lessons/notebooks/probprog/Probabilistic-Programming-2.ipynb

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    "# Probabilistic Programming 2: Message Passing & Analytical Solutions\n",
    "\n",
    "#### Goal \n",
    "  - Understand when and how analytical solutions to Bayesian inference can be obtained.\n",
    "  - Understand how to perform message passing in a Forney-style factor graph.\n",
    "\n",
    "#### Materials        \n",
    "  - Mandatory\n",
    "    - This notebook\n",
    "    - Lecture notes on factor graphs\n",
    "    - Lecture notes on continuous data\n",
    "    - Lecture notes on discrete data\n",
    "  - Optional\n",
    "    - Chapters 2 and 3 of [Model-Based Machine Learning](http://www.mbmlbook.com/LearningSkills.html).\n",
    "    - [Differences between Julia and Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that none of the material below is new. The point of the Probabilistic Programming sessions is to solve practical problems so that the concepts from Bert's lectures become less abstract."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Pkg\n",
    "Pkg.activate(\"./workspace/\")\n",
    "Pkg.instantiate();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using SpecialFunctions\n",
    "using ForneyLab\n",
    "using PyCall\n",
    "using Plots\n",
    "pyplot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll be using the toolbox [ForneyLab.jl](https://github.com/biaslab/ForneyLab.jl) to visualize factor graphs and compute messages passed within the graph."
   ]
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  {
   "cell_type": "markdown",
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    "## Problem: A Job Interview\n",
    "\n",
    "After you finish your master's degree, you will need to start looking for jobs. You will get one or more job interviews and some will be fun while others will be frustrating. The company you applied at wants a talented and skilled employee, but measuring a person's skill is tricky. Even a highly-skilled person makes mistakes and people with few skills can get lucky. In this session, we will look at various ways to assess skills using questions and test assignments. Along the way, you will gain experience with message passing, factor graphs and working with discrete vs continuous data."
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    "### 1: Right or wrong\n",
    "\n",
    "Suppose you head to a job interview for a machine learning engineer position. The company is interested in someone who knows Julia and has set up a test with syntax questions. We will first look at a single question, which we treat as an outcome variable $X_1$. You can either get this question right or wrong, which means we're dealing with a Bernoulli likelihood. The company assumes you have a skill level, denoted $\\theta$, and the higher the skill, the more likely you are to get the question right. Since the company doesn't know anything about you, they chose an uninformative prior distribution: the Beta(1,1). We can write the generative model for answering this question as follows:\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(X_1, \\theta) =&\\ p(X_1 \\mid \\theta) \\cdot p(\\theta) \\\\\n",
    "=&\\ \\text{Bernoulli}(X_1 \\mid \\theta) \\cdot \\text{Beta}(\\theta \\mid \\alpha = 1, \\beta=1) \\, .\n",
    "\\end{align*}$$\n",
    "\n",
    "The factor graph for this model is:\n",
    "\n",
    "<!-- <img align=\"left\" width=50 src=\"../figures/ffg-PP2-01.png\"> -->\n",
    "![](../figures/ffg-PP2-01.png)\n",
    "\n",
    "where $f_b(X_1, \\theta) \\triangleq \\text{Bernoulli}(X_1 \\mid \\theta)$ and $f_a(\\theta) \\triangleq \\text{Beta}(\\theta \\mid 1,1)$. We are now going to construct this factor graph using the toolbox ForneyLab."
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    "# Start building a model by setting up a FactorGraph structure\n",
    "factor_graph1 = FactorGraph()\n",
    "\n",
    "# Add the prior over \n",
    "@RV θ ~ Beta(1.0, 1.0, id=:f_a)\n",
    "\n",
    "# Add the question correctness likelihood\n",
    "@RV X1 ~ Bernoulli(θ, id=:f_b)\n",
    "\n",
    "# The outcome X1 is going to be observed, so we set up a placeholder for the data entry\n",
    "placeholder(X1, :X1)\n",
    "\n",
    "# Visualize the graph\n",
    "ForneyLab.draw(factor_graph1)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Code notes:\n",
    "- @RV is a macro that lets you add Random Variables as nodes to your factor graph.\n",
    "- The symbol ~ means \"is distributed as\". For example, $\\theta \\sim \\text{Beta}(1,1)$ should be read as \"$\\theta$ is distributed according to a Beta($\\theta$ | $a$=1, $b$=1) probability distribution\".\n",
    "\n",
    "----"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Above you can see the factor graph that ForneyLab has generated. It is not as clean as the ones in the theory lectures. For example, ForneyLab generates nodes for the clamped parameters of the Beta prior ($\\alpha = 1$ and $\\beta = 1$), while we ignore these in the manually constructed graphs. Nonetheless, ForneyLab's version is very useful for debugging later on. \n",
    "\n",
    "We are now going to tell ForneyLab to generate a message passing procedure for us."
