Causal Independence (CI) is method of defining a discrete distribution that can dramatically reduce the number of prior probabilities necessary to define a distribution.
Use the diagram view's node context menu to apply a CI distribution to a node. Use the Standard Assessment tool to edit CI distributions.
The fundamental idea is that the individual causes (parents of a variable) influence it in a way that is either dependent or independent of the value of other causes. In other words, is the resulting posterior probability strongly influenced by the different states of each of the parents, or does any given parent being in an abnormal or problematical state dominate the outcome?
Standard (non-CI) nodes represent the dependent case; all of its causes or influences may interact, and every nuance of the combination space can be separately weighted.
CI (causal independence) nodes represent the independent case; all causes are completely separate.
Consider a model designed to diagnose a failure in a computer network server. The "problem" node representing the server would certainly be influenced by such factors as "Power Failure", "Hard Disk Crash" or "Network Cable Unplugged" (along with many other possible causes).
The idea of a causally independent distribution is that there is little value in attempting to assess the prior probability of a simultaneous power failure and hard disk crash. It would be a highly unlikely situation, and almost no one would have enough experience to assess such an outcome correctly.
In addition (and perhaps more to the point), there is virtually no value in such a diagnosis. Both of the fundamental underlying causes would need to be rectified before the server could be back on-line. Even if this were a real-world situation, the diagnosis would first indicate a power failure; after restoring power, the diagnosis would then indicate a hard disk crash.
A CI distribution reduces the number of assessments from 2^(N+M) to M*(N+1), where N is the sum of the number of states of the parent nodes and M the number of states of the child node. It also speeds up inference substantially if there many parent states.
When working with a CI distribution, the assessment dialog requires a set of prior probabilities for each abnormal state of each parent. Finally, there is also what is known as a "leak" parameter, which indicates the probabilities for the node when none of its parents is in an abnormal state.
