Learning BBNs

• If the network structure was given in advance and the variables are fully observable, then just use the Naive Bayes formula modulo only some of the variables are conditionally independent.
• If the network structure is given but only some of the variables are observable, the problem is analogous to learn weights for the hidden units in an ANN.
• Similarly, use a gradient ascent procedure to search through the space of hypotheses that corresponds to all possible entries in the conditional probability tables. The objective function that is maximized is .
• By definition this corresponds to searching for the maximum likelihood hypothesis for the table entries.