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   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "# Indicate which variables you want posteriors for\n",
    "q = PosteriorFactorization(θ, ids=[:θ])\n",
    "\n",
    "# Generate a message passing inference algorithm\n",
    "algorithm = messagePassingAlgorithm(θ, q)\n",
    "\n",
    "# Compile algorithm code\n",
    "source_code = algorithmSourceCode(algorithm)\n",
    "\n",
    "# Bring compiled code into current scope\n",
    "eval(Meta.parse(source_code))\n",
    "\n",
    "# Visualize message passing schedule\n",
    "pfθ = q.posterior_factors[:θ]\n",
    "ForneyLab.draw(pfθ, schedule=pfθ.schedule);"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code notes:\n",
    "- ForneyLab.jl compiles the specified model and inference procedure into a string. This string is human-readable and portable across devices. The functions `eval(Meta.parse())` are used to bring that string into the current scope, so the generated code can be used.\n",
    "- In `ForneyLab.draw()`, only the edge of interest is shown with the two connecting nodes and their inputs. All other parts of the graph are ignored.\n",
    "\n",
    "----"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "ForneyLab's visualization of the message passing procedure for a specific variable isolates that variable in the graph and shows where the incoming messages come from. In this case, we are interested in $\\theta$ (your skill level), which receives message ((2)) from the likelihood node (the \"Ber\" node above $\\theta$) and message ((1)) from the prior node (the \"Beta\" node below $\\theta$). \n",
    "\n",
    "In the message passing framework, the combination of these two messages produces the \"marginal\" distribution for $\\theta$. We are using message passing to do Bayesian inference, so note that the \"marginal\" for $\\theta$ corresponds to the posterior distribution $p(\\theta \\mid X_1)$. \n",
    "\n",
    "Let's inspect these messages."
   ]
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   "cell_type": "code",
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     "name": "stdout",
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     "text": [
      "\n",
      "Message ((1)) = Beta(a=1.00, b=1.00)\n",
      "Message ((2)) = Beta(a=2.00, b=1.00)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initialize data structure for messages\n",
    "messages = Array{Message}(undef, 2)\n",
    "\n",
    "# Initalize data structure for marginal distributions\n",
    "marginals = Dict()\n",
    "\n",
    "# Suppose you got question 1 correct\n",
    "data = Dict(:X1 => 1)\n",
    "\n",
    "# Update coefficients\n",
    "stepθ!(data, marginals, messages);\n",
    "\n",
    "# Print messages\n",
    "print(\"\\nMessage ((1)) = \"*string(messages[1].dist))\n",
    "println(\"Message ((2)) = \"*string(messages[2].dist))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code notes:\n",
    "- A `Dict` is a [dictionary data structure](https://docs.julialang.org/en/v1/base/collections/#Base.Dict). In the `marginals` dictionary we only have one entry: the key is the variable `θ` (as a Symbol, i.e. as `:θ`) and the value is a `ProbabilityDistribution` object. It is the initial distribution for that variable. In the `data` dictionary, we also only have one entry: the key is the variable `X1` and the value is a Float. This is because `X1` is observed. We know its value without uncertainty.\n",
    "- The `stepθ!` function comes from the algorithm compilation.\n",
    "\n",
    "----"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Alright. So, they are both Beta distributions. Do they actually make sense? Where do these parameters come from?\n",
    "\n",
    "Recall from the lecture notes that the formula for messages sent by factor nodes is:\n",
    "\n",
    "$$ \\boxed{\n",
    "\\underbrace{\\overrightarrow{\\mu}_{Y}(y)}_{\\substack{ \\text{outgoing}\\\\ \\text{message}}} = \\sum_{x_1,\\ldots,x_n} \\underbrace{\\overrightarrow{\\mu}_{X_1}(x_1)\\cdots \\overrightarrow{\\mu}_{X_n}(x_n)}_{\\substack{\\text{incoming} \\\\ \\text{messages}}} \\cdot \\underbrace{f(y,x_1,\\ldots,x_n)}_{\\substack{\\text{node}\\\\ \\text{function}}} }\n",
    "$$\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"../figures/ffg-sum-product.png\" width=\"500px\"></p>\n",
    "\n",
    "The prior node is not connected to any other unknown variables and so does not receive incoming messages. Its outgoing message is therefore:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\overrightarrow{\\mu}(\\theta) =&\\ f(\\theta) \\\\\n",
    "=&\\ \\text{Beta}(\\theta \\mid 1,1) \\, .\n",
    "\\end{align}$$\n",
    "\n",
    "So that confirms the correctness of Message ((1)).\n",
    "\n",
