Suppose we generate a training data set from a given Bayesian network and then we learn a Bayesian network from the generated training set. Will the learning algorithm eventually return the same Bayesian network that we used to generate the training data as the size of the training set goes to infinity? Explain your answer.

 

The algorithm may not return the same Bayesian network, but it will return a network that is logically equivalent, assuming that the method for generating the training set eventually generates all possible combinations of attributes.

For example, if the method picks the value of each attribute uniformly at random, the probability that it generates all possible combinations goes to one when the training set goes to infinity.

The form of the Bayesian network may not be the same, because there are multiple ways of representing the same logical function.