{
 "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": {
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     "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"
    }
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   "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."
   ]
  },
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   "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 $x_t \\in \\mathbb{R}^M$ is an $M$-dimensional time series, then the $K$-th order AR model for $x_t$ will have $KM^2$ 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"
    }
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   "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": {
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     "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": [
    "### <a id='kalman-filter'>Kalman Filtering</a>\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",
    "$$\\begin{aligned}\n",
    "    p(z_t\\,|\\,z_{t-1}) &= \\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2) \\qquad &&\\text{(state transition)}   \\\\\n",
    "    p(x_t\\,|\\,z_t) &= \\mathcal{N}(x_t\\,|\\,c z_t,\\sigma_x^2) \\qquad &&\\text{(observation)}     \n",
    "\\end{aligned}$$"
   ]
  },
  {
   "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",
    "$$\\begin{align*} \n",
    "p(z_{t-1}\\,|\\,x^{t-1}) = \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\qquad \\text{(prior)}\n",
    "\\end{align*}$$ "
   ]
  },
  {
   "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",
    "$$\\begin{align*}\n",
    "\\underbrace{p(z_t\\,|\\,x^t)}_{\\text{posterior}} &= p(z_t\\,|\\,x_t,x^{t-1}) \\\\\n",
    "  &\\propto p(x_t,z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &= p(x_t\\,|\\,z_t) \\,p(z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &= p(x_t\\,|\\,z_t) \\, \\int p(z_t,z_{t-1}\\,|\\,x^{t-1}) \\mathrm{d}z_{t-1} \\\\\n",
    "  &= \\underbrace{p(x_t\\,|\\,z_t)}_{\\text{observation}} \\, \\int \\underbrace{p(z_t\\,|\\,z_{t-1})}_{\\text{state transition}} \\, \\underbrace{p(z_{t-1}\\,|\\,x^{t-1})}_{\\text{prior}} \\mathrm{d}z_{t-1} \\\\\n",
    "    &= \\mathcal{N}(x_t\\,|\\,c z_t,\\sigma_x^2) \\int \\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2) \\, \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\mathrm{d}z_{t-1} \\\\\n",
    "  &= \\frac{1}{c}\\mathcal{N}\\left(z_t\\bigm| \\frac{x_t}{c} ,\\left(\\frac{\\sigma_x}{c}\\right)^2\\right)  \\int \\frac{1}{a}\\underbrace{\\mathcal{N}\\left(z_{t-1}\\bigm|  \\frac{z_t}{a},\\left(\\frac{\\sigma_z}{a}\\right)^2 \\right) \\, \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2)}_{\\text{use Gaussian multiplication formula SRG-6}} \\mathrm{d}z_{t-1} \\\\\n",
    "  &\\propto \\underbrace{\\mathcal{N}\\left(z_t\\,\\bigm| \\,\\frac{x_t}{c} ,\\left(\\frac{\\sigma_x}{c}\\right)^2\\right) \\cdot \\mathcal{N}\\left(z_t\\, \\bigm|\\,a \\mu_{t-1},\\sigma_z^2 + \\left(a \\sigma_{t-1}\\right)^2 \\right)}_{\\text{use SRG-6 again}} \\\\\n",
    "  &\\propto \\mathcal{N}\\left( z_t \\,|\\, \\mu_t, \\sigma_t^2\\right)\n",
    "\\end{align*}$$\n",
    "with\n",
    "$$\\begin{align*}\n",
    "  \\rho_t^2 &= a^2 \\sigma_{t-1}^2 + \\sigma_z^2 \\quad \\text{(predicted variance)}\\\\\n",
    "  K_t &= \\frac{c \\rho_t^2}{c^2 \\rho_t^2 + \\sigma_x^2} \\quad \\text{(Kalman gain)} \\\\\n",
    "  \\mu_t &= \\underbrace{a \\mu_{t-1}}_{\\text{prior prediction}} + K_t \\cdot \\underbrace{\\left( x_t - c a \\mu_{t-1}\\right)}_{\\text{prediction error}} \\quad \\text{(posterior mean)}\\\\\n",
    "  \\sigma_t^2 &= \\left( 1 - c\\cdot K_t \\right) \\rho_t^2 \\quad \\text{(posterior variance)}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "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",
