Update to the [email protected] interface

[Red-Portal]

This PR aims to update Turing's Variational module to match AdvancedVI's new interface starting from v0.3. I will try not to change the interface too much, but given the new features in AdvancedVI, I think breaking changes will be inevitable. Though the focus will be to provide a good default setting rather than to expose all the features.

Currently proposed interface:

using Turing
using AdvancedVI

d = randn(100)
Turing.@model function model()
   x ~ MvNormal(randn(100), 1)
   y ~ InverseGamma()
end
m = model()
q = Turing.Variational.fullrank_gaussian(Random.default_rng(), m)
n_iters = 1000
Turing.Variational.vi(m, q, n_iters)

Closes #2507
Closes #2508

[yebai]

@Red-Portal, can you fix the tests before I take a look?

[Red-Portal]

@yebai I marked the PR as a draft so that we can first agree on an interface, and then I flesh out the implementation and the tests. Do we wish we proceed in another way?

[yebai]

Let's address the interface later or in a separate PR since that might require more discussions. For this PR, let's try to keep the VI interface non-breaking where possible.

[yebai]

@Red-Portal can you take a look at the following error:

ERROR: LoadError: UndefVarError: `turnprogress` not defined in `AdvancedVI`