center Specify for the following figure, how the Maximum likelihood decision rule applied to to the red class and to the blue class, respectively, will decide

  • ML Classifier chooses the class with the the highest Likelihood
  • From Graph it is visible that
    • , has the highest value. Classification is RED
    • , has the highest value. Classification is BLUE

Now let the red class be only as frequent as the blue class

Specify depending on the feature , to which class the ML classifier, and to which class the MAP classifier decides.

MAP uses the Prior which can be calculated as follows

Given:

center From the Prior the decision boundary can be expected to shift with the new decision boundary The Decision Boundary in MAP is where the Posterior Probabilities are equal.1

center

  • i.e. , MAP chooses red class
  • i.e. , MAP chooses blue class

The exact value of is where , which appears to be around in the graph.

source

Footnotes

  1. If you’re slightly to one side of this boundary, one class becomes more likely; if you’re slightly to the other side, the other class becomes more likely. Thus the Decision Boundary is where the both classes are equally likely.