    "Similarly, we can also derive the message from the likelihood node by hand. For this, we need to know that the message coming from the observation $\\overleftarrow{\\mu}(x)$ is a delta function, which, if you gave the right answer ($X_1 = 1$), has the form $\\delta(X_1 - 1)$. The \"node function\" is the Bernoulli likelihood $\\text{Bernoulli}(X_1 \\mid \\theta)$. Another thing to note is that this is essentially a convolution with respect to a delta function and that its [sifting property](https://en.wikipedia.org/wiki/Dirac_delta_function#Translation) holds: $\\int_{X_1} \\delta(X_1 - x) \\ f(X_1, \\theta) \\mathrm{d}X_1 = f(x, \\theta)$. The fact that $X_1$ is a discrete variable instead of a continuous one, does not negate this. Using these facts, we can perform the message computation by hand:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\overleftarrow{\\mu}(\\theta) =&\\ \\sum_{X_1} \\overleftarrow{\\mu}(X_1) \\ f(X_1, \\theta) \\\\\n",
    "=&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\text{Bernoulli}(X_1 \\mid \\theta) \\\\\n",
    "=&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\theta^{X_1} (1 - \\theta)^{1-X_1} \\\\\n",
    "=&\\ \\theta^{1} (1 - \\theta)^{1-1} \\, .\n",
    "\\end{align}$$\n",
    "\n",
    "Remember that the pdf of a Beta distribution is proportional to $\\theta^{\\alpha-1} (1 - \\theta)^{\\beta-1}$. So, if you read the second-to-last line above as $\\theta^{2-1} (1 - \\theta)^{1-1}$, then the outgoing message $\\overleftarrow{\\mu}(\\theta)$ is proportional to a Beta distribution with $\\alpha=2$ and $\\beta=1$. So, our manual derivation verifies ForneyLab's Message ((2)).\n",
    "\n",
    "Let's now look at these messages visually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Probability density function of a Beta distribution\n",
    "Beta(θ, α, β) = 1/beta(α,β) * θ^(α-1) * (1-θ)^(β-1)\n",
    "\n",
    "# Extract parameters from message ((1))\n",
    "α1 = messages[1].dist.params[:a]\n",
    "β1 = messages[1].dist.params[:b]\n",
    "\n",
    "# Extract parameters from message ((2))\n",
    "α2 = messages[2].dist.params[:a]\n",
    "β2 = messages[2].dist.params[:b]\n",
    "\n",
    "# Plot messages\n",
    "θ_range = range(0, step=0.01, stop=1.0)\n",
    "plot(θ_range, Beta.(θ_range, α1, β1), color=\"red\", linewidth=3, label=\"Message ((1))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, Beta.(θ_range, α2, β2), color=\"blue\", linewidth=3, label=\"Message ((2))\", size=(800,300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The marginal distribution for $\\theta$, representing the posterior $p(\\theta \\mid X_1)$, is obtained by taking the product (followed by normalization) of the two messages: $\\overrightarrow{\\mu}(\\theta) \\cdot \\overleftarrow{\\mu}(\\theta)$. Multiplying two Beta distributions produces another Beta distribution with parameter:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\alpha \\leftarrow&\\ \\alpha_1 + \\alpha_2 - 1 \\\\\n",
    "\\beta \\leftarrow&\\ \\beta_1 + \\beta_2 - 1 \\, ,\n",
    "\\end{align}$$\n",
    "\n",
    "In our case, the new parameters would be $\\alpha = 1 + 2 - 1 = 2$ and $\\beta = 1 + 1 - 1 = 1$. Let's check with ForneyLab what it computed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Beta(a=2.00, b=1.00)\n"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marginals[:θ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, ForneyLab matches our manual derivations. Let's visualize the messages as well as the marginal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract marginal's parameters\n",
    "α_marg = marginals[:θ].params[:a]\n",
    "β_marg = marginals[:θ].params[:b]\n",
    "\n",
    "# Plot messages\n",
    "θ_range = range(0, step=0.01, stop=1.0)\n",
    "plot(θ_range, Beta.(θ_range, α1, β1), color=\"red\", linewidth=3, label=\"Message ((1))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, Beta.(θ_range, α2, β2), color=\"blue\", linewidth=3, label=\"Message ((2))\", size=(800,300))\n",
    "plot!(θ_range, Beta.(θ_range, α_marg, β_marg), color=\"purple\", linewidth=6, linestyle=:dash, label=\"Marginal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pdf of the marginal distribution lies on top of the pdf of Message ((2)). That's not always going to be the case; the Beta(1,1) distribution is special in that when you multiply Beta(1,1) with a general Beta(a,b) the result will always be Beta(a,b), kinda like multiplying by $1$. We call prior distributions that have this special effect \"non-informative priors\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple questions\n",
    "\n",
    "Of course, you won't be evaluated on just a single question: it's still possible for you to get one question wrong even if you have a high skill level. You would consider it unfair to be rejected based on only one question. So, we are going to add another question. We're also going to change the prior: the company now assumes that you must have _some_ skill if you applied for the position. This is reflected in a prior Beta distributions with $\\alpha = 3.0$ and $\\beta = 2.0$. \n",
    "\n",
