New ADVI API

[jessegrabowski]

This PR moves the work from pymc-devs/pymc#7799 over here to extras. The key idea is to copy the numpyro guide model API, but with our own PyMC flair.

I also added:

• stick the landing estimator
• forward sampling helper
• LLM sketch for a training API patterned after pytorch-lightning

I updated the notebook to use the proposed training API. It obviously needs a lot of work (being that it's llm trash) but hopefully it can get some ideas flowing.

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Codecov Report

❌ Patch coverage is 28.57143% with 160 lines in your changes missing coverage. Please review.
✅ Project coverage is 48.54%. Comparing base (12a18c2) to head (bfdb98b).

Files with missing lines	Patch %	Lines
pymc_extras/inference/advi/training.py	0.00%	140 Missing ⚠️
pymc_extras/inference/advi/objective.py	0.00%	13 Missing ⚠️
pymc_extras/inference/advi/pytensorf.py	75.00%	7 Missing ⚠️

❌ Your patch status has failed because the patch coverage (28.57%) is below the target coverage (50.00%). You can increase the patch coverage or adjust the target coverage.

Additional details and impacted files

@@             Coverage Diff             @@
##             main     #635       +/-   ##
===========================================
+ Coverage   32.93%   48.54%   +15.60%     
===========================================
  Files          69       73        +4     
  Lines        7555     7779      +224     
===========================================
+ Hits         2488     3776     +1288     
+ Misses       5067     4003     -1064     

Files with missing lines	Coverage Δ
pymc_extras/inference/advi/autoguide.py	100.00% <100.00%> (ø)
pymc_extras/inference/advi/pytensorf.py	75.00% <75.00%> (ø)
pymc_extras/inference/advi/objective.py	0.00% <0.00%> (ø)
pymc_extras/inference/advi/training.py	0.00% <0.00%> (ø)

... and 14 files with indirect coverage changes

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