Where Does Contextual Independence Arise?

## Where Does Contextual Independence Arise?

Most of the examples in this paper are abstract as they are designed to show off the various features of the algorithms or to show pathological cases. In this section we will give some examples to show natural examples. We are not claiming that contextual independence is always present or able to be exploited. Exploiting contextual independence should be seen as one of the tools to solve large probabilistic reasoning tasks.

Example. When a child goes into an emergency ward the staff may want to determine if they are a likely carrier of chicken pox (in order to keep them away from other children). If they haven't been exposed to chicken pox within the previous few weeks, they are unlikely to be a carrier. Thus whether they are a carrier is independent of the other background conditions given they haven't been exposed. If they have been exposed, but have not had chicken pox before they are likely to be a carrier. Thus whether they are a carrier is independent of the other background conditions given they have been exposed and haven't had chicken pox before. The other case can involve many other variables (e.g., the severity and the age of the last time they had chicken pox) to determine how likely the child is to be a carrier.

Example. Many engineered systems are designed to insulate something from other conditions. The classic example is central air conditioning (heating and/or cooling in a house). The temperature inside a house depends on the outside temperature if the air conditioning is off. If the air conditioning is on, the temperature depends on the setting of the thermostat and not on the outside temperature. Thus the inside temperature is contextually independent of the outside temperature given the air conditioning is on and is contextually independent of the thermostat setting given the air conditioning is off.

Example. Consider a case where someone is to make a decision based on a questionnaire and the questions asked depend on previous answers. In this case the decision6 is contextually independent of the answers to the questions that are not asked given the context of the questions asked. For example, consider a questionnaire to determine if a bank customer should get a loan that starts asking the customer if they rent or own their current home. If they own, they are asked a number of questions about the value of the house which are not asked if they rent. The probability that they get a loan is contextually independent of the value of the home (and the other information that was not available to the decision maker) given that the applicant rents their home.

Example. When learning a decision network from data, it is often advantageous to build a decision tree for each variable given its parents [13][6]. These decision trees provide contextual independence (a variable is independent of it's predecessors given the context along a path to a leaf in the tree). The reason that this is a good representation to learn is because there are fewer parameters and more fine control over adding parameters; splitting a leaf adds many fewer parameters than adding a new parent (adding a new variable to every context).

David Poole and Nevin Lianwen Zhang,Exploiting Contextual Independence In Probabilistic Inference, Journal of Artificial Intelligence Research, 18, 2003, 263-313.

 Where Does Contextual Independence Arise?