    "$$\\begin{align*}\n",
    "P_t &= A V_{t-1} A^T + \\Gamma \\qquad &&\\text{(predicted variance)}\\\\\n",
    "K_t &= P_t C^T \\cdot \\left(C P_t C^T  + \\Sigma \\right)^{-1} \\qquad &&\\text{(Kalman gain)} \\\\\n",
    "\\mu_t &= A \\mu_{t-1} + K_t\\cdot\\left(x_t - C A \\mu_{t-1} \\right) \\qquad &&\\text{(posterior state mean)}\\\\\n",
    "V_t &= \\left(I-K_t C \\right) P_{t}  \\qquad &&\\text{(posterior state variance)}\n",
    "\\end{align*}$$\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": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: MvNormalMeanCovariance(\n",
      "μ: [40.81475989078067, 3.8792027585569526]\n",
      "Σ: [1.2958787328575079 0.3921572953097835; 0.3921572953130242 0.3415636711134632]\n",
      ")\n",
      "\n",
      "Measurement: MvNormalMeanCovariance(\n",
      "μ: [41.26691427784205, 2.6610823772108425]\n",
      "Σ: [1.0 0.0; 0.0 2.0]\n",
      ")\n",
      "\n",
      "Posterior: MvNormalMeanCovariance(\n",
      "μ: [40.97269820495181, 3.8000643123843214]\n",
      "Σ: [0.5516100293973586 0.15018972175285758; 0.15018972175409862 0.24143326063188655]\n",
      ")\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Rocket, ReactiveMP, RxInfer, 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: \",MvNormalMeanCovariance(m_pred_z,V_pred_z))\n",
    "println(\"Measurement: \", MvNormalMeanCovariance(noisy_x[n],Σx))\n",
    "println(\"Posterior: \", MvNormalMeanCovariance(m_z,V_z))\n",
    "plotCartPrediction(m_pred_z[1], V_pred_z[1], m_z[1], V_z[1], noisy_x[n][1], Σx[1][1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 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 let [RxInfer](https://biaslab.github.io/rxinfer-website/) execute the message passing schedule. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "@model function cart_tracking(n, A, b, Σz, Σx, z_prev_m_0, z_prev_v_0, u)\n",
    "    \n",
    "    # We create constvar references for better efficiency\n",
    "    cA = constvar(A)\n",
    "    cB = constvar(b)\n",
    "    cΣz = constvar(Σz)\n",
    "    cΣx = constvar(Σx)\n",
    "    \n",
    "    znodes = Vector{Any}(undef, n)\n",
    "    # `z` is a sequence of hidden states\n",
    "    z = randomvar(n)\n",
    "    # `x` is a sequence of \"clamped\" observations\n",
    "    x = datavar(Vector{Float64}, n)\n",
    "    \n",
    "    z_prior ~ MvNormalMeanCovariance(z_prev_m_0, z_prev_v_0)\n",
    "    \n",
    "    z_prev = z_prior\n",
    "    \n",
    "    for i in 1:n\n",
    "        znodes[i],z[i] ~ MvNormalMeanCovariance(cA * z_prev + cB*u[i], cΣz)\n",
    "        x[i] ~ MvNormalMeanCovariance(z[i], cΣx)\n",
    "        z_prev = z[i]\n",
    "    end\n",
    "    \n",
    "    return z, x, znodes\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now that we've built the model, we can perform Kalman filtering by inserting measurement data into the model and performing message passing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: MvNormalMeanCovariance(\n",
      "μ: [40.802612803139645, 3.8754423083271528]\n",
      "Σ: [1.2934227334046857 0.3916229823498387; 0.3916229823498387 0.3414332606222485]\n",
      ")\n",
      "\n",
      "Measurement: MvNormalMeanCovariance(\n",
      "μ: [41.26691427784205, 2.6610823772108425]\n",
      "Σ: [1.0 0.0; 0.0 2.0]\n",
      ")\n",
      "\n",
      "Posterior: MvNormalMeanCovariance(\n",
      "μ: [40.96734677603605, 3.7985715143001206]\n",
      "Σ: [0.551150997075792 0.1501469959500068; 0.1501469959500068 0.24141815274489328]\n",
      ")\n",
      "\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_prev_m_0 = noisy_x[1]  \n",
