06-DecisionNetworks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BayesNets\n",
    "using DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "\n"
      ],
      "text/plain": [
       "BayesNet{CPD}({4, 3} directed simple Int64 graph, CPD[StaticCPD{Bernoulli{Float64}}(:D, Symbol[], Bernoulli{Float64}(p=0.01)), FunctionalCPD{Bernoulli}(:O3, Symbol[:D], getfield(Main, Symbol(\"##5#6\"))()), StaticCPD{Bernoulli{Float64}}(:O1, Symbol[:D], Bernoulli{Float64}(p=0.5)), FunctionalCPD{Bernoulli}(:O2, Symbol[:D], getfield(Main, Symbol(\"##3#4\"))())], Dict(:O2 => 4,:D => 1,:O1 => 3,:O3 => 2))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = BayesNet()\n",
    "push!(b, StaticCPD(:D, Bernoulli(0.01)))\n",
    "push!(b, StaticCPD(:O1, [:D], Bernoulli(0.5))) # no real signal of whether disease is present\n",
    "push!(b, FunctionalCPD{Bernoulli}(:O2, [:D], a->Bernoulli(a[:D] == true ? 0.9 : 0.01)))\n",
    "push!(b, FunctionalCPD{Bernoulli}(:O3, [:D], a->Bernoulli(a[:D] == true ? 0.6 : 0.3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>D</th><th>U</th></tr><tr><th></th><th>Bool</th><th>Bool</th><th>Int64</th></tr></thead><tbody><p>4 rows × 3 columns</p><tr><th>1</th><td>0</td><td>0</td><td>0</td></tr><tr><th>2</th><td>0</td><td>1</td><td>-10</td></tr><tr><th>3</th><td>1</td><td>0</td><td>-1</td></tr><tr><th>4</th><td>1</td><td>1</td><td>-1</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& T & D & U\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Bool & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 0 & 0 \\\\\n",
       "\t2 & 0 & 1 & -10 \\\\\n",
       "\t3 & 1 & 0 & -1 \\\\\n",
       "\t4 & 1 & 1 & -1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×3 DataFrame\n",
       "│ Row │ T    │ D    │ U     │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mBool\u001b[39m │ \u001b[90mInt64\u001b[39m │\n",
       "├─────┼──────┼──────┼───────┤\n",
       "│ 1   │ 0    │ 0    │ 0     │\n",
       "│ 2   │ 0    │ 1    │ -10   │\n",
       "│ 3   │ 1    │ 0    │ -1    │\n",
       "│ 4   │ 1    │ 1    │ -1    │"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U = DataFrame()\n",
    "U[!,:T] = [false, false, true, true]\n",
    "U[!,:D] = [false, true, false, true]\n",
    "U[!,:U] = [0, -10, -1, -1]\n",
    "U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "function estimate_table(b::BayesNet, target::NodeName, consistent_with::Assignment; nsamples = 10000)\n",
    "    Random.seed!(0)\n",
    "    t = fit(Table, rand(b, LikelihoodWeightedSampler(consistent_with), nsamples))\n",
    "    normalize(sumout(t, setdiff(names(b), [target])))\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>D</th><th>p</th></tr><tr><th></th><th>Any</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>0.9899</td></tr><tr><th>2</th><td>1</td><td>0.0101</td></tr></tbody></table>"
      ],
      "text/plain": [
       "Table(2×2 DataFrame\n",
       "│ Row │ D   │ p       │\n",
       "│     │ \u001b[90mAny\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼─────┼─────────┤\n",
       "│ 1   │ 0   │ 0.9899  │\n",
       "│ 2   │ 1   │ 0.0101  │)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = estimate_table(b, :D, Assignment(:O1=>true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>D</th><th>U</th><th>p</th></tr><tr><th></th><th>Bool</th><th>Bool</th><th>Int64</th><th>Float64</th></tr></thead><tbody><p>4 rows × 4 columns</p><tr><th>1</th><td>0</td><td>0</td><td>0</td><td>0.9899</td></tr><tr><th>2</th><td>0</td><td>1</td><td>-10</td><td>0.0101</td></tr><tr><th>3</th><td>1</td><td>0</td><td>-1</td><td>0.9899</td></tr><tr><th>4</th><td>1</td><td>1</td><td>-1</td><td>0.0101</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& T & D & U & p\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Bool & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 0 & 0 & 0.9899 \\\\\n",
       "\t2 & 0 & 1 & -10 & 0.0101 \\\\\n",
       "\t3 & 1 & 0 & -1 & 0.9899 \\\\\n",
       "\t4 & 1 & 1 & -1 & 0.0101 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×4 DataFrame\n",
       "│ Row │ T    │ D    │ U     │ p       │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mBool\u001b[39m │ \u001b[90mInt64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼──────┼──────┼───────┼─────────┤\n",
