{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Latent Variable Models and Variational Bayes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "### Preliminaries\n",
    "\n",
    "- Goal \n",
    "  - Introduction to latent variable models and variational inference by Free energy minimization   \n",
    "- Materials\n",
    "  - Mandatory\n",
    "    - These lecture notes\n",
    "    - Ariel Caticha (2010), [Entropic Inference](https://arxiv.org/abs/1011.0723)\n",
    "      - tutorial on entropic inference, which is a generalization to Bayes rule and provides a foundation for variational inference.\n",
    "  - Optional \n",
    "    - Bishop (2016), pp. 461-486 (sections 10.1, 10.2 and 10.3) \n",
    "  - references <a id='references'></a>\n",
    "    - Blei et al. (2017), [Variational Inference: A Review for Statisticians](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1285773) \n",
    "    - Lanczos (1961), [The variational principles of mechanics](https://www.amazon.com/Variational-Principles-Mechanics-Dover-Physics/dp/0486650677)\n",
    "    - Zhang et al. (2017), [Unifying Message Passing Algorithms Under the Framework of Constrained Bethe Free Energy Minimization](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Zhang-2017-Unifying-Message-Passing-Algorithms.pdf)\n",
    "    - Dauwels (2007), [On variational message passing on factor graphs](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Dauwels-2007-on-variational-message-passing-on-factor-graphs)\n",
    "    - Caticha (2010), [Entropic Inference](https://arxiv.org/abs/1011.0723)\n",
    "    - Shore and Johnson (1980), [Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/ShoreJohnson-1980-Axiomatic-Derivation-of-the-Principle-of-Maximum-Entropy.pdf)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Illustrative Example <a id=\"illustrative-example\"></a>: Density Modeling for the Old Faithful Data Set\n",
    "\n",
    "- You're now asked to build a density model for a data set ([Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful), Bishop pg. 681) that clearly is not distributed as a single Gaussian:\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/fig-Bishop-A5-Old-Faithfull.png\" width=\"500\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Unobserved Classes\n",
    "\n",
    "Consider again a set of observed data $D=\\{x_1,\\dotsc,x_N\\}$\n",
    "\n",
    "- This time we suspect that there are _unobserved_ class labels that would help explain (or predict) the data, e.g.,\n",
    "  - the observed data are the color of living things; the unobserved classes are animals and plants.\n",
    "  - observed are wheel sizes; unobserved categories are trucks and personal cars.\n",
    "  - observed is an audio signal; unobserved classes include speech, music, traffic noise, etc.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "   \n",
    "- Classification problems with unobserved classes are called **Clustering** problems. The learning algorithm needs to **discover the classes from the observed data**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Gaussian Mixture Model\n",
    "\n",
    "- The spread of the data in the illustrative example looks like it could be modeled by two Gaussians. Let's develop a model for this data set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Let $D=\\{x_n\\}$ be a set of observations. We associate a one-hot coded hidden class label $z_n$ with each observation:\n",
    "\n",
    "$$\\begin{equation*}\n",
    "z_{nk} = \\begin{cases} 1 & \\text{if } x_n \\in \\mathcal{C}_k \\text{ (the k-th class)}\\\\\n",
    "                       0 & \\text{otherwise} \\end{cases}\n",
    "\\end{equation*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We consider the same model as we did in the [generative classification lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Generative-Classification.ipynb#GDA):\n",
    "$$\\begin{align*}\n",
    "p(x_n | z_{nk}=1) &= \\mathcal{N}\\left( x_n | \\mu_k, \\Sigma_k\\right)\\\\\n",
    "p(z_{nk}=1) &= \\pi_k\n",
    "\\end{align*}$$\n",
    "which can be summarized with the selection variables $z_{nk}$ as\n",
    "$$\\begin{align*}\n",
    "p(x_n,z_n) &= p(x_n | z_n) p(z_n) = \\prod_{k=1}^K (\\underbrace{\\pi_k \\cdot \\mathcal{N}\\left( x_n | \\mu_k, \\Sigma_k\\right) }_{p(x_n,z_{nk}=1)})^{z_{nk}} \n",
    "\\end{align*}$$\n",
    "\n",
    "- *Again*, this is the same model  as we defined for the generative classification model: A Gaussian-Categorical model but now with unobserved classes). \n",
    "\n",
    "- This model (with **unobserved class labels**) is known as a **Gaussian Mixture Model** (GMM)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Marginal Distribution for the GMM\n",
    "\n",
    "- In the literature, the GMM is often introduced the marginal distribution for an _observed_ data point $x_n$, given by\n",
    "\n",
    "$$\\begin{align*}{}\n",
    "p(x_n) &= \\sum_{z_n} p(x_n,z_n)  \\\\\n",
    "  &= \\sum_{k=1}^K \\pi_k \\cdot \\mathcal{N}\\left( x_n | \\mu_k, \\Sigma_k \\right) \\tag{B-9.12}\n",
    "\\end{align*}$$\n",
    "\n",
    "- Full proof as an [exercise](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/exercises/Exercises-Latent-Variable-Models-and-VB.ipynb). \n",
    "\n",
    "- Eq. B-9.12 reveals the link to the name Gaussian *mixture model*. The priors $\\pi_k$ are also called **mixture coefficients**. \n",
    "  \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  GMM is a very flexible model\n",
    "\n",
    "- GMMs are very popular models. They have decent computational properties and are **universal approximators of densities** (as long as there are enough Gaussians of course)\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/fig-ZoubinG-GMM-universal-approximation.png\" width=\"600\"></p>\n",
    "\n",
    "- (In the above figure, the Gaussian components are shown in <font color=red>red</font> and the pdf of the mixture models in <font color=blue>blue</font>)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Latent Variable Models\n",
    "\n",
    "- The GMM contains both _observed_ variables $\\{x_n\\}$, (unobserved) _parameters_ $\\theta= \\{\\pi_k,\\mu_k, \\Sigma_k\\}$ _and_ unobserved (synonym: latent, hidden) variables $\\{z_{nk}\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- From a Bayesian viewpoint, both latent variables $\\{z_{nk}\\}$ and parameters $\\theta$ are just unobserved variables for which we can set a prior and compute a posterior by Bayes rule. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note that $z_{nk}$ has a subscript $n$, hence its value depends not only on the cluster ($k$) but also on the $n$-th observation (in constrast to parameters). These observation-dependent variables are generally a useful tool to encode structure in the model. Here (in the GMM), the latent variables $\\{z_{nk}\\}$ encode (unobserved) class membership. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- By adding model structure through (equations among) latent variables, we can build very complex models. Unfortunately, inference in latent variable models can also be much more complex than for fully observed models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Inference for GMM is Difficult\n",
    "\n",
    "\n",
    "- We recall here the log-likelihood for the Gaussian-Categorial Model, see [generative classification lesson)](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Generative-Classification.ipynb)\n",
    "\n",
    "$$\n",
