## Thursday, September 18, 2008

### Bayes theorem

In artificial intelligence courses, a start into an exploration of the Bayes theorem. In simpler words, Bayes is about discovering (strengths of) relationships between cause and effect. It's looking at events and developing a hypothesis or observing an occurrence which may have led to that event and an expression of the chance that the event occurs based on the occurrence/trueness of the hypothesis (potential cause).

This theorem is used in medical analysis for example (what is the chance for a person to have meningitis, considering the person has a headache?). Of course, the theorem can be expanded by the union of two hypothesis's. When both occur at the same time, *then* what is the chance for the event (meningitis) to occur?

For another direct application, consider credit-card fraud. If you have a large training set and you have a large database of credit-card frauders, you could determine from the data-set the probability that a female, a certain age group or people from a certain neighborhood/city/area commits credit card fraud. You could theoretically even come up with a number for a credit card applicant to state the probability the person would commit credit card fraud and so on. Of course, maintaining the view that you're dealing with probability, not certainty.

Bayes can also be used by learning systems to develop associations or relationships. It doesn't thus produce a boolean true|false relationship between elements, but a probability relationship. Theoretically, I think it should even be possible to organize different kinds of relationships (dependencies, associations, classifications) using Bayes just by looking at a large data-set. The problem here is that such an engine shouldn't be looking at all possible combinations of cause / effect, but logically reason within those, so make deductions about possibly sensible combinations.

Then one can question whether we as human beings absolutely exclude some silly statements. If we did employ true|false for each hypothesis with nothing inbetween, then we would have trouble understanding the world around us too, since it's full of exceptions. Does this suggest that some sort of Bayesian theorem is at the basis of our association determinations in a neural network?

http://www.inference.phy.cam.ac.uk/mackay/Bayes_FAQ.html