Herself’s Artificial Intelligence

Bayesian neural networks and expert systems (a.k.a. Uncertainty represen tation, belief networks, probabilistic networks) are based on “Bayes’ rule” or “Bayes’ theorem” which is a statistical theory. It was developed by Thomas Bayes in the 18th century. It takes and flips the probability given the original conditional probability. This is used to deal with uncertainty in expert systems. They often form the main part of spell correcting and speech recognition programs.

P (y|x) = P (x|y)P (y) / P (x)
Example:
P(A) is the event of a person having cancer (10%)
P(B) is the event of person being a smoker (50%)
P(B–A) is the percent cancer patients who smoke (80%)
We wish to know the likelihood of the smoker having cancer P (A|B) = (.8.1) .5 = .16 or a 16%chance.

A Bayesian network is an acyclic tree graph. An acyclic tree graph can not cycle back to previous conditions. Its nodes, occurrences, contain the possible outcomes and tables of probabilities of each considering the inputs to this node. The connecting edges contain the effects of occurrences on one another. The probabilities of all occurrences must total 100%, and all occurrences must be accounted for.

A node must be conditionally independent of any subset of nodules that are not descendants of it, this reduces the number of possibilities for each node that must be calculated.

There are three commonly used patterns of inference in Bayes Networks; Top-down which uses a chain rule to add up probabilities; Bottom-up which uses Bayes Rule; and a hybrid system. All of these use recursion in the algorithms making them computationally intensive.

Children of a parent node can be independent of each other, none of them contributing to the probabilities of another. In that case the parent is said to d-separate them. This can be used to cut down the number of calculations needed to work through the net.

The is network trained by giving the likely probabilities to seed it. When something new happens the probabilities are re-evaluated. This causes all the probabilities to be re-calculated (remember they must total 100%). The network structure must also be determined. Often this can be done before training occurs. Hidden nodes can sometimes help reduce the size of the network.

More information:
Bayesian Nets
Java Bayes

See also:
Graphical models of knowledge representation