    "\\log\\, p(D|\\theta) =  \\sum_{n,k} y_{nk} \\underbrace{ \\log\\mathcal{N}(x_n|\\mu_k,\\Sigma) }_{ \\text{Gaussian} } + \\underbrace{ \\sum_{n,k} y_{nk} \\log \\pi_k }_{ \\text{multinomial} } \\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Since the class labels $y_{nk} \\in \\{0,1\\}$ were given, this expression decomposed into a set of simple updates for the Gaussian and multinomial distributions. For both distributions, we have conjugate priors, so inference is easily solved. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- However, for the Gaussian mixture model (same log-likelihood function with $z_{nk}$ replacing $y_{nk}$), the class labels $\\{z_{nk}\\}$ are _unobserved_ and need to estimated alongside with the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- There is no conjugate prior on the latent variables for the GMM likelihood function $p(\\underbrace{D}_{\\{x_n\\}}\\,|\\,\\underbrace{\\{z_{nk}\\},\\{\\mu_k,\\Sigma_k,\\pi_k\\}}_{\\text{all latent variables}})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In this lesson, we introduce an approximate Bayesian inference method known as **Variational Bayes** (VB) (also known as **Variational Inference**) that can be used for Bayesian inference in models with latent variables. Later in this lesson, we will use VB to do inference in the GMM.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- As a motivation for variational inference, we first discuss inference by the **Method of Maximum Relative Entropy**, [(Caticha, 2010)](https://arxiv.org/abs/1011.0723). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Inference When Information is in the Form of Constraints \n",
    "\n",
    "- In the [probability theory lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Probability-Theory-Review.ipynb#Bayes-rule), we recognized Bayes rule as the fundamental rule for learning from data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We will now generalize this notion and consider learning as a process that updates a prior into a posterior distribution whenever new information becomes available."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In this context, *new information* is not necessarily a new observation, but could (for instance) also relate to *constraints* on the posterior distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- For example, consider a model $\\prod_n p(x_n,z) = p(z) \\prod_n p(x_n|z)$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Our prior beliefs about $z$ are represented by $p(z)$. In the following, we will write $q(z)$ to denote a posterior distribution for $z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "-  We might be interested in obtaining rational posterior beliefs $q(z)$ in consideration of the following additional constraints:\n",
    "  1. *Data Constraints*: e.g., two observed data points $x_1=5$ and $x_2=3$, which lead to constraints $q(x_1) = \\delta(x_1-5)$ and $q(x_2)=\\delta(x_2-3)$.\n",
    "  2. *Form Constraints*: e.g., we only consider the Gamma distribution for $q(z) = \\mathrm{Gam}(z|\\alpha,\\beta)$.\n",
    "  3. *Factorization Constraints*:, e.g., we consider independent marginals for the posterior distribution: $q(z) = \\prod_k q(z_k)$. \n",
    "  3. *Moment Constraints*: e.g., the first moment of the posterior is given by $\\int z q(z) \\mathrm{d}z = 3$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Note that this is not \"just\" applying Bayes rule to compute a posterior, which can only deal with data constraints as specified by the likelihood function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note also that observations _can_ be rephrased as constraints on the posterior, e.g., observation $x_1=5$ can be phrased as a constraint $q(x_1)=\\delta(x_1-5)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\Rightarrow$ Updating a prior to a posterior on the basis of constraints on the posterior is more general than updating based on observations alone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Method of Maximum Relative Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- [Caticha (2010)](https://arxiv.org/abs/1011.0723) (based on earlier work by [Shore and Johnson (1980)](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/ShoreJohnson-1980-Axiomatic-Derivation-of-the-Principle-of-Maximum-Entropy.pdf)) developed the **method of maximum (relative) entropy** for rational updating of priors to posteriors when faced with new information in the form of constraints."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Consider prior beliefs $p(z)$ about $z$. New information in the form of constraints is obtained and we are interested in the \"best update\" to a posterior $q(z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In order to define what \"best update\" means, we assume a ranking function $S[q,p]$ that generates a preference score for each candidate posterior $q$ for a given $p$. The best update from $p$ to $q$ is identified as $q^* = \\arg\\max_q S[q,p]$.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Similarly to [Cox' method to deriving probability theory](https://en.wikipedia.org/wiki/Cox%27s_theorem), Caticha introduced the following mild criteria based on a rational principle (the **principle of minimal updating**, see [Caticha 2010](https://arxiv.org/abs/1011.0723)) that the ranking function needs to adhere to: \n",
    "  1. *Locality*: local information has local effects.\n",
    "  2. *Coordinate invariance*: the system of coordinates carries no information. \n",
    "  3. *Independence*: When systems are known to be independent, it should not matter whether they are treated separately or jointly. \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- These three criteria **uniquely identify the Relative Entropy** (RE) as the proper ranking function: \n",
    "$$\\begin{align*}\n",
    "S[q,p] = - \\sum_z q(z) \\log \\frac{q(z)}{p(z)}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\Rightarrow$ When information is supplied in the form of constaints on the posterior, we *should* select the posterior that maximizes the Relative Entropy, subject to the constraints. This is the **Method of Maximum (Relative) Entropy** (MRE). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relative Entropy, KL Divergence and Free Energy\n",
    "\n",
    "- Note that the Relative Entropy is technically a *functional*, i.e., a function of function(s) (since it is a function of probability distributions). The calculus of functionals is also called **variational calculus**.\n",
    "  - See  [Lanczos, The variational principles of mechanics (1961)](https://www.amazon.com/Variational-Principles-Mechanics-Dover-Physics/dp/0486650677) for a great book on variational calculus. For a summary, see Bishop (2016), app.D.\n",
    "  - It is customary to use square brackets (like $S[q,p]$) for functionals rather than round brackets, which we use for functions.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Also note the complimentary relation between the Maximum Relative Entropy method and Probability Theory: \n",
    "  - PT describes how to _represent_ beliefs about events and how to _calculate_ beliefs about joint and conditional events. \n",
