probabilistic matrix factorization

File: https://github.com/pymc-devs/pymc-examples/blob/main/examples/case_studies/probabilistic_matrix_factorization.ipynb
Reviewers: @colcarroll

Known changes needed

Changes listed in this section should all be done at some point in order to get this
notebook to a "Best Practices" state. However, these are probably not enough!
Make sure to thoroughly review the notebook and search for other updates.

General updates

• Use numpy Generator. See also https://numpy.org/doc/stable/reference/random/index.html?highlight=random%20sampling%20numpy%20random#quick-start

Changes for discussion

Changes listed in this section are up for discussion, these are ideas on how to improve
the notebook but may not have a clear implementation, or fix some know issue only partially.

ArviZ related

• Use ArviZ and xarray for postprocessing. This will probably be challenging. I'd recommend familiarizing with xarray before working on that. Some ideas:
  • _norms in code cell 23 looks like it could be replaced by xr.apply_ufunc (using input_core_dims)

Notes

Exotic dependencies

None

Computing requirements

Model samples in roughly 1 hour

Start with examples/case_studies/probabilistic_matrix_factorization.ipynb and review the full notebook, beginning with the requested NumPy Generator update. Inspect code cell 23 and research the suggested ArviZ/xarray postprocessing approach, including xr.apply_ufunc. Done means the notebook reaches a Best Practices state, with the listed updates and any additional issues found during review addressed; model samples take roughly one hour.