{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Dynamic Models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "### Preliminaries\n",
    "\n",
    "- Goal \n",
    "  - Introduction to dynamic (=temporal) Latent Variable Models, including the Hidden Markov Model and Kalman filter.   \n",
    "- Materials\n",
    "  - Mandatory\n",
    "    - These lecture notes\n",
    "  - Optional \n",
    "    - Bishop pp.605-615 on Hidden Markov Models\n",
    "    - Bishop pp.635-641 on Kalman filters\n",
    "    - Faragher (2012), [Understanding the Basis of the Kalman Filter](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Faragher-2012-Understanding-the-Basis-of-the-Kalman-Filter.pdf)\n",
    "    - Minka (1999), [From Hidden Markov Models to Linear Dynamical Systems](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Minka-1999-from-HMM-to-LDS.pdf)\n",
    "      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example Problem\n",
    "\n",
    "- We consider a one-dimensional cart position tracking problem, see [Faragher 2012](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Faragher-2012-Understanding-the-Basis-of-the-Kalman-Filter.pdf).  \n",
    "\n",
    "- The hidden states are the position $z_t$ and velocity $\\dot z_t$. We can apply an external acceleration/breaking force $u_t$. (Noisy) observations are represented by $x_t$. \n",
    "\n",
    "- The equations of motions are given by\n",
    "\n",
    "$$\\begin{align}\n",
    "\\begin{bmatrix} z_t \\\\ \\dot{z_t}\\end{bmatrix} &=  \\begin{bmatrix} 1 & \\Delta t \\\\ 0 & 1\\end{bmatrix} \\begin{bmatrix} z_{t-1} \\\\ \\dot z_{t-1}\\end{bmatrix} + \\begin{bmatrix} (\\Delta t)^2/2 \\\\ \\Delta t\\end{bmatrix} u_t + \\mathcal{N}(0,\\Sigma_z) \\\\\n",
    "x_t &= \\begin{bmatrix} z_t \\\\ \\dot{z_t}\\end{bmatrix} + \\mathcal{N}(0,\\Sigma_x) \n",
    "\\end{align}$$\n",
    "\n",
    "- Task: Infer the position $z_t$ after 10 time steps. (Solution later in this lesson).\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/Faragher-2012-cart-1.png\" width=\"600px\"><p style=\"text-align:center;\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Dynamical Models\n",
    "\n",
    "- In this lesson, we consider models where the sequence order of observations matters. \n",
    "\n",
    "- Consider the _ordered_ observation sequence $x^T \\triangleq \\left(x_1,x_2,\\ldots,x_T\\right)$.\n",
    "  - (For brevity, in this lesson we use the notation $x_t^T$ to denote $(x_t,x_{t+1},\\ldots,x_T)$ and drop the subscript if $t=1$, so $x^T = x_1^T = \\left(x_1,x_2,\\ldots,x_T\\right)$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We wish to develop a generative model\n",
    "    $$ p( x^T )$$\n",
    "that 'explains' the time series $x^T$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We cannot use the IID assumption $p( x^T ) = \\prod_t p(x_t )$. In general, we _can_ use the **chain rule** (a.k.a. **the general product rule**)\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(x^T) &= p(x_T|x^{T-1}) \\,p(x^{T-1}) \\\\\n",
    "  &=  p(x_T|x^{T-1}) \\,p(x_{T-1}|x^{T-2}) \\cdots p(x_2|x_1)\\,p(x_1) \\\\\n",
    "  &= p(x_1)\\prod_{t=2}^T p(x_t\\,|\\,x^{t-1})\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Generally, we will want to limit the depth of dependencies on previous observations. For example, a $K$th-order linear **Auto-Regressive** (AR) model that is given by\n",
    "$$\\begin{align*}\n",
