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Supposing to have a 3-layer DBN. I don't understand the specific reason for which the connections between the top two layers are undirected and the connections between all other layers are directed. Moreover, the arrows, representing the weights, points toward the layer that is closest to the data.

What is the explanation of having such both directed and undirected structure?

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It has to do with the construction of DBN. You get a DBN by stacking RBM each on the top of the other and learning the new one with the visible input taken as the hidden features of the previous one.

This changes the nature of the graphical model : while the top 2 layers are still a RBM, all the structure underneath becomes a deep sigmoid network (a directed model).

These explanations can be found in Hinton's Coursera Lecture 14.1.

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