John T. Langton : artificial intelligence : Influence Diagrams

Influence Diagrams

• Influence Diagrams

  or Decision Networks add action and utility node types to Bayesian networks. This is different from decision trees but similar.

• Decision nodes

  usually represented by rectangles are where the user can choose from possible actions which will influence any child nodes

• Chance nodes

  usually represented by ovals are the same as regular nodes in Bayesian networks.

• Utility nodes

  usually represented by diamonds are an evaluation of a utility function with parent nodes as inputs (usually chance nodes).
  
  

• The Decision node here will influence the result of the lottery in the chance node which in turn will figure into the result of the utility function in the utility node. Referring back to utility theory we can interpret the decision node as the set of possible actions to take, the chance node as the possible results of each action (and their probability of happening), and the utility node as the set of utility values for each configuration of the chance node.

• You can have the decision node feed directly in to the utility node which would eliminate the type of "outcome chance node" we have in our example graph. It could still be the case that other chance nodes feed into the utility node which are not affected by the decision node (i.e. aren't connected to it). This however is less flexible as you can't simply change the conditional probability table associated with a chance outcome node.

• Evaluating:

  Once a decision is made, the decision node acts as any chance node that is given evidence. To evaluate an influence diagram, for each possible value of the decision node:

  1. set the decision node to that value

  2. calculate posterior probabilities for parents of utility node

  3. calculate the utility