    "  p(x_t\\,|\\,x^{t-1}) = \\mathcal{N}\\left(x_t \\,\\middle|\\,  \\sum_{k=1}^K a_k x_{t-k}\\,,\\sigma^2\\,\\right)  \n",
    "\\end{align*}$$\n",
    "limits the dependencies to the past $K$ samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### State-space Models\n",
    "\n",
    "- A limitation of AR models is that they need a lot of parameters in order to create a flexible model. E.g., if $x_t$ is an $M$-dimensional discrete variable, then a $K$th-order AR model will have about $M^{K}$ parameters. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Similar to our work on Gaussian Mixture models, we can create a flexible dynamic system by introducing _latent_ (unobserved) variables  $z^T \\triangleq \\left(z_1,z_2,\\dots,z_T\\right)$ (one $z_t$ for each observation $x_t$). In dynamic systems, $z_t$ are called _state variables_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- A **state space model** is a particular latent variable dynamical model defined by\n",
    "$$\\begin{align*}\n",
    " p(x^T,z^T) &= \\underbrace{p(z_1)}_{\\text{initial state}} \\prod_{t=2}^T \\underbrace{p(z_t\\,|\\,z_{t-1})}_{\\text{state transitions}}\\,\\prod_{t=1}^T \\underbrace{p(x_t\\,|\\,z_t)}_{\\text{observations}}\n",
    "\\end{align*}$$\n",
    "  - The condition $p(z_t\\,|\\,z^{t-1}) = p(z_t\\,|\\,z_{t-1})$ is called a $1$st-order Markov condition.\n",
    "\n",
    "<!--- - In a Markovian state-space model, the observation sequence $x^T$ is not a first-order Markov chain, i.e., for the state-space model\n",
    "    $$\\begin{align*}\n",
    " p(x^T,z^T) &= p(z_1) \\prod_{t=2}^T p(z_t\\,|\\,z_{t-1})\\,\\prod_{t=1}^T p(x_t\\,|\\,z_t)\n",
    "\\end{align*}$$\n",
    "the following statement holds: \n",
    "    $$p(x_t\\,|\\,x_{t-1},x_{t-2}) \\neq p(x_t\\,|\\,x_{t-1})\\,.$$\n",
    "In other words, the latent variables $z_t$ represent a memory bank for past observations beyond $t-1$. (Proof as exercise). \n",
    "--->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The Forney-style factor graph for a state-space model:\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/ffg-state-space.png\" width=\"600px\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hidden Markov Models and Linear Dynamical Systems\n",
    "\n",
    "- A **Hidden Markov Model** (HMM) is a specific state-space model with <span class=\"emphasis\">discrete-valued</span> state variables $z_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Typically, $z_t$ is a $K$-dimensional one-hot coded latent 'class indicator' with transition probabilities $a_{jk} \\triangleq p(z_{tk}=1\\,|\\,z_{t-1,j}=1)$, or equivalently,\n",
    "  $$p(z_t|z_{t-1}) = \\prod_{k=1}^K \\prod_{j=1}^K a_{jk}^{z_{t-1,j}\\cdot z_{tk}}$$\n",
    "which is usually accompanied by an initial state distribution $p(z_{1k}=1) = \\pi_k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "  \n",
    "- The classical HMM has also discrete-valued observations but in pratice any (probabilistic) observation model $p(x_t|z_t)$ may be coupled to the hidden Markov chain. \n",
    "\n",
    "<!---\n",
    "- The following figure shows the typical trellis structure of the many possible state transitions paths.   \n",
    "<img src=\"./figures/Figure13.7.png\" width=\"400px\">\n",
    "--->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Another well-known state-space model with <span class=\"emphasis\">continuous-valued</span> state variables $z_t$ is the **(Linear) Gaussian Dynamical System** (LGDS), which is defined as\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(z_t\\,|\\,z_{t-1}) &= \\mathcal{N}\\left(\\, A z_{t-1}\\,,\\,\\Sigma_z\\,\\right) \\\\ \n",
