##### Experience

There has been considerable controversy over the best way to represent uncertainty, with some of the suggestions being: probability, fuzzy logic, nonmonotonic logic, belief functions, Dempster-Shafer, etc.  Currently probability and fuzzy logic are the most practical methods for most applications.  Of these two, probability has a much sounder theoretical basis (at least with respect to the way they are actually used).  However, probability by itself does not represent the confidence one has in one's beliefs, or lack thereof (e.g. "ignorance")

Example:  Suppose you had to draw a ball from a bag full of black and white balls, and you couldn’t observe how many white balls or black balls are in the bag.  If you had to supply a probability that you were going to draw a white ball, it should be 0.5, providing you had no additional information.

Contrast that with a situation in which you can count the balls in the bag beforehand (there are 10 of each), and you will shake the bag before you draw.  In this situation the probability of drawing a white ball is 0.5, but whereas in the first situation you were in a state of ignorance, now you feel much more informed.

If you needed to do probabilistic inference or solve decision problems, then the 0.5 probability would be sufficient in either situation.  In both situations you should believe and act as if there was an equal chance of drawing a white or a black ball.  So the concept of experience is not required for these types of problems, and you do not need to be able to represent ignorance (ignorance is the endpoint of the experience spectrum).  However, for learning and communicating knowledge, it is useful to be able to represent the degree of experience as well as the probability, as we shall see.

Suppose you then sequentially draw a number of balls from the bag.  If you drew 3 white balls in a row, then in the first situation your probability that the next ball will be white should be greater than 0.5, because you are learning (perhaps incorrectly) that there seem to be a lot of white balls.  In the second situation your probability of the next ball being white should be less than 0.5, because you know that now there are more black than white balls left in the bag.  Since you should arrive at different conclusions in each of the two situations, you need some more detailed way of representing the original knowledge than just P(white) = 0.5.

One way to handle this using just probabilities is to keep track of your beliefs about the ratio of white to black balls in the bag.  Then you will have many probabilities, one for each possible ratio.  Each of these probabilities will change as you draw a ball, and when you are asked to supply a probability that the next ball drawn will be white, they will all be involved in the calculation.  These are sometimes called second order probabilities, but in this example they are really just a probability distribution over possible ratios of balls.  It would be easy to create a Bayes net for this, which would have an extra continuous node representing the actual ratio of balls in the bag, and beliefs for each possible ratio would be updated with each observation (for an example of this, see the "Beta Updating" net).  That approach works fine for this simple problem, but you can imagine that if you had many interrelated variables, that it would become too complicated, because you would need a separate extra node for each probability number of each CPT of the original net.

Instead Netica uses the concept of experience, which is a measure of the confidence that Netica has in its probabilities.

At each node Netica keeps an experience table, which has a single experience number for each row of the CPT. The experience value corresponds closely to the number of cases that have been seen or its equivalent (normally it is 1 more than the number of cases).  This form of experience has sometimes been called the “equivalent sample size” or “ess”.  To save space, Netica doesn’t keep experience tables for nodes that haven’t been involved in any learning and haven’t had a manual entry of experience.  You can view or edit experience tables with the table editor.

The experience numbers are not involved in probabilistic inference or decision problems, since they aren’t needed then.  But whenever Netica does learning, they are involved (and that will effect the CPTs, which will effect future probabilistic inference and decision problem results). (More info on how experience is calculated)