文档介绍：Learning Structure in s (Typically also learn CPTs here)
Given the set of random variables (features), the space of all works is well-defined and finite.
Unfortunately, it is super-exponential in the number of variables.
We can define a transition function between states (network structures), such as adding an arc, deleting an arc, or changing the
Learning Structure (Continued)
(Continued)… direction of an arc.
For each state (structure), we take our best guess of the CPTs given the data as before.
We define the score of work to be either the probability of the data given work (maximum likelihood framework) or the posterior probability of work (the product of the prior probability of the
Learning Structure (Continued)
(Continued)… network and the probability of the data given work, normalized over all works).
Given a state space with transition function and scoring function, we now have a traditional AI search space to which we can apply greedy hill-climbing, randomized walks with multiple restarts, or a variety of
Learning Structure (Continued)
(Continued)… other heuristic search techniques.
The balance of opinion currently appears to favor greedy hill-climbing search for this applications, but search techniques for learning structure are wide open for further research -- nice thesis task.
Structural Equivalence
Independence Equivalent: 2 structures are independence equivalent if they encode the same conditional independence relations.
Distribution Equivalent with respect to a family of CPT formats: 2 structures are equivalent if they represent the same sets of possible distributions.
Likelihood Equivalent:the data does not help discriminate between the 2 structures.