05-roc_curve.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<main>:6: warning: already initialized constant Variances\n",
      "<main>:6: warning: previous definition of Variances was here\n"
     ]
    },
    {
     "data": {
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       "        var id_name = '#vis-fbe738a8-094e-4de8-9fb4-ca7a7fce7373';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
      ],
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   "source": [
    "# ロジスティック回帰のROC曲線\n",
    "\n",
    "require 'daru'\n",
    "require 'nyaplot'\n",
    "require 'numo/narray'\n",
    "\n",
    "Variances = [50, 150] # 両クラス共通の分散（2種類の分散で計算を実施）\n",
    "\n",
    "def normal_rand(mu = 0, sigma = 1.0)\n",
    "  random = Random.new\n",
    "  (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu\n",
    "end\n",
    "\n",
    "# データセット {x_n,y_n,type_n} を用意\n",
    "def prepare_dataset(variance)\n",
    "  n1 = 80\n",
    "  n2 = 200\n",
    "  mu1 = [9, 9]\n",
    "  mu2 = [-3, -3]\n",
    "\n",
    "  sigma = Math.sqrt(variance)\n",
    "\n",
    "  df1 = n1.times.map do\n",
    "    [normal_rand(mu1[0], sigma), normal_rand(mu1[1], sigma)]\n",
    "  end\n",
    "  df1 = df1.transpose\n",
    "  df1 = Daru::DataFrame.new(x: df1[0], y: df1[1], type: Array.new(n1).fill(1))\n",
    "\n",
    "  df2 = n2.times.map do\n",
    "    [normal_rand(mu2[0], sigma), normal_rand(mu2[1], sigma)]\n",
    "  end\n",
    "  df2 = df2.transpose\n",
    "  df2 = Daru::DataFrame.new(x: df2[0], y: df2[1], type: Array.new(n2).fill(0))\n",
    "\n",
    "  df = df1.concat(df2)\n",
    "  df = df.reindex(Daru::Index.new(df.index.to_a.shuffle))\n",
    "  df[:index] = (n1 + n2).times.to_a\n",
    "  df.set_index(:index)\n",
    "end\n",
    "\n",
    "# ロジスティック回帰\n",
    "def run_logistic(train_set, plot)\n",
    "  w = Numo::NArray[[0], [0.1], [0.1]]\n",
    "  phi = train_set[:x, :y]\n",
    "  phi[:bias] = Array.new(phi.size).fill(1)\n",
    "  t = train_set[:type]\n",
    "  t = t.to_matrix\n",
    "\n",
    "  # 最大100回のIterationを実施\n",
    "  100.times do\n",
    "    # IRLS法によるパラメータの修正\n",
    "    y = []\n",
    "    phi.each_row do |line|\n",
    "      a = Vector[*line.to_a].dot(w)\n",
    "      y << (1.0 / (1.0 + Math.exp(-a)))\n",
    "    end\n",
    "    r = Matrix.diagonal(*(Numo::NArray[*y] * (1 - Numo::NArray[*y]).to_a))\n",
    "    y = Numo::NArray[y].transpose\n",
    "    tmp1 = Matrix[*Numo::NArray[*phi.to_matrix.transpose.to_a].dot(Numo::NArray[*r.to_a]).dot(Numo::NArray[*phi.to_matrix.to_a]).to_a].inverse\n",
    "    tmp2 = Numo::NArray[*phi.to_matrix.transpose.to_a].dot(y - Numo::NArray[*t.transpose.to_a])\n",
    "    w_new = w - Numo::NArray[*tmp1.to_a].dot(tmp2)\n",
    "\n",
    "    # パラメータの変化が 0.1% 未満になったら終了\n",
    "    if (w_new - w).transpose.dot(w_new - w).flatten[0] < (0.001 * (w.transpose.dot(w))).flatten[0]\n",
    "      w = w_new\n",
    "      break\n",
    "    end\n",
    "  end\n",
    "\n",
    "  # 分類誤差の計算と確率付きデータの用意\n",
    "  d0 = w[0]\n",
    "  dx = w[1]\n",
    "  dy = w[2]\n",
    "  err = 0\n",
    "  train_set[:probability] = Array.new(train_set.size).fill(0.0)\n",
    "\n",
    "  train_set.each_row_with_index do |line, index|\n",
    "    a = Vector[1, line.x, line.y].dot(w)\n",
    "    p = 1.0 / (1.0 + Math.exp(-a))\n",
    "    v = train_set.row[index]\n",
    "    v[:probability] = p\n",
    "    train_set.set_row_at([index], v)\n",