    "For now, the second question is also a right-or-wrong question. The outcome of this new question is denoted with variable $X_2$. With this addition, the generative model becomes\n",
    "\n",
    "$$p(X_1, X_2, \\theta) = p(X_1 \\mid \\theta) p(X_2 \\mid \\theta) p(\\theta) \\, ,$$ \n",
    "\n",
    "with the accompanying factor graph\n",
    "\n",
    "![](../figures/ffg-PP2-02.png)\n",
    "\n",
    "where $f_c \\triangleq \\text{Bernoulli}(X_2 \\mid \\theta)$ and $f_a, f_b$ are still the same. Notice that we now have an equality node as well. That is because the variable $\\theta$ is used in three factor nodes. ForneyLab automatically generates the same factor graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "# Start building a model\n",
    "factor_graph2 = FactorGraph()\n",
    "\n",
    "# Add the prior\n",
    "@RV θ ~ Beta(3.0, 2.0, id=:f_a)\n",
    "\n",
    "# Add question 1 correctness likelihood\n",
    "@RV X1 ~ Bernoulli(θ, id=:f_b)\n",
    "\n",
    "# Add question 2 correctness likelihood\n",
    "@RV X2 ~ Bernoulli(θ, id=:f_c)\n",
    "\n",
    "# The question outcomes are going to be observed\n",
    "placeholder(X1, :X1)\n",
    "placeholder(X2, :X2)\n",
    "\n",
    "# Visualize the graph\n",
    "ForneyLab.draw(factor_graph2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will go through the message passing operations below. First, we generate an algorithm and visualize where all the messages for $\\theta$ come from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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   "source": [
    "# Indicate which variables you want posteriors for\n",
    "q = PosteriorFactorization(θ, ids=[:θ])\n",
    "\n",
    "# Generate a message passing inference algorithm\n",
    "algorithm = messagePassingAlgorithm(θ, q)\n",
    "\n",
    "# Compile algorithm code\n",
    "source_code = algorithmSourceCode(algorithm)\n",
    "\n",
    "# Bring compiled code into current scope\n",
    "eval(Meta.parse(source_code))\n",
    "\n",
    "# Visualize message passing schedule\n",
    "pfθ = q.posterior_factors[:θ]\n",
    "ForneyLab.draw(pfθ, schedule=pfθ.schedule);"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 4 messages, one from the prior ((1)), one from the first likelihood ((2)), one from the second likelihood ((3)) and one from the equality node ((4)). ForneyLab essentially combines messages 2 and 3 into message 4 and then multiplies messages 1 and 4 to produce the marginal. We can see this if we look in the source code:"
   ]
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  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "begin\n",
      "\n",
      "function stepθ!(data::Dict, marginals::Dict=Dict(), messages::Vector{Message}=Array{Message}(undef, 4))\n",
      "\n",
      "messages[1] = ruleVBBetaOut(nothing, ProbabilityDistribution(Univariate, PointMass, m=3.0), ProbabilityDistribution(Univariate, PointMass, m=2.0))\n",
      "messages[2] = ruleVBBernoulliIn1(ProbabilityDistribution(Univariate, PointMass, m=data[:X1]), nothing)\n",
      "messages[3] = ruleVBBernoulliIn1(ProbabilityDistribution(Univariate, PointMass, m=data[:X2]), nothing)\n",
      "messages[4] = ruleSPEqualityBeta(nothing, messages[2], messages[3])\n",
      "\n",
      "marginals[:θ] = messages[1].dist * messages[4].dist\n",
      "\n",
      "return marginals\n",
      "\n",
      "end\n",
      "\n",
      "end # block\n"
     ]
    }
   ],
   "source": [
    "println(source_code)"
   ]
  },
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   "source": [
    "You can see that `messages[4]` is a function of `messages[2]` and `messages[3]` and that `marginals[:θ]` is the product of `messages[1]` and `messages[4]`. \n",
    "\n",
    "\n",
    "Suppose you got the first question right and the second question wrong. Let's execute the message passing procedure and take a look at the functional form of the messages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Message ((1)) = Beta(a=3.00, b=2.00)\n",
      "Message ((2)) = Beta(a=2.00, b=1.00)\n",
      "Message ((3)) = Beta(a=1.00, b=2.00)\n",
      "Message ((4)) = Beta(a=2.00, b=2.00)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initialize a message data structure\n",
    "messages = Array{Message}(undef, 4)\n",
    "\n",
    "# Initalize marginal distributions data structure\n",
    "marginals = Dict()\n",
    "\n",
    "# Suppose you got question 1 right and question 2 wrong\n",
    "data = Dict(:X1 => 1,\n",
    "            :X2 => 0)\n",
    "\n",
    "# Update coefficients\n",
    "stepθ!(data, marginals, messages);\n",
    "\n",
    "# Print messages\n",
    "print(\"\\nMessage ((1)) = \"*string(messages[1].dist))\n",
    "print(\"Message ((2)) = \"*string(messages[2].dist))\n",
    "print(\"Message ((3)) = \"*string(messages[3].dist))\n",
    "println(\"Message ((4)) = \"*string(messages[4].dist))"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Messages ((1)) and ((2)) are clear, but Message ((3)) and Message ((4)) are new. \n",
