I was looking the HMM and the DMM example. I was wondering if there is a way to combine the two to make a Switching DMM (like Switching linear dynamical system).
y1 ---> y2 ----> y3
z1----> z2 ----> z3
Note: there are also arrows between y2 --> z2 and y3 --> z3
i was thinking alternating optimization between the vae z --> x and a standard HMM y1 --> z (using message passing)
any pointers on that? or would you recommend using Gumbel trick to build this kind of model and train the whole thing using variational inference.