Update variational inference interface to match AdvancedVI@0.6

[Red-Portal]

This PR does the following:

• The interface to AdvancedVI is updated to match the new v0.6 version.
• The way vi calls optimize is slightly changed so that algorithms that expect an unconstrained space can be used without being aware of Bijectors. In particular, the user is now expected to provide a q <: Bijectors.TransformedDistribution. vi will then unwrap the underlying unconstrained distribution, which is passed to AdvancedVI. Once the algorithm terminates, the result will be wrapped back and then returned. (See also this PR for a more detailed explanation.)
• The main file is renamed from VariationalInference.jl to Variational.jl to match the submodule name Variational.
• The deprecated v0.2-era interface is removed.

[github-actions]

Turing.jl documentation for PR #2699 is available at:
https://TuringLang.github.io/Turing.jl/previews/PR2699/

[codecov]

Codecov Report

❌ Patch coverage is 88.46154% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 87.49%. Comparing base (ea9bb54) to head (a319962).

Files with missing lines	Patch %	Lines
src/variational/Variational.jl	88.46%	3 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##           breaking    #2699      +/-   ##
============================================
+ Coverage     86.54%   87.49%   +0.94%     
============================================
  Files            21       20       -1     
  Lines          1412     1415       +3     
============================================
+ Hits           1222     1238      +16     
+ Misses          190      177      -13     

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[mhauru]

Thanks @Red-Portal.

Since this changes the user-interface, could you please set the target branch of this PR to be breaking? We use that branch to collect breaking changes into a single, larger release. Currently breaking points at the same commit as main, so you shouldn't have to mess with git history for this.

In that same process, could you also please add an entry in HISTORY.md describing to users all interface changes (arguments, return values, behaviour) and what they can do to adapt to them. Maybe a code example of "this is how you used to call vi, this is how you do the same thing now", that sort of thing.

[penelopeysm]

I'm actually sorry to butt in on this, but are there new features available in 0.5, or is it just an interface change?

[Red-Portal]

@penelopeysm No new features.

[penelopeysm]

Okay. The reason why I asked is because this is an interface change for Turing and that is kind of annoying for end users if they don't get any benefit. I wonder in that case if it is worth doing either:

1. Not bumping the compat in Turing, waiting for the next release of AdvancedVI that has new features; or

2. Mapping the existing Turing interface to the new AdvancedVI interface, so that it's not a breaking change. I don't know how possible this is.

Other than that, I second everything that @mhauru brought up here, so I won't also review the details of this.

[Red-Portal]

Hi @penelopeysm @mhauru @yebai , I've updated the code to match the new v0.6 version. Let me know if you have any comments!