    "p(x_t\\,|\\,z_t) &= \\mathcal{N}\\left(\\, C z_t\\,,\\,\\Sigma_x\\,\\right) \\\\\n",
    "p(z_1) &= \\mathcal{N}\\left(\\, \\mu_1\\,,\\,\\Sigma_1\\,\\right)\n",
    "\\end{align*}$$\n",
    "<!---or, equivalently (in the usual state-space notation)\n",
    "$$\\begin{align*}\n",
    "z_k &= A z_{k-1} + \\mathcal{N}\\left(0,\\Sigma_z \\right) \\\\ \n",
    "x_k &= C z_k + \\mathcal{N}\\left( 0, \\Sigma_x \\right) \\\\\n",
    "z_1 &= \\mu_1 + \\mathcal{N}\\left( 0, \\Sigma_1\\right)\n",
    "\\end{align*}$$\n",
    "--->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Note that the joint distribution over all states and observations $\\{(x_1,z_1),\\ldots,(x_t,z_t)\\}$ is a (large-dimensional) Gaussian distribution. This means that, in principle, every inference problem on the LGDS model also leads to a Gaussian distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- HMM's and LGDS's (and variants thereof) are at the basis of a wide range of complex information processing systems, such as speech and language recognition, robotics and automatic car navigation, and even processing of DNA sequences.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Common Signal Processing Tasks as Message Passing-based Inference\n",
    "\n",
    "- As we have seen, inference tasks in linear Gaussian state space models can be analytically solved.\n",
    "\n",
    "- However, these derivations quickly become cumbersome and prone to errors.\n",
    "\n",
    "- Alternatively, we could specify the generative model in a (Forney-style) factor graph and use automated message passing to infer the posterior over the hidden variables. Here follows some examples.\n",
    "\n",
    "- **Filtering**, a.k.a. state estimation: estimation of a state (at time step $t$), based on past and current (at $t$) observations. \n",
    "<p style=\"text-align:center;\"><img src=\"./figures/ffg-state-space-filtering.png\" width=\"600px\"></p>\n",
    "\n",
    "- **Smoothing**: estimation of a state based on both past and future observations. Needs backward messages from the future.  \n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/ffg-state-space-smoothing.png\" width=\"600px\"></p>\n",
    "\n",
    "- **Prediction**: estimation of future state or observation based only on observations of the past.\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/ffg-state-space-prediction.png\" width=\"600px\"></p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Kalman Filtering\n",
    "\n",
    "- Technically, a [**Kalman filter**](https://en.wikipedia.org/wiki/Kalman_filter) is the solution to the recursive estimation (inference) of the hidden state $z_t$ based on past observations in an LGDS, i.e., Kalman filtering solves the problem $p(z_t\\,|\\,x^t)$ based on the previous estimate $p(z_{t-1}\\,|\\,x^{t-1})$ and a new observation $x_t$ (in the context of the given model specification of course). \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " \n",
    "- Let's infer the Kalman filter for a scalar linear Gaussian dynamical system:\n",
    "$$\\begin{align*}\n",
    "    p(z_t\\,|\\,z_{t-1}) &= \\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2) \\tag{state transition}   \\\\\n",