    "  - In contrast, the MRE method describes how to _update_ beliefs when new information becomes available.\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- PT and the MRE method are both needed to describe the theory of optimal information processing. (As we will see below, Bayes rule is a special case of the MRE method.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In principle, entropies can always be considered as a *relative* score against a reference distribution. For instance, the score $-\\sum_{z_i} q(z_i) \\log q(z_i)$ can be interpreted as a score against the uniform distribution, i.e., $-\\sum_{z_i} q(z_i) \\log q(z_i) \\propto -\\sum_{z_i} q(z_i) \\log \\frac{q(z_i)}{\\mathrm{Uniform(z_i)}}$. Therefore, the \"method of maximum relative entropy\" is often simply known as the \"method of maximum entropy\". "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The negative relative entropy is known as the **Kullback-Leibler** (KL) divergence:\n",
    "$$\n",
    "\\mathrm{KL}[q,p] \\triangleq \\sum_z q(z) \\log \\frac{q(z)}{p(z)} \\tag{B-1.113}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The [Gibbs inequality](https://en.wikipedia.org/wiki/Gibbs%27_inequality) ([proof](https://en.wikipedia.org/wiki/Gibbs%27_inequality#Proof)), is a famous theorem in information theory that states that \n",
    "$$\\mathrm{KL}[q,p] \\geq 0 $$\n",
    "with equality only iff $p=q$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "  - The KL divergence can be interpreted as a \"distance\" between two probability distributions. Note however that the KL divergence is an asymmetric distance measure, i.e., in general $\\mathrm{KL}[q,p] \\neq \\mathrm{KL}[p,q]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We also introduce here the notion of a (variational) **Free Energy** (FE) functional, which is just a generalization of the KL-divergence that allows the prior to be unnormalized. Let $f(z) = Z \\cdot p(z)$ be an unnormalized distribution, then the FE is defined as\n",
    "$$\\begin{align*}\n",
    "F[q,p] &\\triangleq \\sum_z q(z) \\log \\frac{q(z)}{f(z)} \\\\\n",
    "&= \\sum_z q(z) \\log \\frac{q(z)}{Z\\cdot p(z)} \\\\\n",
    "&= \\underbrace{\\sum_z q(z) \\log \\frac{q(z)}{p(z)}}_{\\text{KL divergence }\\geq 0} - \\log Z\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Since the second term ($\\log Z$) is constant, FE minimization (subject to constraints) with respect to $q$ leads to the same posteriors as KL minimization and RE maximization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- If we are only interested in minimizing FE with respect to $q$, then we'll write $F[q]$ (rather than $F[q,p]$) fo brevity. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- In this class, we prefer to discuss inference in terms of minimizing Free Energy (subject to the constraints) rather than maximizing Relative Entropy, but note that these two concepts are equivalent. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example KL divergence for Gaussians\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/KL-Gauss-Example.png\" width=\"600\"></p>\n",
    "\n",
    "<span style=\"font-size:40%;text-align:center;\">source: By <a href=\"https://en.wikipedia.org/wiki/User:Mundhenk\" class=\"extiw\" title=\"w:User:Mundhenk\">Mundhenk</a> at <a href=\"https://en.wikipedia.org/wiki/\" class=\"extiw\" title=\"w:\">English Wikipedia</a>, <a href=\"https://creativecommons.org/licenses/by-sa/3.0\" title=\"Creative Commons Attribution-Share Alike 3.0\">CC BY-SA 3.0</a>, <a href=\"https://commons.wikimedia.org/w/index.php?curid=75315685\">Link</a></span>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Free Energy Functional and Variational Bayes\n",
    "\n",
    "- Let's get back to the issue of doing inference for models with latent variables (such as the GMM). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Consider a generative model specified by $p(x,z)$ where $x$ and $z$ represent the observed and unobserved variables, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Assume further that $x$ has been observed as $x=\\hat{x}$ and we are interested in performing inference, i.e., we want to compute the posterior $p(z|x=\\hat{x})$ for the latent variables and we want to compute the evidence $p(x=\\hat{x})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- According to the Method of Maximum Relative Entropy, in order to find the correct posterior $q(x,z)$, we should minimize\n",
    "\n",
    "$$\n",
    "\\mathrm{F}[q] = \\sum_{x,z} q(x,z) \\log \\frac{q(x,z)}{p(x,z)}\\,, \\quad \\text{subject to data constraint }x=\\hat{x}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The data constraint $x=\\hat{x}$ fixes posterior $q(x) = \\delta(x-\\hat{x})$, so the Free Energy evaluates to  \n",
    "\n",
    "$$\\begin{align*}\n",
    "F[q] &= \\sum_{z} \\sum_{x}q(z|x)q(x) \\log \\frac{q(z|x) q(x)}{p(z|x) p(x)} \\\\\n",
    "  &= \\sum_{z} \\sum_{x} q(z|x)\\delta(x-\\hat{x}) \\log \\frac{q(z|x)\\delta(x-\\hat{x})}{p(z|x) p(x)} \\\\\n",
    "  &= \\sum_{z} q(z|\\hat{x}) \\log \\frac{q(z|\\hat{x})}{p(z|\\hat{x}) p(\\hat{x}) } \\\\\n",
    "  &=  \\underbrace{\\sum_{z}q(z|\\hat{x}) \\log \\frac{q(z|\\hat{x})}{p(z|\\hat{x})}}_{\\text{KL divergence }\\geq 0} - \\underbrace{\\log p(\\hat{x})  }\\tag{B-10.2\n",
    "}_{\\text{log-evidence}}\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The log-evidence term does not depend on $q$. Hence, the global minimum $q(z|\\hat{x})^* \\triangleq \\arg\\min_q F[q]$ is obtained for $$q^*(z|\\hat{x}) = p(z|\\hat{x})\\,,$$ which is the correct **Bayesian posterior**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Furthermore, the minimal free energy $$F^* \\triangleq F[q^*] = -\\log p(\\hat{x})$$ equals minus **log-evidence**. (Or, equivalently, the evidence is given by $p(\\hat{x}) = \\exp\\left(-F[q^*] \\right)$.)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center>\n",
    "<div style=\"font-size:large; color:red\">\n",
    "$\\Rightarrow$ <font color=red>Bayesian inference can be executed by FE minimization.\n",
    "</div>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "-  This is an amazing result!  Note that FE minimization transforms an inference problem (that involves integration) to an optimization problem! Generally, optimization problems are easier to solve than integration problems. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Executing inference by minimizing the variational FE functional is called **Variational Bayes** (VB) or variational inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "-  (As an aside), note that Bishop introduces in Eq. B-10.2 an _Evidence Lower BOund_ (in modern machine learning literature abbreviated as **ELBO**) $\\mathcal{L}(z)$ that equals the _negative_ FE. We prefer to discuss variational inference in terms of a free energy (but it is the same story as he discusses with the ELBO).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  FE Minimization as Approximate Bayesian Inference\n",
    "\n",
    "- In the rest of this lesson, we are concerned with how to execute FE minimization (FEM) w.r.t $q$ for the functional\n",
    "$$\n",
    " F[q] = \\sum_{z}q(z) \\log \\frac{q(z)}{p(z|x)} - \\log p(x)  \n",
    " $$\n",
    "where $x$ has been observed and $z$ represent all latent variables.\n",
    "  - To keep the notation uncluttered, in the following we write $x$ rather than $\\hat{x}$, and we write simply $q(z)$ (rather than $q(z|\\hat{x})$) for the posterior.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Due to restrictions in our optimization algorithm, we are often unable to fully minimize the FE to the global minimum $q^*(z)$, but rather get stuck in a local minimum $\\hat{q}(z)$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note that, since $\\mathrm{KL}[q(z),p(z|x)]\\geq 0$ for any $q(z)$, the FE is always an upperbound on (minus) log-evidence, i.e.,\n",
    "$$\n",
