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 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.