Improve factor analysis notebook #612
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erik-werner
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twiecki
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Also add short sampling of amortized model, to show that it works but is slow.
Positive-only works for the particular data we have here, where the latent factors are defined as positive. But it makes it impossible to fit models without this constraint.
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twiecki
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Fixes #587
Updating factor analysis notebook to
Fix some small errors in the mathematical derivations and related code
Spell out some steps in the derivations that were not obvious (to me at least)
Replace the least-squares derivation of$F$ by a Bayesian derivation
Add a section at the end that compares the factors we have identified to the true ones for the synthetic data we have used
Do some minor edits to the text, in particular to fit the text to the updated sampling results
Notebook follows style guide https://docs.pymc.io/en/latest/contributing/jupyter_style.html
PR description contains a link to the relevant issue:
Check the notebook is not excluded from any pre-commit check: https://github.com/pymc-devs/pymc-examples/blob/main/.pre-commit-config.yaml
📚 Documentation preview 📚: https://pymc-examples--612.org.readthedocs.build/en/612/