    "F[q] \\geq -\\log p(x) \\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In practice, even if we cannot attain the global minimum, we can still use the local minimum $\\hat{q}(z) \\approx \\arg\\min_q F[q]$ to accomplish **approximate Bayesian inference**:   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\begin{align*}\n",
    "   \\text{posterior: } \\hat{q}(z) &\\approx p(z|x) \\\\\n",
    "   \\text{evidence: } p(x) &\\approx \\exp\\left( -F[\\hat{q}]\\right) \n",
    "    \\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Constrained FE Minimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Generally speaking, it can be very helpful in the FE minimization task to add some additional constraints on $q(z)$ (i.e., in addition to the data constraints)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Once we add constraints to $q$ (in addition to data constraints), we are no longer guaranteed that the minimum of the (constrained) FE coincides with the solution by Bayes rule (which only takes data as constraints). So again, at best constrained FEM is only an **approximation to Bayes rule**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- There are three important cases of adding constraints to $q(z)$ that often alleviates the FE minimization task:\n",
    "\n",
    "#### 1. mean-field factorization\n",
    "- We constrain the posterior to factorize into a set of _independent_ factors, i.e., \n",
    "$$\n",
    "q(z) = \\prod_{j=1}^m q_j(z_j)\\,, \\tag{B-10.5}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "####  2. fixed-form parameterization\n",
    "- We constrain the posterior to be part of a parameterized probability distribution, e.g., $$q(z) = \\mathcal{N}\\left( z | \\mu, \\Sigma \\right)\\,.$$ \n",
    "  - In this case, the functional minimization problem for $F[q]$ reduces to the minimization of a _function_ $F(\\mu,\\Sigma)$ w.r.t. its parameters.  \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### 3. the Expectation-Maximization (EM) algorithm\n",
    "- We place some constraints both on the prior and posterior for $z$ ([to be discussed in the Optional Slides](#EM-Algorithm)) that simplifies FE minimization to maximum-likelihood estimation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### FE Minimization with Mean-field Factorization Constraints: the CAVI Approach "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Let's work out FE minimization with additional mean-field constraints (=full factorization) constraints:  $$q(z) = \\prod_{j=1}^m q_j(z_j)\\,.$$\n",
    "  - In other words, the posteriors for $z_j$ are all considered independent. This is a strong constraint but leads often to good solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Given the mean-field constraints, it is possible to derive the following expression for the <a id=\"optimal-solutions\">optimal solutions</a> $q_j^*(z_j)$, for $j=1,\\ldots,m$: \n",
    "\n",
    "\\begin{equation*} \\tag{B-10.9}\n",
    "\\boxed{\n",
    "\\begin{aligned}\n",
    "\\log q_j^*(z_j) &\\propto \\mathrm{E}_{q_{-j}^*}\\left[ \\log p(x,z) \\right]  \\\\\n",
    "  &= \\underbrace{\\sum_{z_{-j}} q_{-j}^*(z_{-j}) \\underbrace{\\log p(x,z)}_{\\text{\"field\"}}}_{\\text{\"mean field\"}} \n",
    "\\end{aligned}}\n",
    "\\end{equation*}\n",
    "\n",
    "where we defined $q_{-j}^*(z_{-j}) \\triangleq q_1^*(z_1)q_2^*(z_2)\\cdots q_{j-1}^*(z_{j-1})q_{j+1}^*(z_{j+1})\\cdots q_m^*(z_m)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- **Proof** (from [Blei, 2017](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1285773)): We first rewrite the FE as a function of $q_j(z_j)$ only: \n",
    "  $$ F[q_j] = \\mathbb{E}_{q_{j}}\\left[ \\mathbb{E}_{q_{-j}}\\left[ \\log p(x,z_j,z_{-j})\\right]\\right] - \\mathbb{E}_{q_j}\\left[ \\log q_j(z_j)\\right] + \\mathtt{const.}\\,,$$\n",
    "  where the constant holds all terms that do not depend on $z_j$. This expression can be written as \n",
    "  $$ F[q_j] = \\sum_{z_j} q_j(z_j) \\log \\frac{q_j(z_j)}{\\exp\\left( \\mathbb{E}_{q_{-j}}\\left[ \\log p(x,z_j,z_{-j})\\right]\\right)}$$\n",
    "  which is a KL-divergence that is minimized by Eq. B-10.9.  (end proof)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "  \n",
    "- This is not yet a full solution to the FE minimization task since the solution $q_j^*(z_j)$ depends on expectations that involve other solutions $q_{i\\neq j}^*(z_{i \\neq j})$, and each of these other solutions $q_{i\\neq j}^*(z_{i \\neq j})$ depends on an expection that involves $q_j^*(z_j)$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In practice, we solve this chicken-and-egg problem by an iterative approach: we first initialize all $q_j(z_j)$ (for $j=1,\\ldots,m$) to an appropriate initial distribution and then cycle through the factors in turn by solving eq.B-10.9 and update $q_{-j}^*(z_{-j})$ with the latest estimates. (See [Blei, 2017](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1285773), Algorithm 1, p864).  \n",
    "\n",
    "- This algorithm for approximating Bayesian inference is known **Coordinate Ascent Variational Inference** (CAVI).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: FEM for the Gaussian Mixture Model (CAVI Approach)\n",
    "\n",
    "- Let's get back to the illustrative example at the beginning of this lesson: we want to do [density modeling for the Old Faithful data set](#illustrative-example).\n",
    "\n",
    "#### model specification\n",
    "\n",
    "\n",
    "- We consider a Gaussian Mixture Model, specified by \n",
    "$$\\begin{align*}\n",
    "p(x,z|\\theta) &= p(x|z,\\mu,\\Lambda)p(z|\\pi) \\\\\n",
    "  &= \\prod_{n=1}^N \\prod_{k=1}^K \\left(\\pi_k \\cdot \\mathcal{N}\\left( x_n | \\mu_k, \\Lambda_k^{-1}\\right)\\right)^{z_{nk}} \\tag{B-10.37,38}\n",
    "\\end{align*}$$\n",
    "with tuning parameters $\\theta=\\{\\pi_k, \\mu_k,\\Lambda_k\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Let us introduce some priors for the parameters. We factorize the prior and choose conjugate distributions by\n",
    "$$\n",
    "p(\\theta) = p(\\pi,\\mu,\\Lambda) = p(\\pi) p(\\mu|\\Lambda) p(\\Lambda)\n",
    "$$\n",
    "with \n",
    "$$\\begin{align*}\n",
    "p(\\pi) &= \\mathrm{Dir}(\\pi|\\alpha_0) = C(\\alpha_0) \\prod_k \\pi_k^{\\alpha_0-1} \\tag{B-10.39}\\\\\n",
    "p(\\mu|\\Lambda) &= \\prod_k \\mathcal{N}\\left(\\mu_k | m_0, \\left( \\beta_0 \\Lambda_k\\right)^{-1} \\right) \\tag{B-10.40}\\\\\n",
    "p(\\Lambda) &= \\prod_k \\mathcal{W}\\left( \\Lambda_k | W_0, \\nu_0 \\right) \\tag{B-10.40}\n",
    "\\end{align*}$$\n",
    "where $\\mathcal{W}\\left( \\cdot \\right)$ is a [Wishart distribution](https://en.wikipedia.org/wiki/Wishart_distribution) (i.e., a multi-dimensional Gamma distribution)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The full generative model is now specified by\n",
    "$$\n",
    "p(x,z,\\pi,\\mu,\\Lambda) = p(x|z,\\mu,\\Lambda) p(z|\\pi) p(\\pi) p(\\mu|\\Lambda) p(\\Lambda) \\tag{B-10.41}\n",
    "$$\n",
    "with hyperparameters $\\{ \\alpha_0, m_0, \\beta_0, W_0, \\nu_0\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### inference\n",
    "\n",
    "- Assume that we have observed $D = \\left\\{x_1, x_2, \\ldots, x_N\\right\\}$ and are interested to infer the posterior distribution for the tuning parameters: \n",
    "$$\n",
    "p(\\theta|D) = p(\\pi,\\mu,\\Lambda|D)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The (perfect) Bayesian solution is \n",
    "$$\n",
    "p(\\theta|D) = \\frac{p(x=D,\\theta)}{p(x=D)} = \\frac{\\sum_z p(x=D,z,\\pi,\\mu,\\Lambda)}{\\sum_z \\sum_{\\pi} \\iint p(x=D,z,\\pi,\\mu,\\Lambda) \\,\\mathrm{d}\\mu\\mathrm{d}\\Lambda}\n",