    "    p(x_t\\,|\\,z_t) &= \\mathcal{N}(x_t\\,|\\,c z_t,\\sigma_x^2) \\tag{observation}     \n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "        \n",
    "- Kalman filtering comprises inferring $p(z_t\\,|\\,x^t)$ from a given prior estimate $p(z_{t-1}\\,|\\,x^{t-1})$ (available after the previous time step) and a new observation $x_t$. Let us assume that \n",
    "$$\\begin{align} \n",
    "p(z_{t-1}\\,|\\,x^{t-1}) = \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\tag{prior}\n",
    "\\end{align}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Note that everything is Gaussian, so it is _in principle_ possible to execute inference problems analytically and the result will be a Gaussian posterior:\n",
    "  - (In the following derivation we make use of the renormalization equality $\\mathcal{N}(x\\,|\\,cz,\\sigma^2) = \\frac{1}{c}\\mathcal{N}\\left(z \\,\\big|\\,\\frac{x}{c},\\left(\\frac{\\sigma}{c}\\right)^2\\right)$).\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\underbrace{p(z_t\\,|\\,x^t)}_{\\text{posterior}} &= p(z_t\\,|\\,x_t,x^{t-1}) \\propto p(x_t,z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &\\propto p(x_t\\,|\\,z_t) \\,p(z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &= p(x_t\\,|\\,z_t) \\, \\sum_{z_{t-1}} p(z_t,z_{t-1}\\,|\\,x^{t-1}) \\\\\n",
    "  &= \\underbrace{p(x_t\\,|\\,z_t)}_{\\text{observation}} \\, \\sum_{z_{t-1}} \\underbrace{p(z_t\\,|\\,z_{t-1})}_{\\text{state transition}} \\, \\underbrace{p(z_{t-1}\\,|\\,x^{t-1})}_{\\text{prior}} \\\\\n",
    "    &= \\mathcal{N}(x_t\\,|\\,c z_t,\\sigma_x^2) \\sum_{z_{t-1}} \\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2) \\, \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\\\\n",
    "  &= \\frac{1}{c}\\mathcal{N}\\left(z_t\\bigm| \\frac{x_t}{c} ,\\left(\\frac{\\sigma_x}{c}\\right)^2\\right)  \\sum_{z_{t-1}} \\frac{1}{a}\\underbrace{\\mathcal{N}\\left(z_{t-1}\\bigm|  \\frac{z_t}{a},\\left(\\frac{\\sigma_z}{a}\\right)^2 \\right) \\, \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2)}_{\\text{use Gaussian multiplication formula SRG-6}} \\\\\n",
    "  &\\propto \\underbrace{\\mathcal{N}\\left(z_t\\,\\bigm| \\,\\frac{x_t}{c} ,\\left(\\frac{\\sigma_x}{c}\\right)^2\\right) \\cdot \\mathcal{N}\\left(z_t\\, \\bigm|\\,a \\mu_{t-1},\\sigma_z^2 + \\left(a \\sigma_{t-1}\\right)^2 \\right)}_{\\text{use SRG-6 again}} \\\\\n",
    "  &\\propto \\mathcal{N}\\left( z_t \\,|\\, \\mu_t, \\sigma_t^2\\right)\n",
    "\\end{align*}$$\n",
    "with\n",
    "$$\\begin{align*}\n",
    "  \\rho_t^2 &= a^2 \\sigma_{t-1}^2 + \\sigma_z^2 \\tag{predicted variance}\\\\\n",
    "  K_t &= \\frac{c \\rho_t^2}{c^2 \\rho_t^2 + \\sigma_x^2} \\tag{Kalman gain} \\\\\n",
    "  \\mu_t &= \\underbrace{a \\mu_{t-1}}_{\\text{prior prediction}} + K_t \\cdot \\underbrace{\\left( x_t - c a \\mu_{t-1}\\right)}_{\\text{prediction error}} \\tag{posterior mean}\\\\\n",
    "  \\sigma_t^2 &= \\left( 1 - c\\cdot K_t \\right) \\rho_t^2 \\tag{posterior variance}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Kalman filtering consists of computing/updating these last four equations for each new observation ($x_t$). This is a very efficient recursive algorithm to estimate the state $z_t$ from all observations (until $t$).\n",
    "\n",
    "- It turns out that it's also possible to get an analytical result for $p(x_t|x^{t-1})$, which is the **model evidence** in a filtering context. See [optional slides](#kalman-proof) for details.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Multi-dimensional Kalman Filtering\n",