    "\n",
    "---\n",
    "\n",
    "#### $\\ast$ **Try for yourself**\n",
    "\n",
    "Try deriving the functional form of Message ((3)) for yourself. \n",
    "Tip: the derivation is very similar to that of Message ((2)). The most important change is to use $\\delta(X_2 - 0)$ instead of $\\delta(X_1 - 1)$.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Message ((4)) is the result of the standard message computation formula for the case of an equality node:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\downarrow \\mu(\\theta) =&\\ \\sum_{\\theta',\\ \\theta''} \\overrightarrow{\\mu}(\\theta'')\\ f_{=}(\\theta, \\theta', \\theta'') \\ \\overleftarrow{\\mu}(\\theta') \\\\\n",
    " =&\\ \\overrightarrow{\\mu}(\\theta) \\cdot \\overleftarrow{\\mu}(\\theta) \\\\\n",
    "=&\\ \\text{Beta}(\\theta \\mid 2, 1) \\cdot \\text{Beta}(\\theta \\mid 1, 2) \\\\\n",
    " =&\\ \\text{Beta}(\\theta \\mid 2, 2) \\quad .\n",
    "\\end{align}$$\n",
    "\n",
    "Let's visualize the messages and the marginal again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract parameters from message ((2))\n",
    "α2 = messages[2].dist.params[:a]\n",
    "β2 = messages[2].dist.params[:b]\n",
    "\n",
    "# Extract parameters from message ((3))\n",
    "α3 = messages[3].dist.params[:a]\n",
    "β3 = messages[3].dist.params[:b]\n",
    "\n",
    "# Extract parameters from message ((4))\n",
    "α4 = messages[4].dist.params[:a]\n",
    "β4 = messages[4].dist.params[:b]\n",
    "\n",
    "plot(θ_range, Beta.(θ_range, α2, β2), color=\"black\", linewidth=3, label=\"Message ((2))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, Beta.(θ_range, α3, β3), color=\"green\", linewidth=3, label=\"Message ((3))\", size=(800,300))\n",
    "plot!(θ_range, Beta.(θ_range, α4, β4), color=\"blue\", linewidth=3, label=\"Message ((4))\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Message ((2)) and Message ((3)) are direct opposites: ((2)) increases the estimate and ((3)) decreases the estimate of your skill level.  Message ((4)) end up being centered on $0.5$. With one question right and one question wrong, you have essentially been guessing at random."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract parameters from message ((1))\n",
    "α1 = messages[1].dist.params[:a]\n",
    "β1 = messages[1].dist.params[:b]\n",
    "\n",
    "# Extract parameters from message ((4))\n",
    "α4 = messages[4].dist.params[:a]\n",
    "β4 = messages[4].dist.params[:b]\n",
    "\n",
    "# Extract parameters\n",
    "α_marg = marginals[:θ].params[:a]\n",
    "β_marg = marginals[:θ].params[:b]\n",
    "\n",
    "plot(θ_range, Beta.(θ_range, α1, β1), color=\"red\", linewidth=3, label=\"Message ((1))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, Beta.(θ_range, α4, β4), color=\"blue\", linewidth=3, label=\"Message ((4))\", size=(800,300))\n",
    "plot!(θ_range, Beta.(θ_range, α_marg, β_marg), color=\"purple\", linewidth=4, linestyle=:dash, label=\"Marginal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we now combine the prior (Message ((1)) in red above) with the combined message from both likelihood terms (Message ((4)) in blue), we get the new marginal (purple dotted line). The mean of the marginal lies above $0.5$, which is due to the prior assumption that you must have _some_ skill if you applied. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Score questions\n",
    "\n",
    "So far, the models we have been looking at have been quite simple; they are Beta-Bernoulli combinations which is exactly what we did for the Beer Tasting Experiment. We will now move on to more complicated distributions. These will enrich your toolbox and allow you to do much more.\n",
    "\n",
    "Suppose you are not tested on a right-or-wrong question, but on a score question. For instance, you have to complete a piece of code for which you get a score. If all of it was wrong you get a score of $0$, if some of it was correct you get a score of $1$ and if all of it was correct you get a score $2$. That means we have a likelihood with three outcomes: $X_1 = \\{ 0,1,2\\}$. Suppose we once again ask two questions, $X_1$ and $X_2$. The order in which we ask these questions does not matter, so that means we choose Categorical distributions for these likelihood functions: $X_1, X_2 \\sim \\text{Categorical}(\\theta)$. The parameter $\\theta$ is no longer a single parameter, indicating the probability of getting the question right, but a vector of three parameters: $\\theta = (\\theta_1, \\theta_2, \\theta_3)$. Each $\\theta_k$ indicates the probability of getting the $k$-th outcome. In other words, $\\theta_1$ indicates the probability of getting $0$ points, $\\theta_2$ of getting $1$ point and $\\theta_3$ of getting two points. A highly-skilled applicant will have a parameter vector of $(0.05, 0.1, 0.85)$, for example. The prior distribution conjugate to the Categorical distribution is the Dirichlet distribution. \n",
