Add start_sigma to ADVI

[markusschmaus]

Introduces the start_sigma argument which allows to set a starting value for the sigmas of mean field approximation in ADVI. I am using the ordering property to create the mapping between the variables and the flat 1d array required by ADVI.

See also:
https://discourse.pymc.io/t/quality-of-life-improvements-to-advi/10254

Checklist

• Explain important implementation details 👆
• Make sure that the pre-commit linting/style checks pass.
• Link relevant issues (preferably in nice commit messages)
• Are the changes covered by tests and docstrings?
• Fill out the short summary sections 👇

Major / Breaking Changes

• None

Bugfixes / New features

• Allow start_sigma being given to fit.
• For ASVGD forward the key word arguments start and random_seed to the constructor of the default approximation FullRank instead of sending them to super().__init__ which can't process them
• Enable _iterate_with_loss to run with n=0 by giving an appropriate logger message. This allows to check initialization values, which is useful for testing, but could also be useful for debugging a user model

Docs / Maintenance

• The documentation for the start argument was outdated, it claimed type Point, but it gets passed through to a function that requires StartDict. Since users are probably unfamiliar with this custom type (Dict[Union[Variable, str], Union[np.ndarray, Variable, str]]), I decided to also mention the most relevant and most commonly used subtype dict[str, np.ndarray].

[codecov]

Codecov Report

Merging #6096 (9a894ce) into main (c858f0f) will increase coverage by 3.10%.
The diff coverage is 47.05%.

@@            Coverage Diff             @@
##             main    #6096      +/-   ##
==========================================
+ Coverage   87.29%   90.39%   +3.10%     
==========================================
  Files          72       86      +14     
  Lines       12927    17873    +4946     
==========================================
+ Hits        11284    16157    +4873     
- Misses       1643     1716      +73     

Impacted Files	Coverage Δ
pymc/variational/inference.py	50.77% <37.50%> (-0.56%)	⬇️
pymc/variational/approximations.py	54.79% <55.55%> (-0.61%)	⬇️
pymc/distributions/shape_utils.py	98.43% <0.00%> (-0.84%)	⬇️
pymc/printing.py	86.08% <0.00%> (-0.58%)	⬇️
pymc/distributions/censored.py	92.50% <0.00%> (-0.53%)	⬇️
pymc/distributions/logprob.py	97.31% <0.00%> (-0.42%)	⬇️
pymc/distributions/mixture.py	95.40% <0.00%> (-0.32%)	⬇️
pymc/sampling.py	82.13% <0.00%> (-0.02%)	⬇️
pymc/distributions/__init__.py	100.00% <0.00%> (ø)
pymc/distributions/continuous.py	97.51% <0.00%> (ø)
... and 20 more

[junpenglao]

Hi @markusschmaus sorry we need to revert this because there is a test failing - could you send in the PR again?

[markusschmaus]

@junpenglao
Sorry for missing the failing test. This was caused by me fixing a "bug" which turned out not to be a bug after all.

Here is the new PR:
#6132