I have P(X) (someone standing infront of a house) and I have P(Z|X) (dog is barking given someone is standing infront of a house).
If I would like to find out probability of P(Z) (Dog is barking) or P(X|Z) (Someone is standing infront of a house given dog is barking) I could use a law of total probability or Bayes network. This is really simple model with P(Z), which is tractable.
Now, let's assume P(Z) is not tractablee and I would need to use variational inference to solve this problem.
Could anyone please let me describe how we would do that in pseudo, non algebra way? I know a concept of Kl Divergence and lowerbound, but I just can not visualize the whole concept. Could you let me know what would be steps? I would appreciate it.