    "\n",
    "Let's look at the generative model:\n",
    "\n",
    "$$p(X_1, X_2, \\theta) = p(X_1 \\mid \\theta) p(X_2 \\mid \\theta) p(\\theta) \\, .$$ \n",
    "\n",
    "It's the same as before. The only difference is that:\n",
    "\n",
    "$$\\begin{align}\n",
    "p(X_1 \\mid \\theta) =&\\ \\text{Categorical}(X_1 \\mid \\theta) \\\\\n",
    "p(X_2 \\mid \\theta) =&\\ \\text{Categorical}(X_2 \\mid \\theta) \\\\\n",
    "p(\\theta) =&\\ \\text{Dirichlet}(\\theta)\n",
    "\\end{align}$$\n",
    "\n",
    "The factor graph has the same structure as before. The only change is that the factor nodes $f_a, f_b, f_c$ are now parameterized differently. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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    "# Start building a model\n",
    "factor_graph3 = FactorGraph()\n",
    "\n",
    "# Add the prior\n",
    "@RV θ ~ Dirichlet([1.0, 3.0, 2.0], id=:f_a)\n",
    "\n",
    "# Add question 1 correctness likelihood\n",
    "@RV X1 ~ Categorical(θ, id=:f_b)\n",
    "\n",
    "# Add question 2 correctness likelihood\n",
    "@RV X2 ~ Categorical(θ, id=:f_c)\n",
    "\n",
    "# The question outcomes are going to be observed\n",
    "placeholder(X1, dims=(3,), :X1)\n",
    "placeholder(X2, dims=(3,), :X2)\n",
    "\n",
    "# Visualize the graph\n",
    "ForneyLab.draw(factor_graph3)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "The only difference with the previous graph is the fact that the node called \"prior\" is a 'Dir', short for Dirichlet, and that the two nodes called \"likelihood1\" and \"likelihood2\" are 'Cat' types, short for Categorical. Let's look at the message passing schedule:"
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
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    "# Indicate which variables you want posteriors for\n",
    "q = PosteriorFactorization(θ, ids=[:θ])\n",
    "\n",
    "# Generate a message passing inference algorithm\n",
    "algorithm = messagePassingAlgorithm(θ, q)\n",
    "\n",
    "# Compile algorithm code\n",
    "source_code = algorithmSourceCode(algorithm)\n",
    "\n",
    "# Bring compiled code into current scope\n",
    "eval(Meta.parse(source_code))\n",
    "\n",
    "# Visualize message passing schedule\n",
    "pfθ = q.posterior_factors[:θ]\n",
    "ForneyLab.draw(pfθ, schedule=pfθ.schedule);"
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    "That's the same as before as well: 2 messages from the likelihoods, 1 combined likelihood message from the equality node and 1 message from the prior.\n",
    "\n",
    "If we now setup the message passing procedure, we have to be a little bit more careful. We cannot feed the scores $\\{ 0,1,2\\}$ as outcomes directly. We have to encode them in one-hot vectors (see Bert's lecture notes on discrete distributions). Suppose you had a score of $1$ for the first question and a score of $2$ for the second one. That translates into a vector $[0, 1, 0]$ and $[0, 0, 1]$, respectively. These we enter into the `data` dictionary:"
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   "cell_type": "code",
   "execution_count": 17,
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     "text": [
      "\n",
      "Message ((1)) = Dir(a=[1.00, 3.00, 2.00])\n",
      "Message ((2)) = Dir(a=[1.00, 2.00, 1.00])\n",
      "Message ((3)) = Dir(a=[1.00, 1.00, 2.00])\n",
      "Message ((4)) = Dir(a=[1.00, 2.00, 2.00])\n",
      "Marginal of θ = Dir(a=[1.00, 4.00, 3.00])\n",
      "\n"
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    "# Initialize a message data structure\n",
    "messages = Array{Message}(undef, 4)\n",
    "\n",
    "# Initalize marginal distributions data structure\n",
    "marginals = Dict()\n",
    "\n",
    "# Enter the observed outcomes in the placeholders\n",
    "data = Dict(:X1 => [0, 1, 0],\n",
    "            :X2 => [0, 0, 1])\n",
    "\n",
    "# Update coefficients\n",
    "stepθ!(data, marginals, messages);\n",
    "\n",
    "# Print messages\n",
    "print(\"\\nMessage ((1)) = \"*string(messages[1].dist))\n",
    "print(\"Message ((2)) = \"*string(messages[2].dist))\n",
    "print(\"Message ((3)) = \"*string(messages[3].dist))\n",
    "print(\"Message ((4)) = \"*string(messages[4].dist))\n",
    "println(\"Marginal of θ = \"*string(marginals[:θ]))"
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    "Visualizing a Dirichlet distribution is a bit tricky. In the special case of $3$ parameters, we can plot the probabilities on a simplex. As a reminder, a [simplex](https://en.wikipedia.org/wiki/Simplex) in 3-dimensions is the triangle between the coordinates $[0,0,1]$, $[0,1,0]$ and $[1,0,0]$:\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/2D-simplex.svg/150px-2D-simplex.svg.png\" width=\"150px\"></p>\n",
    "\n",
    "Each vector $\\theta$ is a point on that triangle and its elements sum to $1$. Since the triangle is 2-dimensional, we can plot the Dirichlet's probability density over it."
