In general, neural networks are not graphical models due to the choice of the cost function, but are restricted Boltzmann machines a special type of Bayesian networks?
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Boltzmann machines are graphical models, but they are not Bayesian networks. They're a kind of Markov random field, which has undirected connections between the variables, while Bayesian networks have directed connections.
The difference between the two kinds of connections can be subtle, but the main advantage of undirected connections for an RBM is that inferring the hidden states associated with a set of visible states is much easier when the connections are undirected and there are many hidden variables.
answered May 19, 2013 at 21:38
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1$\begingroup$ But it's not a Bayesian network. Bayesian networks are directed graphical models. $\endgroup$ Commented May 19, 2013 at 21:30