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ROC Curve

Receiver Operating Characteristic Curve

Correspondence between score distributions and the ROC curve (https://en.wikipedia.org/wiki/Receiver_operating_characteristic)
  • d (x-axis) is the score returned by a binary classifier
  • The red and blue hatchings are distributions of the scores of the positive and negative truths
  • Let the distributions be normal, move "<-->" to adjust the location and scale
  • d* is a threshold setting to separate the mixing of the positive and negative classifications
  • The blue shaded region (d < d*) is the distribution of false positive (FP) scores
  • The red shaded region (d > d*) is the distribution of false negative (FN) scores
  • The area of the blue shaded region yields the false positive rate FPR
  • The area of the red hatching less the area of the red shade yields the truth positive rate TPR
  • The ROC curve is the plot of TPR vs FPR as function of the threshold setting d*
  • Move d* on Graph to trace the ROC curve on Graph2
Question: Find an optimal threshold setting d*