you may bug me on this. i work too closely with alp :)
edward does not implement completely implement advi yet. the piece that is missing is the automated transformation of constrained latent variable spaces to the real coordinate space. however, edward offers much more flexibility in specifying the dependency structure of the posterior approximation. diagonal is, just like in stan, the fastest and easiest. however introducing structure (e.g. assigning a dense normal to some of the latent variables while assigning a diagonal to others) is much easier in edward.
OK I would be interested in seeing how to do that. Are there any examples or hints on how to start? I worked a lot with time series models (think nonlinear autoregressive), where there's strong short term autocorrelation, and the coercion to diagonal covariance seemed inappropriate.
I have also a naïve question: why not use the graphical structure of the model itself to add structure to the covariance? For example, in an AR model, each time point places prior on the next time point, so why not assume a banded covariance? More generally, one could use a cutoff on shortest path length (through the model's graphic structure) between parameters to decide if they should have nonzero coefficients.
edward does not implement completely implement advi yet. the piece that is missing is the automated transformation of constrained latent variable spaces to the real coordinate space. however, edward offers much more flexibility in specifying the dependency structure of the posterior approximation. diagonal is, just like in stan, the fastest and easiest. however introducing structure (e.g. assigning a dense normal to some of the latent variables while assigning a diagonal to others) is much easier in edward.