Foward compile_kwargs to ADVI when init = "advi+..."

[jessegrabowski]

Description

See title. Now that we are allowed to pass compile_kwargs to pm.sample, it would be nice if these kwargs were also passed to any subroutines that are called before/after sampling. An obvious example is the call to pm.fit when the user sets init = "advi+something". This PR forwards the compile_kwargs to ADVI.

It also renames fn_kwargs to compile_kwargs in the variational sub-module. This harmonizes the naming convention across the library. A depreciation warning is added when fn_kwargs is used for backwards compatibility.

Related Issue

• Closes Respect compile_kwargs in ADVI when init = 'advi+...' #7638
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

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📚 Documentation preview 📚: https://pymc--7640.org.readthedocs.build/en/7640/

[codecov]

Codecov Report

Attention: Patch coverage is 54.54545% with 10 lines in your changes missing coverage. Please review.

Project coverage is 92.17%. Comparing base (82716fb) to head (ce09972).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
pymc/variational/opvi.py	50.00%	8 Missing ⚠️
pymc/variational/inference.py	66.66%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7640      +/-   ##
==========================================
- Coverage   92.85%   92.17%   -0.68%     
==========================================
  Files         106      106              
  Lines       17771    17765       -6     
==========================================
- Hits        16501    16375     -126     
- Misses       1270     1390     +120     

Files with missing lines	Coverage Δ
pymc/pytensorf.py	90.66% <ø> (+0.09%)	⬆️
pymc/sampling/mcmc.py	86.18% <ø> (ø)
pymc/variational/inference.py	87.12% <66.66%> (-0.82%)	⬇️
pymc/variational/opvi.py	86.83% <50.00%> (-0.60%)	⬇️

... and 3 files with indirect coverage changes