    "$$\n",
    "but this is intractable (See [Blei (2017), p861, eqs. 8 and 9](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1285773))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- <a id=\"mf-constraint\"></a>Alternatively, we can use **FE minimization with factorization constraint** \n",
    "$$\\begin{equation}\n",
    "q(\\theta) = q(z) \\cdot q(\\pi,\\mu,\\Lambda) \\tag{B-10.42}\n",
    "\\end{equation}$$ \n",
    "on the posterior. For the specified model, this leads to FE minimization wrt the hyperparameters, i.e., we need to minimize the function $F(\\alpha_0, m_0, \\beta_0, W_0, \\nu_0)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Bishop shows that the equations for the [optimal solutions (Eq. B-10.9)](#optimal-solutions) are analytically solvable for the GMM as specified above, leading to the following variational update equations (for $k=1,\\ldots,K$): \n",
    "$$\n",
    "\\begin{align*}\n",
    "\\alpha_k &= \\alpha_0 + N_k  \\tag{B-10.58} \\\\\n",
    "\\beta_k &= \\beta_0 + N_k  \\tag{B-10.60} \\\\\n",
    "m_k &= \\frac{1}{\\beta_k} \\left( \\beta_0 m_0 + N_k \\bar{x}_k \\right) \\tag{B-10.61} \\\\\n",
    "W_k^{-1} &= W_0^{-1} + N_k S_k + \\frac{\\beta_0 N_k}{\\beta_0 + N_k}\\left( \\bar{x}_k - m_0\\right) \\left( \\bar{x}_k - m_0\\right)^T \\tag{B-10.62} \\\\\n",
    "\\nu_k &= \\nu_0 + N_k \\tag{B-10.63}\n",
    "\\end{align*}\n",
    "$$\n",
    "where we used\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log \\rho_{nk} &= \\mathbb{E}\\left[ \\log \\pi_k\\right] + \\frac{1}{2}\\mathbb{E}\\left[ \\log | \\Lambda_k | \\right] - \\frac{D}{2} \\log(2\\pi) \\\\ \n",
    " & \\qquad - \\frac{1}{2}\\mathbb{E}\\left[(x_k - \\mu_k)^T \\Lambda_k(x_k - \\mu_k)  \\right]  \\tag{B-10.46} \\\\\n",
    "r_{nk} &= \\frac{\\rho_{nk}}{\\sum_{j=1}^K \\rho_{nj}} \\tag{B-10.49} \\\\\n",
    "N_k &= \\sum_{n=1}^N r_{nk} x_n \\tag{B-10.51} \\\\\n",
    "\\bar{x}_k &= \\frac{1}{N_k} \\sum_{n=1}^N r_{nk} x_n \\tag{B-10.52} \\\\\n",
    "S_k &= \\frac{1}{N_k} \\sum_{n=1}^N r_{nk} \\left( x_n - \\bar{x}_k\\right) \\left( x_n - \\bar{x}_k\\right)^T \\tag{B-10.53}\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Exam guide: Working out FE minimization for the GMM to these update equations (eqs B-10.58 through B-10.63) is not something that you need to reproduce without assistance at the exam. Rather, the essence is that *it is possible* to arrive at closed-form variational update equations for the GMM. You should understand though how FEM works conceptually and in principle be able to derive variational update equations for very simple models that do not involve clever mathematical tricks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Code Example: FEM for GMM on Old Faithfull data set\n",
    "\n",
    "- Below we exemplify training of a Gaussian Mixture Model on the Old Faithful data set by Free Energy Minimization, using the constraints as specified above, e.g., [(B-10.42)](#mf-constraint). "
   ]
  },
  {
   "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": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 6 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DataFrames, CSV, LinearAlgebra, PDMats, SpecialFunctions\n",
    "include(\"scripts/gmm_plot.jl\") # Holds plotting function \n",
    "old_faithful = CSV.read(\"datasets/old_faithful.csv\",DataFrame);\n",
    "X = convert(Matrix{Float64}, [old_faithful[!,1] old_faithful[!,2]]');#data matrix\n",
    "N = size(X, 2) #number of observations\n",
    "K = 6\n",
    "\n",
    "function sufficientStatistics(X,r,k::Int) #function to compute sufficient statistics\n",
    "    N_k = sum(r[k,:])\n",
    "    hat_x_k = sum([r[k,n]*X[:,n] for n in 1:N]) ./ N_k\n",
    "    S_k = sum([r[k,n]*(X[:,n]-hat_x_k)*(X[:,n]-hat_x_k)' for n in 1:N]) ./ N_k\n",
    "    return N_k, hat_x_k, S_k\n",
    "end\n",
    "\n",
    "function updateMeanPrecisionPi(m_0,β_0,W_0,ν_0,α_0,r) #variational maximisation function\n",
    "    m = Array{Float64}(undef,2,K) #mean of the clusters \n",
    "    β = Array{Float64}(undef,K) #precision scaling for Gausian distribution\n",
    "    W = Array{Float64}(undef,2,2,K) #precision prior for Wishart distributions\n",
    "    ν = Array{Float64}(undef,K) #degrees of freedom parameter for Wishart distribution\n",
    "    α = Array{Float64}(undef,K) #Dirichlet distribution parameter \n",
    "    for k=1:K\n",
    "        sst = sufficientStatistics(X,r,k)\n",
    "        α[k] = α_0[k] + sst[1]; β[k] = β_0[k] + sst[1]; ν[k] = ν_0[k] .+ sst[1]\n",
    "        m[:,k] = (1/β[k])*(β_0[k].*m_0[:,k] + sst[1].*sst[2])\n",
    "        W[:,:,k] = inv(inv(W_0[:,:,k])+sst[3]*sst[1] + ((β_0[k]*sst[1])/(β_0[k]+sst[1])).*(sst[2]-m_0[:,k])*(sst[2]-m_0[:,k])')\n",
    "    end\n",
    "    return m,β,W,ν,α\n",
    "end\n",
    "\n",
    "function updateR(Λ,m,α,ν,β) #variational expectation function\n",
    "    r = Array{Float64}(undef,K,N) #responsibilities \n",
    "    hat_π = Array{Float64}(undef,K) \n",
    "    hat_Λ = Array{Float64}(undef,K)\n",
    "    for k=1:K\n",
    "        hat_Λ[k] = 1/2*(2*log(2)+logdet(Λ[:,:,k])+digamma(ν[k]/2)+digamma((ν[k]-1)/2))\n",
    "        hat_π[k] = exp(digamma(α[k])-digamma(sum(α)))\n",
    "        for n=1:N\n",
    "           r[k,n] = hat_π[k]*exp(-hat_Λ[k]-1/β[k] - (ν[k]/2)*(X[:,n]-m[:,k])'*Λ[:,:,k]*(X[:,n]-m[:,k]))\n",
    "        end\n",
    "    end\n",
    "    for n=1:N\n",
    "        r[:,n] = r[:,n]./ sum(r[:,n]) #normalize to ensure r represents probabilities \n",
    "    end\n",
    "    return r\n",
    "end\n",
    "\n",
    "max_iter = 15\n",
    "#store the inference results in these vectors\n",
    "ν = fill!(Array{Float64}(undef,K,max_iter),3)\n",
    "β = fill!(Array{Float64}(undef,K,max_iter),1.0)\n",
    "α = fill!(Array{Float64}(undef,K,max_iter),0.01)\n",
    "R = Array{Float64}(undef,K,N,max_iter)\n",
    "M = Array{Float64}(undef,2,K,max_iter)\n",
    "Λ = Array{Float64}(undef,2,2,K,max_iter)\n",
    "clusters_vb = Array{Distribution}(undef,K,max_iter) #clusters to be plotted\n",
    "#initialize prior distribution parameters\n",
    "M[:,:,1] = [[3.0; 60.0];[4.0; 70.0];[2.0; 50.0];[2.0; 60.0];[3.0; 100.0];[4.0; 80.0]]\n",
    "for k=1:K\n",
    "    Λ[:,:,k,1] = [1.0 0;0 0.01]\n",
    "    R[k,:,1] = 1/(K)*ones(N)\n",
    "    clusters_vb[k,1] = MvNormal(M[:,k,1],PDMats.PDMat(convert(Matrix,Hermitian(inv(ν[1,1].*Λ[:,:,k,1])))))\n",
    "end\n",
    "#variational inference\n",
    "for i=1:max_iter-1\n",
    "    #variational expectation \n",
    "    R[:,:,i+1] = updateR(Λ[:,:,:,i],M[:,:,i],α[:,i],ν[:,i],β[:,i]) \n",
    "    #variational minimisation\n",
    "    M[:,:,i+1],β[:,i+1],Λ[:,:,:,i+1],ν[:,i+1],α[:,i+1] = updateMeanPrecisionPi(M[:,:,i],β[:,i],Λ[:,:,:,i],ν[:,i],α[:,i],R[:,:,i+1])\n",
    "    for k=1:K\n",
    "        clusters_vb[k,i+1] = MvNormal(M[:,k,i+1],PDMats.PDMat(convert(Matrix,Hermitian(inv(ν[k,i+1].*Λ[:,:,k,i+1])))))\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "subplot(2,3,1); plotGMM(X, clusters_vb[:,1], R[:,:,1]); title(\"Initial situation\")\n",
    "for i=2:6\n",
    "    subplot(2,3,i)\n",
    "    plotGMM(X, clusters_vb[:,i*2], R[:,:,i*2]); title(\"After $(i*2) iterations\")\n",
    "end\n",
    "PyPlot.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The generated figure looks much like Figure 10.6 in Bishop. The plots show results for Variational Bayesian\n",
    "mixture of K = 6 Gaussians applied to the Old Faithful data set, in\n",
    "which the ellipses denote the one\n",
