Bayesian Networks

True or False

1. Given some variables that each can take finitely many values, we can specify any probability distribution over these variables using a Bayesian network.

2. Given some variables that each can take finitely many values, and given any order over these variables (so that some variables come "before" others), we can specify any probability distribution over these variables using a Bayesian network that is consistent with that order (we never draw an edge from a "later" variable to an "earlier" one).

3. Suppose we have determined the structure of our Bayesian network, that is, the nodes and the edges; but we have not yet determined the conditional probability tables. There are some probability distributions that we can model with this structure (by choosing the right conditional probability tables (CPTs)), and some that we cannot. Now suppose we add an edge to the structure, without changing anything else. Then we can still model any probability distribution that we could model before we added the edge.

4. Consider a Bayesian network that has many nodes, and where none of the nodes have any parents, except for one node which does have parents. It is possible that this Bayesian network requires exponential space to represent (exponential in the number of nodes).

5. Given a Bayesian network, the time that variable elimination requires depends on the order in which we eliminate the variables.