Third edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, 2023 is now available (including the full text).
11.2.5 General Case of Belief Network Learning
The general case is with unknown structure, hidden variables, and missing data; we do not even know what variables exist. Two main problems exist. The first is the problem of missing data discussed earlier. The second problem is computational; although there is a well-defined search space, it is prohibitively large to try all combinations of variable ordering and hidden variables. If one only considers hidden variables that simplify the model (as seems reasonable), the search space is finite, but enormous.
One can either select the best model (e.g, the model with the highest a posteriori probability) or average over all models. Averaging over all models gives better predictions, but it is difficult to explain to a person who may have to understand or justify the model.
The problem with combining this approach with missing data seems to be much more difficult and requires more knowledge of the domain.
