{
 "cells": [
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   "source": [
    "# Dynamic Latent Variable Models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   },
   "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](./files/Faragher-2012-Understanding-the-Basis-of-the-Kalman-Filter.pdf)\n",
    "    - Minka (1999), [From Hidden Markov Models to Linear Dynamical Systems](./files/Minka-1999-from-HMM-to-LDS.pdf)\n",
    "      \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example Problem\n",
    "\n",
    "- <span class=\"exercise\">We consider a one-dimensional cart position tracking problem, see</span>  [Faragher 2012](./files/Faragher-2012-Understanding-the-Basis-of-the-Kalman-Filter.pdf).  \n",
    "\n",
    "- <span class=\"exercise\">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 $x_t$.</span> \n",
    "\n",
    "- <span class=\"exercise\">The equations of motions are given by</span>\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",
    "- <span class=\"exercise\">Infer the position after 10 time steps.</span> \n",
    "\n",
    "<img src=\"./figures/Faragher-2012-cart-1.png\" width=\"600px\">\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",
    "\n",
    "- Consider the _ordered_ observation sequence $x^T \\triangleq \\left(x_1,x_2,\\ldots,x_T\\right)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We wish to develop a generative model\n",
    "    $$ p( x^T \\,|\\, \\theta)$$\n",
    "that 'explains' the time series $x^T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We cannot use the IID assumption $p( x^T  | \\theta) = \\prod_t p(x_t \\,|\\, \\theta)$. In general, we _can_ use the [**chain rule**](https://en.wikipedia.org/wiki/Chain_rule_(probability) (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, the $M$th-order linear **Auto-Regressive** (AR) model\n",
    "    $$\\begin{align*}\n",
    "  p(x_t\\,|\\,x^{t-1}) = \\mathcal{N}\\left(x_t \\,\\middle|\\,  \\sum_{m=1}^M a_m x_{t-m}\\,,\\sigma^2\\,\\right)  \n",
    "    \\end{align*}$$\n",
    "    limits the dependencies to the past $M$ 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 $K$-dimensional discrete variable, then an $M$th-order AR model will have $K^{M-1}(K-1)$ 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 general **state space model** is 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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- A common assumption is to let state transitions be ruled by a _first-order Markov chain_ as\n",
    "$$\n",
    " p(z_t\\,|\\,z^{t-1}) = p(z_t\\,|\\,z_{t-1})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- <span class=\"exercise\">Exercise: Show that in a Markovian state-space model, the observation sequence $x^T$ is not a first-order Markov chain, i.e., show that for the 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 $t-1$. \n",
    "</span>"
   ]
  },
  {
   "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": {
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     "slide_type": "fragment"
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   },
   "source": [
    "- E.g., $Z_t$ is a $K$-dimensional hidden binary 'class indicator' with transition probabilities $A_{jk} \\triangleq p(z_{tk}=1\\,|\\,z_{t-1,j}=1)$, or equivalently\n",
    "  $$p(z_t|z_{t-1}) = \\prod_{k=1}^K \\prod_{j=1}^K A_{jk}^{z_{t-1,j}z_{tk}}$$\n",
    "which is usually accompanied by an initial state distribution $\\pi_k \\triangleq p(z_{1k}=1)$."