    "\n",
    "- The Kalman filter equations can also be derived for multidimensional state-space models. In particular, for the model\n",
    "$$\\begin{align*}\n",
    "z_t &= A z_{t-1} + \\mathcal{N}(0,\\Gamma) \\\\\n",
    "x_t &= C z_t + \\mathcal{N}(0,\\Sigma)\n",
    "\\end{align*}$$\n",
    "the Kalman filter update equations for the posterior $p(z_t |x^t) = \\mathcal{N}\\left(z_t \\bigm| \\mu_t, V_t \\right)$ are given by (see Bishop, pg.639)\n",
    "$$\\begin{align*}\n",
    "P_t &= A V_{t-1} A^T + \\Gamma \\tag{predicted variance}\\\\\n",
    "K_t &= P_t C^T \\cdot \\left(C P_t C^T  + \\Sigma \\right)^{-1} \\tag{Kalman gain} \\\\\n",
    "\\mu_t &= A \\mu_{t-1} + K_t\\cdot\\left(x_t - C A \\mu_{t-1} \\right) \\tag{posterior state mean}\\\\\n",
    "V_t &= \\left(I-K_t C \\right) P_{t}  \\tag{posterior state variance}\n",
    "\\end{align*}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Code Example: Kalman Filtering and the Cart Position Tracking Example Revisited\n",
    "\n",
    "\n",
    "- We can now solve the cart tracking problem of the introductory example by implementing the Kalman filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "using Pkg;Pkg.activate(\"probprog/workspace/\");Pkg.instantiate()\n",
    "IJulia.clear_output();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: 𝒩(m=[42.21, 4.51], v=[[1.30, 0.39][0.39, 0.34]])"
     ]
    },
    {
     "data": {
      "image/png": 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FMiHEAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 1500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Measurement: 𝒩(m=[40.88, 5.41], v=[[1.00, 0.00][0.00, 2.00]])\n",
      "\n",
      "Posterior: 𝒩(m=[41.55, 4.42], v=[[0.55, 0.15][0.15, 0.24]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra, PyPlot\n",
    "include(\"scripts/cart_tracking_helpers.jl\")\n",
    "\n",
    "# Specify the model parameters\n",
    "Δt = 1.0                     # assume the time steps to be equal in size\n",
    "A = [1.0 Δt;\n",
    "     0.0 1.0]\n",
    "b = [0.5*Δt^2; Δt] \n",
    "Σz = convert(Matrix,Diagonal([0.2*Δt; 0.1*Δt])) # process noise covariance\n",
    "Σx = convert(Matrix,Diagonal([1.0; 2.0]))     # observation noise covariance;\n",
    "\n",
    "# Generate noisy observations\n",
    "n = 10                # perform 10 timesteps\n",
    "z_start = [10.0; 2.0] # initial state\n",
    "u = 0.2 * ones(n)     # constant input u\n",
    "noisy_x = generateNoisyMeasurements(z_start, u, A, b, Σz, Σx);\n",
    "\n",
    "m_z = noisy_x[1]                                    # initial predictive mean\n",
    "V_z = A * (1e8*Diagonal(I,2) * A') + Σz             # initial predictive covariance\n",
    "\n",
    "for t = 2:n\n",
    "    global m_z, V_z, m_pred_z, V_pred_z\n",
    "    #predict\n",
    "    m_pred_z = A * m_z + b * u[t]                   # predictive mean\n",
    "    V_pred_z = A * V_z * A' + Σz                    # predictive covariance\n",
    "    #update\n",
    "    gain = V_pred_z * inv(V_pred_z + Σx)            # Kalman gain\n",
    "    m_z = m_pred_z + gain * (noisy_x[t] - m_pred_z) # posterior mean update\n",
    "    V_z = (Diagonal(I,2)-gain)*V_pred_z             # posterior covariance update\n",
    "end\n",
    "println(\"Prediction: \",ProbabilityDistribution(Multivariate,GaussianMeanVariance,m=m_pred_z,v=V_pred_z))\n",
    "println(\"Measurement: \", ProbabilityDistribution(Multivariate,GaussianMeanVariance,m=noisy_x[n],v=Σx))\n",
    "println(\"Posterior: \", ProbabilityDistribution(Multivariate,GaussianMeanVariance,m=m_z,v=V_z))\n",
    "plotCartPrediction2(m_pred_z[1], V_pred_z[1], m_z[1], V_z[1], noisy_x[n][1], Σx[1][1]);"
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    "### The Cart Tracking Problem Revisited: Inference by Message Passing\n",
    "\n",
    "- Let's solve the cart tracking problem by sum-product message passing in a factor graph like the one depicted above. All we have to do is create factor nodes for the state-transition model $p(z_t|z_{t-1})$ and the observation model $p(x_t|z_t)$. Then we just build the factor graph and let [ForneyLab](http://forneylab.org) execute the message passing schedule. "
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    "- Since the factor graph is just a concatination of $n$ identical \"sections\" (one for each time step), we only have to specify a single section. When running the message passing algorithm we will explictly use the posterior of the previous timestep as prior in the next one. Let's build a section of the factor graph:"
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  {
   "cell_type": "code",
   "execution_count": 3,
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    "fg = FactorGraph()\n",
    "z_prev_m = Variable(id=:z_prev_m); placeholder(z_prev_m, :z_prev_m, dims=(2,))\n",
    "z_prev_v = Variable(id=:z_prev_v); placeholder(z_prev_v, :z_prev_v, dims=(2,2))\n",
    "bu = Variable(id=:bu); placeholder(bu, :bu, dims=(2,))\n",
    "\n",
    "@RV z_prev ~ GaussianMeanVariance(z_prev_m, z_prev_v, id=:z_prev) # p(z_prev)\n",
    "@RV noise_z ~ GaussianMeanVariance(constant(zeros(2), id=:noise_z_m), constant(Σz, id=:noise_z_v)) # process noise\n",
    "@RV z = constant(A, id=:A) * z_prev + bu + noise_z; z.id = :z # p(z|z_prev) (state transition model)\n",
    "@RV x ~ GaussianMeanVariance(z, constant(Σx, id=:Σx)) # p(x|z) (observation model)\n",
    "placeholder(x, :x, dims=(2,));\n",
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    "Now that we've built the factor graph, we can perform Kalman filtering by inserting measurement data into the factor graph and performing message passing."
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: 𝒩(m=[42.21, 4.51], v=[[1.30, 0.39][0.39, 0.34]])\n",
      "\n",
      "Measurement: 𝒩(m=[40.88, 5.41], v=[[1.00, 0.00][0.00, 2.00]])\n",
      "\n",
      "Posterior: 𝒩(m=[41.55, 4.42], v=[[0.55, 0.15][0.15, 0.24]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "include(\"scripts/cart_tracking_helpers.jl\")\n",
    "algo = messagePassingAlgorithm(z)\n",
    "source_code = algorithmSourceCode(algo)\n",
    "eval(Meta.parse(source_code))\n",
    "marginals = Dict()\n",
    "messages = Array{Message}(undef,6)\n",
    "z_prev_m_0 = noisy_x[1]  \n",
    "z_prev_v_0 = A * (1e8*Diagonal(I,2) * A') + Σz \n",
    "for t=2:n\n",
    "    data = Dict(:x => noisy_x[t], :bu => b*u[t],:z_prev_m => z_prev_m_0, :z_prev_v => z_prev_v_0)\n",
    "    step!(data, marginals, messages) # perform msg passing (single timestep)\n",
    "    # Posterior of z becomes prior of z in the next timestep:\n",
    "    z_prev_m_0 = ForneyLab.unsafeMean(marginals[:z])\n",
    "    z_prev_v_0 = ForneyLab.unsafeCov(marginals[:z])\n",
    "end\n",
    "# Collect prediction p(z[n]|z[n-1]), measurement p(z[n]|x[n]), corrected prediction p(z[n]|z[n-1],x[n])\n",
    "prediction      = messages[5].dist # the message index is found by manual inspection of the schedule\n",
    "measurement     = messages[6].dist\n",
    "corr_prediction = convert(ProbabilityDistribution{Multivariate, GaussianMeanVariance}, marginals[:z])\n",
    "println(\"Prediction: \",prediction)\n",
    "println(\"Measurement: \",measurement)\n",
    "println(\"Posterior: \", corr_prediction)\n",
    "\n",
    "# Make a fancy plot of the prediction, noisy measurement, and corrected prediction after n timesteps\n",
    "plotCartPrediction(prediction, measurement, corr_prediction);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Note that both the analytical Kalman filtering solution and the message passing solution lead to the same results. The advantage of message passing-based inference with ForneyLab is that we did not need to derive any inference equations. ForneyLab took care of all that. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Recap Dynamical Models \n",
    "\n",
    "- Dynamical systems do not obey the sample-by-sample independence assumption, but still can be specified, and state and parameter estimation equations can be solved by similar tools as for static models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Two of the more famous and powerful models with latent states include the hidden Markov model (with discrete states) and the Linear Gaussian dynamical system (with continuous states)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- For the LGDS, the Kalman filter is a well-known recursive state estimation procedure. The Kalman filter can be derived through Bayesian update rules on Gaussian distributions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- If anything changes in the model, e.g., the state noise is not Gaussian, then you have to re-derive the inference equations again from scratch and it may not lead to an analytically pleasing answer. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\Rightarrow$ Generally, we will want to automate the inference processes. As we discussed, message passing in a factor graph is a visually appealing method to automate inference processes. We showed how Kalman filtering emerged naturally by automated message passing. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <center> OPTIONAL SLIDES</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <a id='kalman-proof'>Proof of Kalman filtering equations including evidence updating</a>\n",
    "\n",
    "- Now let's proof the Kalman filtering equations including evidence updating by probabilistic calculus:\n",
    "$$\\begin{align*}\n",
    "\\overbrace{p(z_t\\,|\\,x^t)}^{\\text{posterior}} &= p(z_t\\,|\\,x_t,x^{t-1}) \\\\\n",
    " &= \\frac{p(x_t,z_t\\,|\\,x^{t-1})}{p(x_t\\,|\\,x^{t-1})} \\\\\n",
    " &= \\frac{p(x_t\\,|\\,z_t) \\,p(z_t\\,|\\,x^{t-1})}{p(x_t\\,|\\,x^{t-1})} \\\\\n",
    " &= \\frac{p(x_t\\,|\\,z_t) \\, \\sum_{z_{t-1}} p(z_t,z_{t-1}\\,|\\,x^{t-1}) }{p(x_t\\,|\\,x^{t-1})} \\\\\n",
    " &= \\frac{p(x_t\\,|\\,z_t) \\, \\sum_{z_{t-1}} p(z_t\\,|\\,z_{t-1}) \\, p(z_{t-1}\\,|\\,x^{t-1})}{p(x_t\\,|\\,x^{t-1})} \\\\\n",
    " &= \\frac{\\overbrace{\\mathcal{N}(x_t|c z_t, \\sigma_x^2)}^{\\text{likelihood}} \\, \\sum_{z_{t-1}} \\overbrace{\\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2)}^{\\text{state transition}} \\, \\overbrace{\\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) }^{\\text{prior}} }{\\underbrace{p(x_t\\,|\\,x^{t-1})}_{\\text{evidence}}}\n",
    "\\end{align*}$$\n",
    " \n",
    "- The posterior  $p(z_t\\,|\\,x^t)$ is proportional to the numerator, which by making use of the renormalization equality \n",
    "$$\\begin{align}\n",
    "\\mathcal{N}(x\\,|\\,cz,\\sigma^2) = \\frac{1}{c}\\cdot \\mathcal{N}\\left(z \\,\\big|\\,\\frac{x}{c},\\left(\\frac{\\sigma}{c}\\right)^2\\right) \\tag{renormalization}\\,,\n",
    "\\end{align}$$\n",
    "can be evaluated with Gaussian multiplication rules:\n",
    "\n",
    "$$\\begin{align*} \n",
    "\\mathcal{N}(x_t|c z_t, &\\sigma_x^2) \\, \\sum_{z_{t-1}} \\underbrace{\\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2)}_{\\text{use renormalization}} \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\\\\n",
    "&= \\mathcal{N}(x_t|c z_t, \\sigma_x^2) \\, \\sum_{z_{t-1}} \\frac{1}{a}\\underbrace{\\mathcal{N}\\left(z_{t-1}\\bigm|  \\frac{z_t}{a},\\left(\\frac{\\sigma_z}{a}\\right)^2 \\right) \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2)}_{\\text{use Gaussian multiplication formula SRG-6}}  \\\\\n",
    "&= \\frac{1}{a} \\mathcal{N}(x_t|c z_t, \\sigma_x^2) \\, \\sum_{z_{t-1}} \\underbrace{\\mathcal{N}\\left(\\mu_{t-1}\\bigm|  \\frac{z_t}{a},\\left(\\frac{\\sigma_z}{a}\\right)^2 + \\sigma_{t-1}^2 \\right)}_{\\text{not a function of }z_{t-1}} \\underbrace{\\mathcal{N}(z_{t-1} \\,|\\, \\cdot, \\cdot)}_{\\text{sums to }1} \\\\\n",
    "&= \\frac{1}{a} \\underbrace{\\mathcal{N}(x_t|c z_t, \\sigma_x^2)}_{\\text{use renormalization rule}} \\, \\underbrace{\\mathcal{N}\\left(\\mu_{t-1}\\bigm|  \\frac{z_t}{a},\\left(\\frac{\\sigma_z}{a}\\right)^2 + \\sigma_{t-1}^2 \\right)}_{\\text{use renormalization rule}} \\\\\n",
    "&= \\frac{1}{c} \\underbrace{\\mathcal{N}\\left(z_t \\bigm|  \\frac{x_t}{c}, \\left( \\frac{\\sigma_x}{c}\\right)^2 \\right) \\mathcal{N}\\left(z_t\\, \\bigm|\\,a \\mu_{t-1},\\sigma_z^2 + \\left(a \\sigma_{t-1}\\right)^2 \\right)}_{\\text{use SRG-6 again}} \\\\\n",
    "&= \\underbrace{\\frac{1}{c} \\mathcal{N}\\left( \\frac{x_t}{c} \\bigm| a \\mu_{t-1}, \\left( \\frac{\\sigma_x}{c}\\right)^2+ \\sigma_z^2 + \\left(a \\sigma_{t-1}\\right)^2\\right)}_{\\text{use renormalization}} \\, \\mathcal{N}\\left( z_t \\,|\\, \\mu_t, \\sigma_t^2\\right)\\\\\n",
    "  &= \\underbrace{\\mathcal{N}\\left(x_t \\,|\\, ca \\mu_{t-1}, \\sigma_x^2 + c^2(\\sigma_z^2+a^2\\sigma_{t-1}^2) \\right)}_{\\text{evidence } p(x_t|x^{t-1})} \\underbrace{\\mathcal{N}\\left( z_t \\,|\\, \\mu_t, \\sigma_t^2\\right)}_{\\text{posterior }p(z_t|x^t) }\n",
    "\\end{align*}$$\n",
    "with\n",
    "$$\\begin{align*}\n",
    "  \\rho_t^2 &= a^2 \\sigma_{t-1}^2 + \\sigma_z^2 \\tag{predicted variance}\\\\\n",
    "  K_t &= \\frac{c \\rho_t^2}{c^2 \\rho_t^2 + \\sigma_x^2} \\tag{Kalman gain} \\\\\n",
    "  \\mu_t &= \\underbrace{a \\mu_{t-1}}_{\\text{prior prediction}} + K_t \\cdot \\underbrace{\\left( x_t - c a \\mu_{t-1}\\right)}_{\\text{prediction error}} \\tag{posterior mean}\\\\\n",
    "  \\sigma_t^2 &= \\left( 1 - c\\cdot K_t \\right) \\rho_t^2 \\tag{posterior variance}\n",
    "\\end{align*}$$\n"
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    "### Extensions of Generative Gaussian Models\n",
    "\n",
    "- Using the methods of the previous lessons, it is possible to create your own new models based on stacking Gaussian and categorical distributions in new ways: \n",
    "\n",
    "<img src=\"./figures/fig-generative-Gaussian-models.png\" width=\"600px\">"
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