05-roc_curve.rb

# ロジスティック回帰のROC曲線

require 'daru'
require 'nyaplot'
require 'numo/narray'

Variances = [50, 150] # 両クラス共通の分散（2種類の分散で計算を実施）

def normal_rand(mu = 0, sigma = 1.0)
  random = Random.new
  (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu
end

# データセット {x_n,y_n,type_n} を用意
def prepare_dataset(variance)
  n1 = 80
  n2 = 200
  mu1 = [9, 9]
  mu2 = [-3, -3]

  sigma = Math.sqrt(variance)

  df1 = n1.times.map do
    [normal_rand(mu1[0], sigma), normal_rand(mu1[1], sigma)]
  end
  df1 = df1.transpose
  df1 = Daru::DataFrame.new(x: df1[0], y: df1[1], type: Array.new(n1).fill(1))

  df2 = n2.times.map do
    [normal_rand(mu2[0], sigma), normal_rand(mu2[1], sigma)]
  end
  df2 = df2.transpose
  df2 = Daru::DataFrame.new(x: df2[0], y: df2[1], type: Array.new(n2).fill(0))

  df = df1.concat(df2)
  df = df.reindex(Daru::Index.new(df.index.to_a.shuffle))
  df[:index] = (n1 + n2).times.to_a
  df.set_index(:index)
end

# ロジスティック回帰
def run_logistic(train_set, plot)
  w = Numo::NArray[[0], [0.1], [0.1]]
  phi = train_set[:x, :y]
  phi[:bias] = Array.new(phi.size).fill(1)
  t = train_set[:type]
  t = t.to_matrix

  # 最大100回のIterationを実施
  100.times do
    # IRLS法によるパラメータの修正
    y = []
    phi.each_row do |line|
      a = Vector[*line.to_a].dot(w)
      y << (1.0 / (1.0 + Math.exp(-a)))
    end
    r = Matrix.diagonal(*(Numo::NArray[*y] * (1 - Numo::NArray[*y]).to_a))
    y = Numo::NArray[y].transpose
    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
    tmp2 = Numo::NArray[*phi.to_matrix.transpose.to_a].dot(y - Numo::NArray[*t.transpose.to_a])
    w_new = w - Numo::NArray[*tmp1.to_a].dot(tmp2)

    # パラメータの変化が 0.1% 未満になったら終了
    if (w_new - w).transpose.dot(w_new - w).flatten[0] < (0.001 * (w.transpose.dot(w))).flatten[0]
      w = w_new
      break
    end
  end

  # 分類誤差の計算と確率付きデータの用意
  d0 = w[0]
  dx = w[1]
  dy = w[2]
  err = 0
  train_set[:probability] = Array.new(train_set.size).fill(0.0)

  train_set.each_row_with_index do |line, index|
    a = Vector[1, line.x, line.y].dot(w)
    p = 1.0 / (1.0 + Math.exp(-a))
    v = train_set.row[index]
    v[:probability] = p
    train_set.set_row_at([index], v)
    if (p - 0.5) * (line[:type] * 2 - 1) < 0
      err += 1
    end
  end

  err_rate = err * 100 / train_set.size

  # 境界線（P=0.5）を表示
  xmin = train_set.x.min - 5
  xmax = train_set.x.max + 5
  linex = Numo::NArray[*(xmin.to_i-5..xmax.to_i+4).to_a]
  liney = -linex * dx / dy - d0 / dy
  label = "ERR %.2f%%" % err_rate

  line_err = plot.add(:line, linex.cast_to(Numo::Int64).to_a, liney.cast_to(Numo::Int64).to_a)
  line_err.title(label)
  line_err.color('blue')

  # 確率付きデータを返却
  sorted_train_set = train_set.sort([:probability], ascending: false)
  sorted_train_set[:index] = sorted_train_set.size.times.to_a
  sorted_train_set.set_index(:index)
end

def run_simulation(variance, plot)
  train_set = prepare_dataset(variance)
  train_set1 = train_set.filter_rows {|row| row[:type] == 1 }
  train_set2 = train_set.filter_rows {|row| row[:type] == 0 }
  ymin = train_set.y.min - 5
  xmin = train_set.x.min - 5
  ymax = train_set.y.max + 10
  xmax = train_set.x.max + 10
  plot.configure do
    x_label("Variance: #{variance}")
    y_label('')
    xrange([xmin, xmax])
    yrange([ymin, ymax])
    legend(true)
    height(300)
    width(490)
  end

  scatter_true = plot.add_with_df(train_set1.to_nyaplotdf, :scatter, :x, :y)
  scatter_true.color('green')
  scatter_true.title('1')
  scatter_false = plot.add_with_df(train_set2.to_nyaplotdf, :scatter, :x, :y)
  scatter_false.color('orange')
  scatter_false.title('0')

  run_logistic(train_set, plot)
end

def draw_roc(result, plot)
  positives = result.filter_rows {|row| row[:type] == 1 }.size
  negatives = result.filter_rows {|row| row[:type] == 0 }.size
  tp = result.size.times.map { 0.0 }
  fp = result.size.times.map { 0.0 }
  result.each_row_with_index do |line, index|
    result.size.times do |c|
      if index < c
        if line[:type] == 1
          tp[c] += 1
        else
          fp[c] += 1
        end
      end
    end
  end
  
  tp_rate = Numo::NArray[*tp] / positives
  fp_rate = Numo::NArray[*fp] / negatives

  plot.configure do
    x_label('False positive rate')
    y_label('True positive rate')
    xrange([0, 1])
    yrange([0, 1])
    height(300)
    width(400)
  end

  plot.add(:line, fp_rate, tp_rate)
end

fig = Nyaplot::Frame.new

Variances.each do |variance|
  plot = Nyaplot::Plot.new
  result = run_simulation(variance, plot)
  fig.add(plot)

  plot = Nyaplot::Plot.new
  draw_roc(result, plot)
  fig.add(plot)
end

fig.show