    "z_prev_v_0 = A * (1e8*Diagonal(I,2) * A') + Σz ;\n",
    "result = inference(model=cart_tracking(n, A,b, Σz, Σx, z_prev_m_0, z_prev_v_0,u), data=(x=noisy_x,), free_energy=true);\n",
    "μz_posterior, Σz_posterior = mean.(result.posteriors[:z])[end], cov.(result.posteriors[:z])[end];\n",
    "prediction_z_1 =  ReactiveMP.messageout(ReactiveMP.getinterface(result.returnval[end][end], :out))\n",
    "prediction = ReactiveMP.materialize!(Rocket.getrecent(prediction_z_1));\n",
    "println(\"Prediction: \",MvNormalMeanCovariance(mean(prediction), cov(prediction)))\n",
    "println(\"Measurement: \", MvNormalMeanCovariance(noisy_x[n], Σx))\n",
    "println(\"Posterior: \", MvNormalMeanCovariance(μz_posterior, Σz_posterior))\n",
    "plotCartPrediction(mean(prediction)[1], cov(prediction)[1], μz_posterior[1], Σz_posterior[1], noisy_x[n][1], Σx[1][1]);"
   ]
  },
  {
   "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 RxInfer is that we did not need to derive any inference equations. RxInfer 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",
    "$$\\begin{align*}\n",
    "\\overbrace{p(z_t\\,|\\,x^t)}^{\\text{posterior}} \\cdot \\overbrace{p(x_t\\,|\\,x^{t-1})}^{\\text{evidence}} \n",
    " &= p(x_t,z_t\\,|\\,x^{t-1}) \\\\\n",
    " &= p(x_t\\,|\\,z_t) \\,p(z_t\\,|\\,x^{t-1}) \\\\\n",
    " &= p(x_t\\,|\\,z_t) \\, \\int p(z_t,z_{t-1}\\,|\\,x^{t-1}) \\mathrm{d}z_{t-1}  \\\\\n",
    " &= p(x_t\\,|\\,z_t) \\, \\int p(z_t\\,|\\,z_{t-1}) \\, p(z_{t-1}\\,|\\,x^{t-1}) \\mathrm{d}z_{t-1} \\\\\n",
    " &=  \\underbrace{\\mathcal{N}(x_t|c z_t, \\sigma_x^2)}_{\\text{likelihood}} \\, \\int \\underbrace{\\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2)}_{\\text{state transition} } \\, \\underbrace{\\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) }_{\\text{prior}}  \\mathrm{d}z_{t-1} \n",
    "\\end{align*}$$\n",
    " \n",
    "- The RHS can be further evaluated by making use of the Gaussian multiplication rules and the following renormalization equality: \n",
    "$$\\begin{align*}\n",
    "\\mathcal{N}(x\\,|\\,cz,\\sigma^2) = \\frac{1}{c}\\cdot \\mathcal{N}\\left(z \\,\\big|\\,\\frac{x}{c},\\left(\\frac{\\sigma}{c}\\right)^2\\right) \\qquad &&\\text{(renormalization)}\\,.\n",
    "\\end{align*}$$\n",
    "\n",
    "In particular, the RHS evaluates to\n",
    "$$\\begin{align*} \n",
    "\\mathcal{N}(x_t|c z_t, &\\sigma_x^2) \\, \\int \\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) \\mathrm{d}z_{t-1} \\\\\n",
    "&= \\mathcal{N}(x_t|c z_t, \\sigma_x^2) \\, \\int \\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}} \\mathrm{d}z_{t-1} \\\\\n",
    "&= \\frac{1}{a} \\mathcal{N}(x_t|c z_t, \\sigma_x^2) \\, \\int \\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{integrates to }1} \\mathrm{d}z_{t-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})} \\cdot \\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",
    "$$\\begin{align*}\n",
    "  \\rho_t^2 &= a^2 \\sigma_{t-1}^2 + \\sigma_z^2 \\qquad &&\\text{(predicted variance)}\\\\\n",
    "  K_t &= \\frac{c \\rho_t^2}{c^2 \\rho_t^2 + \\sigma_x^2} \\qquad &&\\text{(Kalman gain)} \\\\\n",
    "  \\mu_t &= \\underbrace{a \\mu_{t-1}}_{\\text{prior prediction}} + K_t \\cdot \\underbrace{\\left( x_t - c a \\mu_{t-1}\\right)}_{\\text{prediction error}} \\qquad &&\\text{(posterior mean)}\\\\\n",
    "  \\sigma_t^2 &= \\left( 1 - c\\cdot K_t \\right) \\rho_t^2 \\qquad &&\\text{(posterior variance)}\n",
    "\\end{align*}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 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\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
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