model specification (the tilde $\\sim$ means: 'is distributed as'):\n", " \n", "\\begin{align*}\n", "x &= \\theta + \\epsilon \\\\\n", "\\theta &\\sim \\mathcal{N}(\\mu_\\theta,\\sigma_\\theta^2) \\\\\n", "\\epsilon &\\sim \\mathcal{N}(0,\\sigma^2_{\\epsilon})\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "[Answer]\n", "\n", "- **1. Model specification**\n", "Note that you can rewrite these specifications in probabilistic notation as follows:\n", "\\begin{align}\n", " p(x|\\theta) &=\\mathcal{N}(x|\\theta,\\sigma^2_{\\epsilon}) \\tag{likelihood}\\\\\n", " p(\\theta) &=\\mathcal{N}(\\theta|\\mu_\\theta,\\sigma_\\theta^2) \\tag{prior}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- **2. Inference** for the posterior PDF $p(\\theta|x)$\n", "\\begin{align*}\n", "p(\\theta|x) &= \\frac{p(x|\\theta)p(\\theta)}{p(x)} = \\frac{p(x|\\theta)p(\\theta)} { \\int p(x|\\theta)p(\\theta) \\, \\mathrm{d}\\theta } \\notag \\\\\n", " &= \\frac{1}{C} \\,\\mathcal{N}(x|\\theta,\\sigma^2_{\\epsilon})\\, \\mathcal{N}(\\theta|\\mu_\\theta,\\sigma_\\theta^2) \\notag \\\\\n", " &= \\frac{1}{C_1} \\mathrm{exp} \\left\\{ -\\frac{(x-\\theta)^2}{2\\sigma^2_{\\epsilon}} - \\frac{(\\theta-\\mu_\\theta)^2}{2\\sigma_\\theta^2} \\right\\} \\notag \\\\\n", " &= \\frac{1}{C_1} \\mathrm{exp} \\left\\{ \\theta^2\\left( -\\frac{1}{2\\sigma^2_{\\epsilon}} - \\frac{1}{2\\sigma_\\theta^2} \\right) + \\theta \\left( \\frac{x}{\\sigma^2_{\\epsilon}} + \\frac{\\mu_\\theta}{\\sigma_\\theta^2} \\right) + C_2 \\right\\} \\notag \\\\\n", " &= \\frac{1}{C_1} \\mathrm{exp} \\left\\{ -\\frac{\\sigma_\\theta^2 + \\sigma^2_{\\epsilon}}{2\\sigma_\\theta^2 \\sigma^2_{\\epsilon}} \\left( \\theta - \\frac{x\\sigma_\\theta^2 + \\mu_\\theta \\sigma^2_{\\epsilon}}{\\sigma_\\theta^2 + \\sigma^2_{\\epsilon}} \\right)^2 + C_3 \\right\\}\n", "\\end{align*}\n", "which we recognize as a Gaussian distribution." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " - This computational 'trick' for multiplying two Gaussians is called **completing the square**. The procedure makes use of the equality $$ax^2+bx+c_1 = a\\left(x+\\frac{b}{2a}\\right)^2+c_2$$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " \n", "- Hence, it follows that the posterior for $\\theta$ is\n", "\n", "$$\\begin{equation*}\n", " p(\\theta|x) = \\mathcal{N} (\\theta |\\, \\mu_{\\theta|x}, \\sigma_{\\theta|x}^2)\n", "\\end{equation*}$$\n", "\n", "where\n", "\n", "\\begin{align*}\n", " \\frac{1}{\\sigma_{\\theta|x}^2} &= \\frac{\\sigma^2_{\\epsilon} + \\sigma_\\theta^2}{\\sigma^2_{\\epsilon}\\sigma_\\theta^2} = \\frac{1}{\\sigma_\\theta^2} + \\frac{1}{\\sigma^2_{\\epsilon}}\\\\\n", " \\mu_{\\theta|x} &= \\sigma_{\\theta|x}^2 \\, \\left( \\frac{1}{\\sigma^2_{\\epsilon}}x + \\frac{1}{\\sigma_\\theta^2} \\mu_\\theta \\right) \n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- So, multiplication of two Gaussian distributions yields another (unnormalized) Gaussian with\n", " - posterior precision equals **sum of prior precisions**\n", " - posterior precision-weighted mean equals **sum of prior precision-weighted means**\n", "- (This is worth remembering)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### CODE EXAMPLE\n", "\n", "Let's plot the exact product of two Gaussian PDFs as well as the normalized product according to the above derivation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject