# How to get the joint distribution of multimodal deep Boltzmann machine?

Here is the graph model of the multimodal dbm. I want to know how to inference the joint distribution of this probability graph model.

Some example equations are here. For the expression, I have two questions.

1. How to get the second line?
2. Why $$p(v^m,h^{1m}|h^{2m})$$ is a Boltzmann distribution?

It would be great if you could provide the whole process to get the final expression of $$p(v^m,v^t)$$.

The source of these photos are from http://jmlr.org/papers/volume15/srivastava14b/srivastava14b.pdf and https://slideplayer.com/slide/13728662/

• Thank you. The source of these photos are from jmlr.org/papers/volume15/srivastava14b/srivastava14b.pdf and slideplayer.com/slide/13728662 Jul 29 '19 at 2:52
• The second line follows from the structure of the graphical model (independence of the two sides of the model given $h^{2m}$, $h^{2t}$, and $h^3$). Beyond that, I do not understand what exactly you are asking. Jul 29 '19 at 10:32