   ]
  },
  {
   "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 $\\{(x_1,z_1),\\ldots,(x_t,z_t)\\}$ 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": {
    "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",
    " "
   ]
  },
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   "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 $p(z_{t-1}\\,|\\,x^{t-1})$ 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 this is _in principle_ possible to execute inference problems analytically and the result will be a Gaussian posterior:\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\underbrace{p(z_t\\,|\\,x^t)}_{\\text{posterior}} &= p(z_t\\,|\\,x_t,x^{t-1}) \\propto p(x_t,z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &\\propto p(x_t\\,|\\,z_t) \\,p(z_t\\,|\\,x^{t-1}) \\\\\n",
    "  &= p(x_t\\,|\\,z_t) \\, \\sum_{z_{t-1}} p(z_t,z_{t-1}\\,|\\,x^{t-1}) \\\\\n",
    "  &= \\underbrace{p(x_t\\,|\\,z_t)}_{\\text{observation}} \\, \\sum_{z_{t-1}} \\underbrace{p(z_t\\,|\\,z_{t-1})}_{\\text{state transition}} \\, \\underbrace{p(z_{t-1}\\,|\\,x^{t-1})}_{\\text{prior}} \\\\\n",
    "  &= \\mathcal{N}(x_t\\,|\\,c z_t,\\sigma_x^2) \\sum_{z_{t-1}} \\mathcal{N}(z_t\\,|\\,a z_{t-1},\\sigma_z^2) \\, \\mathcal{N}(z_{t-1} \\,|\\, \\mu_{t-1}, \\sigma_{t-1}^2) \\\\\n",
    "  &\\propto \\mathcal{N}\\left(z_t\\,\\bigm| \\,\\frac{x_t}{c} ,\\left(\\frac{\\sigma_x}{c}\\right)^2\\right) \\times \\mathcal{N}\\left(z_t\\, \\bigm|\\,a \\mu_{t-1},\\sigma_z^2 + \\left(a \\sigma_{t-1}\\right)^2 \\right) \\\\\n",
    "  &= \\mathcal{N}\\left( z_t \\,|\\, \\mu_t, \\sigma_t^2\\right)\n",
    "\\end{align*}$$\n",
    "with\n",
    "$$\\begin{align*}\n",
    "  \\rho_t^2 &= \\sigma_z^2 + a^2 \\sigma_{t-1}^2 \\tag{auxiliary variable}\\\\\n",
    "  K_t &= \\frac{c \\rho_t^2}{c^2 \\rho_t^2 + \\sigma_x^2} \\tag{'Kalman gain'} \\\\\n",
    "  \\mu_t &= a \\mu_{t-1} + K_t \\cdot \\left( x_t - c a \\mu_{t-1}\\right) \\tag{posterior mean}\\\\\n",
    "  \\sigma_t^2 &= \\left( 1 - K_t \\right) \\rho_t^2 \\tag{posterior variance}\n",
    "\\end{align*}$$\n",
    "\n",
    "- Kalman filtering consists of computing/updating these four equations for each new observation ($x_t$). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Kalman Filtering and the Cart Position Tracking Example Revisited\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 are given by (see Bishop, pg.639)\n",
    "$$\\begin{align*}\n",
    "P_t &= A V_{t-1} A^T + \\Gamma &&\\text{auxiliary variable}\\\\\n",
    "K_t &= P_t C^T \\cdot \\left( \\Sigma + C P_t C^T\\right)^{-1} &&\\text{Kalman gain vector} \\\\\n",
    "\\mu_t &= A \\mu_{t-1} + K_t\\cdot\\left(x_t - C A \\mu_{t-1} \\right) &&\\text{posterior state mean}\\\\\n",
    "V_t &= \\left(I-K_t C \\right) V_{t-1}  &&\\text{posterior state variance}\n",
    "\\end{align*}$$\n",
    "\n",
    "- We can solve the cart tracking problem by implementing the Kalman filter, see the next code example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "outputs": [
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      "text/plain": [
       "Figure(PyObject <Figure size 1500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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",
    "\n",
    "plotCartPrediction2(m_pred_z[1], V_pred_z[1], m_z[1], V_z[1], noisy_x[n][1], Σx[1][1]);"
   ]
  },
  {
   "cell_type": "markdown",
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   "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": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "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."
   ]
  },
  {
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    "- 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",
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    "- 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. "
   ]
  },
  {
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    "- 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",
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     "slide_type": "fragment"
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   "source": [
    "- $\\Rightarrow$ Generally, we will want to automate the inference process. This issue is discussed in the next lesson on inference by message passing in factor graphs."
   ]
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   "cell_type": "code",
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