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
- Actions
- 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.