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sys:1: UserWarning: The following kwargs were not used by contour: 'nlevels'\r\n"
     ]
    }
   ],
   "source": [
    "# Import matplotlib \n",
    "plt = pyimport(\"matplotlib.pyplot\")\n",
    "\n",
    "# Include helper function\n",
    "include(\"../scripts/dirichlet_simplex.jl\")\n",
    "\n",
    "# Extract parameters of Message ((1))\n",
    "α1 = messages[1].dist.params[:a]\n",
    "\n",
    "# Compute pdf contour lines on the simplex\n",
    "trimesh, pvals = pdf_contours_simplex(α1)\n",
    "\n",
    "# Plot using matplotlib's tricontour\n",
    "plt.tricontourf(trimesh, pvals, nlevels=200, cmap=\"jet\");\n",
    "plt.title(\"Message ((1)) = \"*string(messages[1].dist));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code notes:\n",
    "- `pyimport` allows you to import Python modules. \n",
    "- When you `include()` another julia file, it is as if you wrote it at that point in your script.\n",
    "- `tricontourf` is a function from Matplolib, where you create a contour plot over a triangulated mesh (here, the simplex).\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The red spot is the area of high probability, with the contours around indicating increasing uncertainty. The prior, with concentration parameters $[1, 3, 2]$, reflects the belief that applicants are least likely to get the question completely wrong ($\\alpha_1$ = 1, score = 0), most likely to get the question partly right ($\\alpha_2$ = 3, score = 1) and moderately likely to get the question completely correct ($\\alpha_3$ = 2, score = 2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract parameters \n",
    "α4 = messages[4].dist.params[:a]\n",
    "\n",
    "# Compute pdf contour lines on the simplex\n",
    "trimesh, pvals = pdf_contours_simplex(α4)\n",
    "\n",
    "# Plot using matplotlib's tricontour\n",
    "plt.tricontourf(trimesh, pvals, nlevels=200, cmap=\"jet\")\n",
    "plt.title(\"Message ((4)) = \"*string(messages[4].dist));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we got scores $X_1 = 1$ and $X_2 = 2$, the combined message from both likelihoods has concentration parameters $[1,2,2]$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract parameters \n",
    "α_marg = marginals[:θ].params[:a]\n",
    "\n",
    "# Compute pdf contour lines on the simplex\n",
    "trimesh, pvals = pdf_contours_simplex(α_marg)\n",
    "\n",
    "# Plot using matplotlib's tricontour\n",
    "plt.tricontourf(trimesh, pvals, nlevels=200, cmap=\"jet\")\n",
    "plt.title(\"Marginal of θ = \"*string(marginals[:θ]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior is the combination of Messages ((1)) and ((4)) and focuses much more strongly in the area where the two messages overlap."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### $\\ast$ **Try for yourself**\n",
    "\n",
    "Play around with the prior parameters and your responses to the questions. See how they change your posterior.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Rating scale\n",
    "\n",
    "You might want to evaluate someone by an even finer metric. For example, in oral exams you need to provide a score based on a conversation which is hard to quantify. You could do this by taking away the discrete set of responses and replacing it with a continuous response variable. For example, rating scales are forms of continuous response models. You would mark the applicant's performance on a question as a cross on a line:\n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"https://images.slideplayer.com/15/4506022/slides/slide_19.jpg\" width=\"400px\"></p>\n",
    "\n",
    "It is still the case that there is some underlying level of skill, that we'll call $\\theta$, and that the performance on each question is a noisy measurement of that skill, that we'll call $X$. We argue that performance noise is symmetric: the probability of performing a little better than their skill level is equal to performing a little worse. We will therefore use Gaussian, or Normal, likelihood functions: $p(X \\mid \\theta) = \\text{Normal}(X \\mid \\theta, \\sigma^2)$. The conjugate prior to the mean in Gaussian likelihoods is another Gaussian distribution: $p(\\theta) = \\text{Normal}(\\theta \\mid 60, 20)$. Say that we rate performance on a scale from $0$ to $100$, then it makes sense to use a mean of $60$ and a variance of $20$ for the prior.\n",
    "\n",
    "We'll keep the same generative model as before, with new definitions for each distribution:\n",
    "\n",
    "$$\\begin{align}\n",
    "p(X_1 \\mid \\theta) =&\\ \\text{Normal}(X_1 \\mid \\theta, 10) \\\\\n",
    "p(X_2 \\mid \\theta) =&\\ \\text{Normal}(X_2 \\mid \\theta, 15) \\\\\n",
    "p(\\theta) =&\\ \\text{Normal}(\\theta \\mid 60, 20)\n",
    "\\end{align}$$\n",
    "\n",
    "The factor graph will again be the same, but with different parameterizations of factor nodes:"
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    "# Start building a model\n",
    "factor_graph4 = FactorGraph()\n",
    "\n",
    "# Add the prior\n",
    "@RV θ ~ GaussianMeanVariance(60, 20, id=:f_a)\n",
    "\n",
    "# Add question 1 likelihood\n",
    "@RV X1 ~ GaussianMeanVariance(θ, 10, id=:f_b)\n",
    "\n",
    "# Add question 2 likelihood\n",
    "@RV X2 ~ GaussianMeanVariance(θ, 15, id=:f_c)\n",
    "\n",
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    "placeholder(X1, :X1)\n",
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    "\n",
    "# Visualize the graph\n",
    "ForneyLab.draw(factor_graph4)"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Indicate which variables you want posteriors for\n",
    "q = PosteriorFactorization(θ, ids=[:θ])\n",
    "\n",
