Deprecate remaining VI methods

[purna135]

Addressing #5581

[purna135]

Hi @ferrine. Sorry about my previous PR; I believe I made a mistake when resolving merge conflicts and accidentally deleted that branch.

I deleted several flow-related tests and refactored others, but there are still 10 tests that I am unable to refactor and have commented so that other tests can be checked. Could you please assist me in refactoring the tests I commented?
Many thanks

[ferrine]

I've left a lot of comments, the PR is still in a draft state. I hope that helps

[codecov]

Codecov Report

Merging #5806 (b0ef97c) into main (4d2f3a8) will increase coverage by 0.50%.
The diff coverage is 86.36%.

@@            Coverage Diff             @@
##             main    #5806      +/-   ##
==========================================
+ Coverage   89.39%   89.89%   +0.50%     
==========================================
  Files          74       73       -1     
  Lines       13767    13198     -569     
==========================================
- Hits        12307    11865     -442     
+ Misses       1460     1333     -127     

Impacted Files	Coverage Δ
pymc/variational/__init__.py	100.00% <ø> (ø)
pymc/variational/approximations.py	86.51% <62.50%> (+20.44%)	⬆️
pymc/variational/inference.py	85.78% <100.00%> (-1.46%)	⬇️
pymc/variational/opvi.py	87.01% <100.00%> (+4.57%)	⬆️
pymc/sampling.py	82.52% <0.00%> (-6.19%)	⬇️
pymc/distributions/mixture.py	95.72% <0.00%> (-1.04%)	⬇️
pymc/parallel_sampling.py	86.46% <0.00%> (-1.00%)	⬇️
... and 7 more

[purna135]

Hello, @ferrine Thank you for your feedback; I worked on it and am finally finished with it.
I have some question for which I require your assistance.

1. Replacing NormalizingFlowGroup with MeanFieldGroup.
2. Removing NotImplementedInference

I commented them out in the code above please have a look and also please let me know if I missed anything in the docstring.

Thank you : )

[ferrine]

I'll be on these issues in a day or two with a close look

[ferrine]

The last test refactoring is required to go ahead. I've proposed a snippet to resolve the failing test

[purna135]

Sure @ferrine, Thank you.
let me do one more commit with these changes

[twiecki]

@purna135 want to join our dev sprint? https://discord.gg/Hpne6mtJ

[purna135]

Joining in few min, Thank you

[ferrine]

I've created an issue to fix deterministic sampling for Empirical approx (#5837 )

[ferrine]

lgtm

[purna135]

Thnak you so much @ferrine and @twiecki 😊

[twiecki]

Congrats on your first PR @purna135 -- thanks for your help!