    "    if (p - 0.5) * (line[:type] * 2 - 1) < 0\n",
    "      err += 1\n",
    "    end\n",
    "  end\n",
    "\n",
    "  err_rate = err * 100 / train_set.size\n",
    "\n",
    "  # 境界線（P=0.5）を表示\n",
    "  xmin = train_set.x.min - 5\n",
    "  xmax = train_set.x.max + 5\n",
    "  linex = Numo::NArray[*(xmin.to_i-5..xmax.to_i+4).to_a]\n",
    "  liney = -linex * dx / dy - d0 / dy\n",
    "  label = \"ERR %.2f%%\" % err_rate\n",
    "\n",
    "  line_err = plot.add(:line, linex.cast_to(Numo::Int64).to_a, liney.cast_to(Numo::Int64).to_a)\n",
    "  line_err.title(label)\n",
    "  line_err.color('blue')\n",
    "\n",
    "  # 確率付きデータを返却\n",
    "  sorted_train_set = train_set.sort([:probability], ascending: false)\n",
    "  sorted_train_set[:index] = sorted_train_set.size.times.to_a\n",
    "  sorted_train_set.set_index(:index)\n",
    "end\n",
    "\n",
    "def run_simulation(variance, plot)\n",
    "  train_set = prepare_dataset(variance)\n",
    "  train_set1 = train_set.filter_rows {|row| row[:type] == 1 }\n",
    "  train_set2 = train_set.filter_rows {|row| row[:type] == 0 }\n",
    "  ymin = train_set.y.min - 5\n",
    "  xmin = train_set.x.min - 5\n",
    "  ymax = train_set.y.max + 10\n",
    "  xmax = train_set.x.max + 10\n",
    "  plot.configure do\n",
    "    x_label(\"Variance: #{variance}\")\n",
    "    y_label('')\n",
    "    xrange([xmin, xmax])\n",
    "    yrange([ymin, ymax])\n",
    "    legend(true)\n",
    "    height(300)\n",
    "    width(490)\n",
    "  end\n",
    "\n",
    "  scatter_true = plot.add_with_df(train_set1.to_nyaplotdf, :scatter, :x, :y)\n",
    "  scatter_true.color('green')\n",
    "  scatter_true.title('1')\n",
    "  scatter_false = plot.add_with_df(train_set2.to_nyaplotdf, :scatter, :x, :y)\n",
    "  scatter_false.color('orange')\n",
    "  scatter_false.title('0')\n",
    "\n",
    "  run_logistic(train_set, plot)\n",
    "end\n",
    "\n",
    "def draw_roc(result, plot)\n",
    "  positives = result.filter_rows {|row| row[:type] == 1 }.size\n",
    "  negatives = result.filter_rows {|row| row[:type] == 0 }.size\n",
    "  tp = result.size.times.map { 0.0 }\n",
    "  fp = result.size.times.map { 0.0 }\n",
    "  result.each_row_with_index do |line, index|\n",
    "    result.size.times do |c|\n",
    "      if index < c\n",
    "        if line[:type] == 1\n",
    "          tp[c] += 1\n",
    "        else\n",
    "          fp[c] += 1\n",
    "        end\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "  \n",
    "  tp_rate = Numo::NArray[*tp] / positives\n",
    "  fp_rate = Numo::NArray[*fp] / negatives\n",
    "\n",
    "  plot.configure do\n",
    "    x_label('False positive rate')\n",
    "    y_label('True positive rate')\n",
    "    xrange([0, 1])\n",
    "    yrange([0, 1])\n",
    "    height(300)\n",
    "    width(400)\n",
    "  end\n",
    "\n",
    "  plot.add(:line, fp_rate, tp_rate)\n",
    "end\n",
    "\n",
    "fig = Nyaplot::Frame.new\n",
    "\n",
    "Variances.each do |variance|\n",
    "  plot = Nyaplot::Plot.new\n",
    "  result = run_simulation(variance, plot)\n",
    "  fig.add(plot)\n",
    "\n",
    "  plot = Nyaplot::Plot.new\n",
    "  draw_roc(result, plot)\n",
    "  fig.add(plot)\n",
    "end\n",
    "\n",
    "fig.show\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
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   "outputs": [],
   "source": []
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