Most Probable Explanation

Given findings for some nodes, you may want to find the most probable configuration of values for the rest of the nodes.  This can be thought of as providing a plausible explanation for the observed findings, and is called the most probable explanation or MPE (it is a special case of the maximum a-posteriori probability, or MAP).

You cannot determine the MPE simply by taking for each node the state with highest belief after regular belief updating (which finds the marginal posterior probability for each node).  For example, in a lottery for which we know there is one winner, it might be most probable for each individual person to lose, but then the overall configuration would have everybody losing, which contradicts the one winner evidence.  Finding the MPE would select one representative person to win (perhaps who bought the most tickets), and the rest would be losers.

Netica can be used to find the MPE.  To indicate that you wish to do MPE updating for the active net, instead of regular belief updating, toggle Network Most Probable Expl.  You will have to recompile after turning MPE on or off, as is indicated by all the belief-bars turning gray.  You then enter findings in the usual way and it does MPE updating immediately afterwards if Network Automatic Updating is on, or otherwise just after a Network Update command.

After updating, each node will have a belief-bar at the 100% level, and usually some bars at lower levels.  You can read off the most probable configuration by taking for each node the state with the bar at the 100% level.  The shorter bars indicate the relative probabilities of the other states given that the other nodes are in the most probable configuration (scaled by the same factor used to bring the longest bar to 100%).

Of course the bars don’t add to 100%, so if you are ever using Netica and are confused that every node has a 100% bar and there are also some other nonzero bars, it is because MPE updating is on.  To avoid the possibility of accidentally doing MPE updating when regular updating is expected, all nets start with the MPE feature turned off, even if MPE was on when the net was last saved.

Multiple 100% Bars:  Sometimes two or more states of the same node have bars that are at the 100% level.  This indicates that there is more than one configuration with the highest probability (i.e., the configurations have equal probability).  If more than one node has this, then you should choose one of the states and enter artificial evidence that the node is in that state, to see how it changes the multiple 100% bars of other nodes.  By trying each of the possibilities you can map out all the configurations that are at the highest probability level.

Problems:  You must be careful using the MPE.  Generally, it is not as good as posterior probability (i.e. regular updating) for decision problems, or providing prediction or diagnosis probabilities.  Its results can change with the introduction of irrelevant variables.  And, it can be deceptive in situations where even the most probable explanation is extremely unlikely.

When to Use:  The MPE is useful for explaining and aiding understanding.  If an agent finds the results of regular belief updating questionable, and asks you to provide a scenario for which the beliefs are upheld, you can use the MPE to find that scenario.  People sometimes find a completely specified scenario easier to understand.  And sometimes you can gain insights by putting the Bayes net in MPE mode, entering the evidence, observing the most probable configuration, and then experimenting with adding extra “evidence” to explore a set of probable configurations close to the most probable one, while seeing how changing one node effects the others.