I am reading Variational Inference: A Review for Statisticians.
Working in [the exponential] family simplifies variational inference: it is easier to derive the corresponding CAVI algorithm, and it enables variational inference to scale up to massive data.
Coordinate Ascent Variational Inference:
The exponential family assumption simplifies the coordinate update of Equation:
This update reveals the parametric form of the optimal variational factors. [...] When we update each factor, we set its parameter equal to the expected parameter of the complete conditional:
My questions is:
Why does this simplify the CAVI? (It seems to me that the ELBO is easier to compute. But is not completely clear to me.)
