Conditional Risk

The Risk associated with taking a decision given the observation or simply the cost of a decision is given by,

where,

  • represents the action
  • is the loss function, such that states how costly an action given a classification

Note: The Cost function is entered manually. So that the decision that would lead to a negative outcome is weighted with a very high cost.

Example

Consider a Two Class problem such that

  1. Actions
  2. Classification Loss function
  • : Low
  • : High
  • : High
  • : Low

Give that we use a Bayes Classifier to make diagnosis a on the Patient. The Conditional Risk can be calculated as follows.

Bayes Decision Rule for Actions

Thus the best action would be the one that minimizes the risk.