    "# Generate a message passing inference algorithm\n",
    "algorithm = messagePassingAlgorithm(θ, q)\n",
    "\n",
    "# Compile algorithm code\n",
    "source_code = algorithmSourceCode(algorithm)\n",
    "\n",
    "# Bring compiled code into current scope\n",
    "eval(Meta.parse(source_code))\n",
    "\n",
    "# Visualize message passing schedule\n",
    "pfθ = q.posterior_factors[:θ]\n",
    "ForneyLab.draw(pfθ, schedule=pfθ.schedule);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The message passing schedule is still exactly the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Message ((1)) = 𝒩(m=60, v=20)\n",
      "Message ((2)) = 𝒩(m=61.50, v=10)\n",
      "Message ((3)) = 𝒩(m=72, v=15)\n",
      "Message ((4)) = 𝒩(xi=10.95, w=0.17)\n",
      "Marginal of θ = 𝒩(xi=13.95, w=0.22)\n"
     ]
    }
   ],
   "source": [
    "# Initialize a message data structure\n",
    "messages = Array{Message}(undef, 4)\n",
    "\n",
    "# Initalize marginal distributions data structure\n",
    "marginals = Dict()\n",
    "\n",
    "# Enter the scores in the data dictionary\n",
    "data = Dict(:X1 => 61.5,\n",
    "            :X2 => 72)\n",
    "\n",
    "# Update coefficients\n",
    "stepθ!(data, marginals, messages);\n",
    "\n",
    "# Print messages\n",
    "print(\"\\nMessage ((1)) = \"*string(messages[1].dist))\n",
    "print(\"Message ((2)) = \"*string(messages[2].dist))\n",
    "print(\"Message ((3)) = \"*string(messages[3].dist))\n",
    "print(\"Message ((4)) = \"*string(messages[4].dist))\n",
    "print(\"Marginal of θ = \"*string(marginals[:θ]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Message ((4)) has a somewhat unusual form in that uses `xi` as a parameter instead of `m`. When you take the product of Messages ((2)) and ((3)), the resulting mean is the sum of the precision-weighted means of Messages ((2)) and ((3)), normalized by the total precision (see [Bert's lecture](http://nbviewer.ipython.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/The-Gaussian-Distribution.ipynb)). `xi` represents the sum of precision-weighted means of the two messages. Let's look for the mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of Message ((4)) = 65.69999999999999\n",
      "Variance of Message ((4)) = 5.999999999999999\n"
     ]
    }
   ],
   "source": [
    "# Extract parameters from message ((4))\n",
    "m4 = mean(messages[4].dist)\n",
    "v4 = var(messages[4].dist)\n",
    "println(\"Mean of Message ((4)) = \"*string(m4))\n",
    "println(\"Variance of Message ((4)) = \"*string(v4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the mean of Message ((4)) lies in between the means of Messages ((2)) and ((3)). Note that the variance is much lower than that of Messages ((2)) or ((3))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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"
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define probability density function for Gaussian distribution\n",
    "pdf_Normal(θ, m, v) = 1/sqrt(2*π*v) * exp( -(θ - m)^2/(2*v))\n",
    "\n",
    "# Extract parameters from message ((2))\n",
    "m2 = messages[2].dist.params[:m]\n",
    "v2 = messages[2].dist.params[:v]\n",
    "\n",
    "# Extract parameters from message ((3))\n",
    "m3 = messages[3].dist.params[:m]\n",
    "v3 = messages[3].dist.params[:v]\n",
    "\n",
    "# Extract parameters from message ((4))\n",
    "m4 = mean(messages[4].dist)\n",
    "v4 = var(messages[4].dist)\n",
    "\n",
    "# Define new range for skill level θ\n",
    "θ_range = range(0.0, step=0.1, stop=100.0)\n",
    "plot(θ_range, pdf_Normal.(θ_range, m2, v2), color=\"black\", linewidth=3, label=\"Message ((2))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, pdf_Normal.(θ_range, m3, v3), color=\"green\", linewidth=3, label=\"Message ((3))\", size=(800,300))\n",
    "plot!(θ_range, pdf_Normal.(θ_range, m4, v4), color=\"blue\", linewidth=3, label=\"Message ((4))\", xlims=[50., 80.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Message ((4)) is really a weighted average of Messages ((2)) and ((3))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract parameters from message ((1))\n",
    "m1 = messages[1].dist.params[:m]\n",
    "v1 = messages[1].dist.params[:v]\n",
    "\n",
    "# Extract parameters from message ((4))\n",
    "m4 = mean(messages[4].dist)\n",
    "v4 = var(messages[4].dist)\n",
    "\n",
    "# Extract parameters from marginal\n",
    "m_marg = mean(marginals[:θ])\n",
    "v_marg = var(marginals[:θ])\n",
    "\n",
    "# Define new range for skill level θ\n",
    "plot(θ_range, pdf_Normal.(θ_range, m1, v1), color=\"red\", linewidth=3, label=\"Message ((1))\", xlabel=\"θ\", ylabel=\"p(θ)\")\n",
    "plot!(θ_range, pdf_Normal.(θ_range, m4, v4), color=\"blue\", linewidth=3, label=\"Message ((4))\", size=(800,300))\n",
    "plot!(θ_range, pdf_Normal.(θ_range, m_marg, v_marg), color=\"purple\", linewidth=6, linestyle=:dash, label=\"Marginal\", xlims=[50., 80.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior is also a weighted average of two incoming messages. Notice that it is much closer to Message ((4)) than Message ((1)). That is because the variance of Message ((1)) (the prior) is much higher than that of Message ((4)) (the combination of likelihoods). The prior has a smaller weight in the weighted average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### $\\ast$ **Try for yourself**\n",
    "\n",
    "Play around with different values for the prior's variance and the variance of the likelihoods. What happens when you make the variance of $p(X_1 \\mid \\theta)$ different from that of $p(X_2 \\mid \\theta)$?\n",
    "\n",
    "---"
   ]
  }
 ],
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