       "│ 1   │ 0    │ 0    │ 0     │ 0.9899  │\n",
       "│ 2   │ 0    │ 1    │ -10   │ 0.0101  │\n",
       "│ 3   │ 1    │ 0    │ -1    │ 0.9899  │\n",
       "│ 4   │ 1    │ 1    │ -1    │ 0.0101  │"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EU = join(U, D.potential, on = :D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>x1</th></tr><tr><th></th><th>Bool</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>-0.101</td></tr><tr><th>2</th><td>1</td><td>-1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& T & x1\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & -0.101 \\\\\n",
       "\t2 & 1 & -1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ T    │ x1      │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼──────┼─────────┤\n",
       "│ 1   │ 0    │ -0.101  │\n",
       "│ 2   │ 1    │ -1.0    │"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "by(EU, :T, df->LinearAlgebra.dot(df[!,:U], df[!,:p]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "function diseaseEU(b::BayesNet, a::Assignment, U::DataFrame)\n",
    "    D = estimate_table(b, :D, a).potential\n",
    "    EU = join(U, D, on = :D)\n",
    "    t = by(EU, :T, df->LinearAlgebra.dot(df[!,:U], df[!,:p]))\n",
    "    rename!(t, :x1=>:EU)\n",
    "    t\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>EU</th></tr><tr><th></th><th>Bool</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>-0.101</td></tr><tr><th>2</th><td>1</td><td>-1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& T & EU\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & -0.101 \\\\\n",
       "\t2 & 1 & -1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ T    │ EU      │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼──────┼─────────┤\n",
       "│ 1   │ 0    │ -0.101  │\n",
       "│ 2   │ 1    │ -1.0    │"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diseaseEU(b, Assignment(:O1=>true), U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>EU</th></tr><tr><th></th><th>Bool</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>-0.101</td></tr><tr><th>2</th><td>1</td><td>-1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& T & EU\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & -0.101 \\\\\n",
       "\t2 & 1 & -1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ T    │ EU      │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼──────┼─────────┤\n",
       "│ 1   │ 0    │ -0.101  │\n",
       "│ 2   │ 1    │ -1.0    │"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diseaseEU(b, Assignment(:O1=>false), U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>EU</th></tr><tr><th></th><th>Bool</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>-4.78698</td></tr><tr><th>2</th><td>1</td><td>-1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& T & EU\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & -4.78698 \\\\\n",
       "\t2 & 1 & -1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ T    │ EU       │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mFloat64\u001b[39m  │\n",
       "├─────┼──────┼──────────┤\n",
       "│ 1   │ 0    │ -4.78698 │\n",
       "│ 2   │ 1    │ -1.0     │"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diseaseEU(b, Assignment(:O2=>true), U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>T</th><th>EU</th></tr><tr><th></th><th>Bool</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>0</td><td>-0.19998</td></tr><tr><th>2</th><td>1</td><td>-1.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& T & EU\\\\\n",
       "\t\\hline\n",
       "\t& Bool & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & -0.19998 \\\\\n",
       "\t2 & 1 & -1.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ T    │ EU       │\n",
       "│     │ \u001b[90mBool\u001b[39m │ \u001b[90mFloat64\u001b[39m  │\n",
       "├─────┼──────┼──────────┤\n",
       "│ 1   │ 0    │ -0.19998 │\n",
       "│ 2   │ 1    │ -1.0     │"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diseaseEU(b, Assignment(:O3=>true), U)"
   ]
  }
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