    "standard-deviation density contours\n",
    "for each of the components, and the\n",
    "color coding of the data points reflects the \"soft\" class label assignments. Components whose expected\n",
    "mixing coefficient are numerically indistinguishable from zero are not\n",
    "plotted. Note that this procedure learns the number of classes (two), learns the class label for each observation, and learns the mean and variance for the Gaussian data distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Free Energy Decompositions and Fixed-form Constraints\n",
    "\n",
    "\n",
    "- <a id='fe-decompositions'></a> Making use of $p(x,z) = p(z|x)p(x) = p(x|z)p(z)$, the FE functional can be rewritten as \n",
    "\n",
    "$$\\begin{align*}\n",
    "\\mathrm{F}[q] &= \\underbrace{-\\sum_z q(z) \\log p(x,z)}_{\\text{energy}} - \\underbrace{\\sum_z q(z) \\log \\frac{1}{q(z)}}_{\\text{entropy}} \\tag{EE} \\\\\n",
    "&= \\underbrace{\\sum_z q(z) \\log \\frac{q(z)}{p(z|x)}}_{\\text{KL divergence}\\geq 0} - \\underbrace{\\log p(x)}_{\\text{log-evidence}} \\tag{DE}\\\\\n",
    "&= \\underbrace{\\sum_z q(z)\\log\\frac{q(z)}{p(z)}}_{\\text{complexity}} - \\underbrace{\\sum_z q(z) \\log p(x|z)}_{\\text{accuracy}}  \\tag{CA}\n",
    "\\end{align*}$$\n",
    "\n",
    "- These <a id=\"#fe-decompositions\">decompositions</a> are very insightful (we will revisit them later) and we will label them respectively as _energy-entropy_ (EE), _divergence-evidence_ (DE), and _complexity-accuracy_ (CA) decompositions. \n",
    "\n",
    "\n",
    "\n",
    "- In the [Bayesian Machine Learning](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Bayesian-Machine-Learning.ipynb) lecture, we discussed the CA decomposition of Bayesian model evidence to support the interpretation of evidence as a model performance criterion. Here, we recognize that FE allows a similar CA decomposition: minimizing FE increases data accuracy and decreases model complexity. \n",
    "\n",
    "- The CA decomposition makes use of the prior $p(z)$ and likelihood $p(x|z)$, both of which are selected by the engineer, so the FE can be evaluated with this decomposition!\n",
    "\n",
    "- If we now assume some parametric form for $q(z)$, e.g. $q(z) = \\mathcal{N}(z\\mid \\mu, \\Sigma)$, then the FE functional degenerates to a **regular function** $F(\\mu,\\Sigma)$. In principle, this function can be evaluated by the CA decomposition and minimized by standard (function) minimization methods. \n",
    "\n",
    "- The EE decomposition provides a link to a second law of thermodynamics: Minimizing FE leads to entropy maximization. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Summary\n",
    "\n",
    "- Latent variable models (LVM) contain a set of unobserved variables whose size grows with the number of observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- LVMs can model more complex phenomena than fully observed models, but inference in LVM models is usually not analytically solvable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The Free Energy (FE) functional transforms Bayesian inference computations (very large summations or integrals) to an optimization problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Inference by minimizing FE, also known as variational inference, is fully consistent with the \"Method of Maximum Relative Entropy\", which is by design the rational way to update beliefs from priors to posteriors when new information becomes available. Thus, FE mimimization is a \"correct\" inference procedure that generalizes Bayes rule. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In general, global FE minimization is an unsolved problem and finding good local minima is at the heart of current Bayesian technology research. Three simplifying constraints on the posterior $q(z)$ in the FE functional are currently popular in practical settings:\n",
    "    - mean-field assumptions\n",
    "    - assuming a parametric from for $q$\n",
    "    - EM algorithm\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "   \n",
    "- These constraints often makes FE minimization implementable at the price of obtaining approximately Bayesian inference results. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The back-ends of Probabilistic Programming languages often contain lots of methods for constrained FE minimization. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center><a id=\"optional-slides\">OPTIONAL SLIDES</a></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <a id=\"EM-Algorithm\">FE Minimization by the Expectation-Maximization (EM) Algorithm</a>\n",
    "\n",
    "- The EM algorithm is a special case of FE minimization that focusses on Maximum-Likelihood estimation for models with latent variables. \n",
    "- Consider a model $$p(x,z,\\theta)$$ with observations $x = \\{x_n\\}$, latent variables $z=\\{z_n\\}$ and parameters $\\theta$.\n",
    "\n",
    "- We can write the following FE functional for this model:\n",
    "$$\\begin{align*}\n",
    "F[q] =  \\sum_z \\sum_\\theta q(z,\\theta) \\log \\frac{q(z,\\theta)}{p(x,z,\\theta)} \n",
    "\\end{align*}$$\n",
    "\n",
    "- The EM algorithm makes the following simplifying assumptions:\n",
    "  1. The prior for the parameters is uninformative (uniform). This implies that \n",
    "  $$p(x,z,\\theta) = p(x,z|\\theta) p(\\theta) \\propto p(x,z|\\theta)$$\n",
    "  2. A factorization constraint $$q(z,\\theta) = q(z) q(\\theta)$$\n",
    "  3. The posterior for the parameters is a delta function:\n",
    "  $$q(\\theta) = \\delta(\\theta - \\hat{\\theta})$$\n",
    " \n",
    "\n",
    " \n",
    "- Basically, these three assumptions turn FE minimization into maximum likelihood estimation for the parameters $\\theta$ and the FE simplifies to \n",
    "$$\\begin{align*}\n",
    "F[q,\\theta] =  \\sum_z q(z) \\log \\frac{q(z)}{p(x,z|\\theta)} \n",
    "\\end{align*}$$\n",
    "\n",
    "- The EM algorithm minimizes this FE by iterating (iteration counter: $i$) over \n",
    "\n",
    "\\begin{equation*}\n",
    "\\boxed{\n",
    "\\begin{aligned}\n",
    "\\mathcal{L}^{(i)}(\\theta) &= \\sum_z \\overbrace{p(z|x,\\theta^{(i-1)})}^{q^{(i)}(z)}  \\log p(x,z|\\theta) \\quad &&\\text{the E-step} \\\\\n",
    "\\theta^{(i)} &= \\arg\\max_\\theta \\mathcal{L}^{(i)}(\\theta) &&\\text{the M-step}\n",
    "\\end{aligned}}\n",
    "\\end{equation*}\n",
    "\n",
    "- These choices are optimal for the given FE functional. In order to see this, consider the two decompositions\n",
    "$$\\begin{align}\n",
    "F[q,\\theta] &= \\underbrace{-\\sum_z q(z) \\log p(x,z|\\theta)}_{\\text{energy}} - \\underbrace{\\sum_z q(z) \\log \\frac{1}{q(z)}}_{\\text{entropy}} \\tag{EE}\\\\\n",
    "  &= \\underbrace{\\sum_z q(z) \\log \\frac{q(z)}{p(z|x,\\theta)}}_{\\text{divergence}} - \\underbrace{\\log p(x|\\theta)}_{\\text{log-likelihood}}  \\tag{DE}\n",
    "\\end{align}$$\n",
    "\n",
    "- The DE decomposition shows that the FE is minimized for the choice $q(z) := p(z|x,\\theta)$. Also, for this choice, the FE equals the (negative) log-evidence (, which is this case simplifies to the log-likelihood). \n",
    "\n",
    "- The EE decomposition shows that the FE is minimized wrt $\\theta$ by minimizing the energy term. The energy term is computed in the E-step and optimized in the M-step.\n",
    "  - Note that in the EM literature, the energy term is often called the _expected complete-data log-likelihood_.)\n",
    "\n",
    "- In order to execute the EM algorithm, it is assumed that we can analytically execute the E- and M-steps. For a large set of models (including models whose distributions belong to the exponential family of distributions), this is indeed the case and hence the large popularity of the EM algorithm. \n",
    "\n",
    "- The EM algorihm imposes rather severe assumptions on the FE (basically approximating Bayesian inference by maximum likelihood estimation). Over the past few years, the rise of Probabilistic Programming languages has dramatically increased the range of models for which the parameters can by estimated autmatically by (approximate) Bayesian inference, so the popularity of EM is slowly waning. (More on this in the Probabilistic Programming lessons). \n",
    "\n",
    "- Bishop (2006) works out EM for the GMM in section 9.2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code Example: EM-algorithm for the GMM on the Old-Faithful data set\n",
    "\n",
    "We'll perform clustering on the data set from the [illustrative example](#illustrative-example) by fitting a GMM consisting of two Gaussians using the EM algorithm. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 6 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Pkg; Pkg.activate(\"probprog/workspace\");Pkg.instantiate();\n",
    "IJulia.clear_output();\n",
    "\n",
    "using DataFrames, CSV, LinearAlgebra\n",
    "include(\"scripts/gmm_plot.jl\") # Holds plotting function \n",
    "old_faithful = CSV.read(\"datasets/old_faithful.csv\", DataFrame);\n",
    "\n",
    "X =  Array(Matrix{Float64}(old_faithful)')\n",
    "N = size(X, 2)\n",
    "\n",
    "# Initialize the GMM. We assume 2 clusters.\n",
    "clusters = [MvNormal([4.;60.], [.5 0;0 10^2]); \n",
    "            MvNormal([2.;80.], [.5 0;0 10^2])];\n",
    "π_hat = [0.5; 0.5]                    # Mixing weights\n",
    "γ = fill!(Matrix{Float64}(undef,2,N), NaN)  # Responsibilities (row per cluster)\n",
    "\n",
    "# Define functions for updating the parameters and responsibilities\n",
    "function updateResponsibilities!(X, clusters, π_hat, γ)\n",
    "    # Expectation step: update γ\n",
    "    norm = [pdf(clusters[1], X) pdf(clusters[2], X)] * π_hat\n",
    "    γ[1,:] = (π_hat[1] * pdf(clusters[1],X) ./ norm)'\n",
    "    γ[2,:] = 1 .- γ[1,:]\n",
    "end\n",
    "function updateParameters!(X, clusters, π_hat, γ)\n",
    "    # Maximization step: update π_hat and clusters using ML estimation\n",
    "    m = sum(γ, dims=2)\n",
    "    π_hat = m / N\n",
    "    μ_hat = (X * γ') ./ m'\n",
    "    for k=1:2\n",
    "        Z = (X .- μ_hat[:,k])\n",
    "        Σ_k = Symmetric(((Z .* (γ[k,:])') * Z') / m[k])\n",
    "        clusters[k] = MvNormal(μ_hat[:,k], convert(Matrix, Σ_k))\n",
    "    end\n",
    "end\n",
    "\n",
    "# Execute the algorithm: iteratively update parameters and responsibilities\n",
    "subplot(2,3,1); plotGMM(X, clusters, γ); title(\"Initial situation\")\n",
    "updateResponsibilities!(X, clusters, π_hat, γ)\n",
    "subplot(2,3,2); plotGMM(X, clusters, γ); title(\"After first E-step\")\n",
    "updateParameters!(X, clusters, π_hat, γ)\n",
    "subplot(2,3,3); plotGMM(X, clusters, γ); title(\"After first M-step\")\n",
    "iter_counter = 1\n",
    "for i=1:3\n",
    "    for j=1:i+1\n",
    "        updateResponsibilities!(X, clusters, π_hat, γ)\n",
    "        updateParameters!(X, clusters, π_hat, γ)\n",
    "        iter_counter += 1\n",
    "    end\n",
    "    subplot(2,3,3+i); \n",
    "    plotGMM(X, clusters, γ); \n",
    "    title(\"After $(iter_counter) iterations\")\n",
    "end\n",
    "PyPlot.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that you can step through the interactive demo yourself by running [this script](https://github.com/bertdv/AIP-5SSB0/blob/master/lessons/notebooks/scripts/interactive_em_demo.jl) in julia. You can run a script in julia by    \n",
    "`julia> include(\"path/to/script-name.jl\")`"
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    "### Message Passing for Free Energy Minimization\n",
    "\n",
    "- The Sum-Product (SP) update rule implements perfect Bayesian inference. \n",
    "- Sometimes, the SP update rule is not analytically solvable. \n",
    "- Fortunately, for many well-known Bayesian approximation methods, a message passing update rule can be created, e.g. [Variational Message Passing](https://en.wikipedia.org/wiki/Variational_message_passing) (VMP) for variational inference. \n",
    "- In general, all of these message passing algorithms can be interpreted as minimization of a constrained free energy (e.g., see [Zhang et al. (2017)](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Zhang-2017-Unifying-Message-Passing-Algorithms.pdf), and hence these message passing schemes comply with [Caticha's Method of Maximum Relative Entropy](https://arxiv.org/abs/1011.0723), which, as discussed in the [variational Bayes lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Latent-Variable-Models-and-VB.ipynb) is the proper way for updating beliefs. \n",
    "- Different message passing updates rules can be combined to get a hybrid inference method in one model. "
   ]
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    "### The Local Free Energy in a Factor Graph \n",
    "\n",
    "- Consider an edge $x_j$ in a Forney-style factor graph for a generative model $p(x) = p(x_1,x_2,\\ldots,x_N)$.\n",
    "\n",
    "\n",
    "\n",
    "- Assume that the graph structure (factorization) is specified by\n",
    "$$\n",
    "p(x) = \\prod_{a=1}^M p_a(x_a)\n",
    "$$\n",
    "where $a$ is a set of indices.\n",
    "- Also, we assume a mean-field approximation for the posterior:\n",
    "$$\n",
    "q(x) = \\prod_{i=1}^N q_i(x_i)\n",
    "$$\n",
    "and consequently a corresponding free energy functional  \n",
    "$$\\begin{align*}\n",
    "F[q] &= \\sum_x q(x) \\log \\frac{q(x)}{p(x)} \\\\\n",
    "  &= \\sum_i \\sum_{x_i} \\left(\\prod_{i=1}^N q_i(x_i)\\right) \\log \\frac{\\prod_{i=1}^N q_i(x_i)}{\\prod_{a=1}^M p_a(x_a)}\n",
    "\\end{align*}$$\n",
    "\n",
    "- With these assumptions, it can be shown that the FE evaluates to (exercise)\n",
    "$$\n",
    "F[q] = \\sum_{a=1}^M \\underbrace{\\sum_{x_a} \\left( \\prod_{j\\in N(a)} q_j(x_j)\\cdot \\left(-\\log p_a(x_a)\\right) \\right) }_{\\text{node energy }U[p_a]} - \\sum_{i=1}^N \\underbrace{\\sum_{x_i} q_i(x_i) \\log \\frac{1}{q_i(x_i)}}_{\\text{edge entropy }H[q_i]}\n",
    "$$\n",
    "\n",
    "- In words, the FE decomposes into a sum of (expected) energies for the nodes minus the entropies on the edges. \n",
    " "
   ]
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   "source": [
    "### Variational Message Passing\n",
    "\n",
    "- Let us now consider the local free energy that is associated with edge corresponding to $x_j$. \n",
    "  \n",
    "  <p style=\"text-align:center;\"><img src=\"./figures/VMP-two-nodes.png\" width=\"600\"></p>\n",
    "  \n",
    "  \n",
    "- Apparently (see previous slide), there are three contributions to the free energy for $x_j$:\n",
    "    - one entropy term for the edge $x_j$\n",
    "    - two energy terms: one for each node that attaches to $x_j$ (in the figure: nodes $p_a$ and $p_b$)\n",
    "    \n",
    "- The local free energy for $x_j$ can be written as (exercise)\n",
    "  $$\n",
    "  F[q_j] \\propto \\sum_{x_j} q(x_j) \\log \\frac{q_j(x_j)}{\\nu_a(x_j)\\cdot \\nu_b(x_j)}\n",
    "  $$\n",
    "  where\n",
    "  $$\\begin{align*} \n",
    "  \\nu_a(x_j) &\\propto \\exp\\left( \\mathbb{E}_{q_{k}}\\left[ \\log p_a(x_a)\\right]\\right) \\\\\n",
    "  \\nu_b(x_j) &\\propto \\exp\\left( \\mathbb{E}_{q_{l}}\\left[ \\log p_b(x_b)\\right]\\right) \n",
    "  \\end{align*}$$\n",
    "  and $\\mathbb{E}_{q_{k}}\\left[\\cdot\\right]$ is an expectation w.r.t. all $q(x_k)$ with $k \\in N(a)\\setminus {j}$.\n",
    "  \n",
    "- $\\nu_a(x_j)$ and $\\nu_b(x_j)$  can be locally computed in nodes $a$ and $b$ respectively and can be interpreted as colliding messages over edge $x_j$. \n",
    "  \n",
    "- Local free energy minimization is achieved by setting\n",
    "  $$\n",
    "  q_j(x_j) \\propto \\nu_a(x_j) \\cdot \\nu_b(x_j)\n",
    "  $$\n",
    "  \n",
    "- Note that message $\\nu_a(x_j)$ depends on posterior beliefs over incoming edges ($k$) for node $a$, and in turn, the message from node $a$ towards edge $x_k$ depends on the belief $q_j(x_j)$. I.o.w., direct mutual dependencies exist between posterior beliefs over edges that attach to the same node. \n",
    "  \n",
    "- These considerations lead to the [Variational Message Passing](https://en.wikipedia.org/wiki/Variational_message_passing) procedure, which is an iterative free energy minimization procedure that can be executed completely through locally computable messages.  \n",
    "\n",
    "- Procedure VMP, see [Dauwels (2007), section 3](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Dauwels-2007-on-variational-message-passing-on-factor-graphs)\n",
    "  > 1. Initialize all messages $q$ and $ν$, e.g., $q(\\cdot) \\propto 1$ and $\\nu(\\cdot) \\propto 1$. <br/>\n",
    "  > 2. Select an edge $z_k$ in the factor graph of $f(z_1,\\ldots,z_m)$.<br/>\n",
    "  > 3. Compute the two messages $\\overrightarrow{\\nu}(z_k)$ and $\\overleftarrow{\\nu}(z_k)$ by applying the following generic rule:\n",
    "  $$\n",
    "  \\overrightarrow{\\nu}(y) \\propto \\exp\\left( \\mathbb{E}_{q}\\left[ \\log g(x_1,\\dots,x_n,y)\\right] \\right) \n",
    "  $$\n",
    "  > 4. Compute the marginal $q(z_k)$\n",
    "  $$\n",
    "  q(z_k) \\propto \\overrightarrow{\\nu}(z_k) \\overleftarrow{\\nu}(z_k)\n",
    "  $$\n",
    "  and send it to the two nodes connected to the edge $x_k$.<br/>\n",
    "  > 5. Iterate 2–4 until convergence. "
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    "### The Bethe Free Energy and Belief Propagation\n",
    "\n",
    "- We showed that, under mean field assumptions, the FE can be decomposed into a sum of local FE contributions for the nodes ($a$) and edges ($i$):\n",
    "$$\n",
    "F[q] = \\sum_{a=1}^M \\underbrace{\\sum_{x_a} \\left( \\prod_{j\\in N(a)} q_j(x_j)\\cdot \\left(-\\log p_a(x_a)\\right) \\right) }_{\\text{node energy }U[p_a]} - \\sum_{i=1}^N \\underbrace{\\sum_{x_i} q_i(x_i) \\log \\frac{1}{q_i(x_i)}}_{\\text{edge entropy }H[q_i]}\n",
    "$$\n",
    "\n",
    "- The mean field assumption is very strong and may lead to large inference costs ($\\mathrm{KL}(q(x),p(x|\\text{data}))$). A more relaxed assumption is to allow joint posterior beliefs over the variables that attach to a node. This idea is expressed by the Bethe Free Energy:\n",
    "$$\n",
    "F_B[q] = \\sum_{a=1}^M \\left( \\sum_{x_a} q_a(x_a) \\log \\frac{q_a(x_a)}{p_a(x_a)} \\right)  - \\sum_{i=1}^N (d_i - 1) \\sum_{x_i} q_i(x_i) \\log {q_i(x_i)}\n",
    "$$\n",
    "where $q_a(x_a)$ is the posterior joint belief over the variables $x_a$ (i.e., the set of variables that attach to node $a$), $q_i(x_i)$ is the posterior marginal belief over the variable $x_i$ and $d_i$ is the number of factor nodes that link to edge $i$. Moreover, $q_a(x_a)$ and $q_i(x_i)$ are constrained to obey the following equalities:\n",
    "$$\n",
    "  \\sum_{x_a \\backslash x_i} q_a(x_a) = q_i(x_i), ~~~ \\forall i, \\forall a \\\\\n",
    "  \\sum_{x_i} q_i(x_i) = 1, ~~~ \\forall i \\\\\n",
    "  \\sum_{x_a} q_a(x_a) = 1, ~~~ \\forall a \\\\\n",
    "$$\n",
    "\n",
    "- We form the Lagrangian by augmenting the Bethe Free Energy functional with the constraints:\n",
    "$$\n",
    "L[q] = F_B[q] + \\sum_i\\sum_{a \\in N(i)} \\lambda_{ai}(x_i) \\left(q_i(x_i) - \\sum_{x_a\\backslash x_i} q(x_a) \\right) + \\sum_{i} \\gamma_i \\left(  \\sum_{x_i}q_i(x_i) - 1\\right) + \\sum_{a}\\gamma_a \\left(  \\sum_{x_a}q_a(x_a) -1\\right)\n",
    "$$\n",
    "\n",
    "- The stationary solutions for this Lagrangian are given by\n",
    "$$\n",
    "q_a(x_a) = f_a(x_a) \\exp\\left(\\gamma_a -1 + \\sum_{i \\in N(a)} \\lambda_{ai}(x_i)\\right) \\\\ \n",
    "q_i(x_i) = \\exp\\left(1- \\gamma_i + \\sum_{a \\in N(i)} \\lambda_{ai}(x_i)\\right) ^{\\frac{1}{d_i - 1}}\n",
    "$$\n",
    "where $N(i)$ denotes the factor nodes that have $x_i$ in their arguments and $N(a)$ denotes the set of variables in the argument of $f_a$.\n",
    "\n",
    "- Stationary solutions are functions of Lagrange multipliers. This means that Lagrange multipliers need to be determined. Lagrange multipliers can be determined by plugging the stationary solutions back into the constraint specification and solving for the multipliers which ensure that the constraint is satisfied. The first constraint we consider is normalization, which yields the following identification:\n",
    "$$\n",
    "\\gamma_a = 1 - \\log \\Bigg(\\sum_{x_a}f_a(x_a)\\exp\\left(\\sum_{i \\in N(a)}\\lambda_{ai}(x_i)\\right)\\Bigg)\\\\\n",
    "\\gamma_i = 1 + (d_i-1) \\log\\Bigg(\\sum_{x_i}\\exp\\left( \\frac{1}{d_i-1}\\sum_{a \\in N(i)} \\lambda_{ai}(x_i)\\right)\\Bigg).\n",
    "$$\n",
    "\n",
    "- The functional form of the Lagrange multipliers that corresponds to the normalization constraint enforces us to obtain the Lagrange multipliers that correspond to the marginalization constraint. To do so we solve for \n",
    "$$ \\sum_{x_a \\backslash x_i} f_a(x_a) \\exp\\left(\\sum_{i \\in N(a)} \\lambda_{ai}(x_i)\\right) = \\exp\\left(\\sum_{a \\in N(i)} \\lambda_{ai}(x_i)\\right) ^{\\frac{1}{d_i - 1}} \\\\ \\exp\\left(\\lambda_{ai}(x_i)\\right)\\sum_{x_a \\backslash x_i} f_a(x_a) \\exp\\Bigg(\\sum_{\\substack{{j \\in N(a)} \\\\ j \\neq i}}\\lambda_{aj}(x_j)\\Bigg) = \\exp\\left(\\sum_{a \\in N(i)} \\lambda_{ai}(x_i)\\right) ^{\\frac{1}{d_i - 1}}\\\\ \\exp\\left(\\lambda_{ai}(x_i) + \\lambda_{ia}(x_i)\\right) = \\exp\\left(\\sum_{a \\in N(i)} \\lambda_{ai}(x_i)\\right) ^{\\frac{1}{d_i - 1}}\\,, $$ \n",
    "where we defined an auxilary function\n",
    "$$\n",
    "\\exp(\\lambda_{ia}(x_i)) \\triangleq \\sum_{x_a \\backslash x_i} f_a(x_a) \\exp\\Bigg(\\sum_{\\substack{{j \\in N(a)} \\\\ j \\neq i}}\\lambda_{aj}(x_j)\\Bigg) \\,.\n",
    "$$\n",
    "This definition is valid since it can be inverted by the relation\n",
    "$$\n",
    "\\lambda_{ia}(x_i) = \\frac{2-d_i}{d_i - 1}\\lambda_{ai}(x_i) + \\frac{1}{d_i -1}\\sum_{\\substack{c \\in N(i)\\\\c \\neq a}}\\lambda_{ci}(x_i)\n",
    "$$\n",
    "\n",
    "- In general it is not possible to solve for the Lagrange multipliers analytically and we resort to iteratively obtaining the solutions. This leads to the **Belief Propagation algorithm** where the exponentiated Lagrange multipliers (messages) are updated iteratively via \n",
    "$$ \\mu_{ia}^{(k+1)}(x_i) = \\sum_{x_a \\backslash x_i} f_a(x_a) \\prod_{\\substack{{j \\in N(a)} \\\\ j \\neq i}}\\mu^{(k)}_{aj}(x_j) \\\\ \\mu_{ai}^{(k)}(x_i) = \\prod_{\\substack{c \\in N(i) \\\\ c \\neq a}}\\mu^{(k)}_{ic}(x_i)\\,, $$ \n",
    "where $k$ denotes iteration number and the messages are defined as\n",
    "$$\n",
    "\\mu_{ia}(x_i) \\triangleq \\exp(\\lambda_{ia}(x_i))\\\\\n",
    "\\mu_{ai}(x_i) \\triangleq \\exp(\\lambda_{ai}(x_i))\\,.\n",
    "$$\n",
    "\n",
    "- For a more complete overview of message passing as Bethe Free Energy minimization, see Zhang (2017)."
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