Beta geo expected probability no purchase

[DylanZammit]

Description

The linked issue below describes the motivation and derivation of the newly introduced method. Only 2 files have been updated:

• pymc_marketing/clv/models/beta_geo.py: Introduction of BetaGeoModel.expected_probability_no_purchase, which implements the derivation in aforementioned document.
• docs/source/notebooks/bg_nbd.ipynb: Includes an example of how to use it with some example customers.

I might require guidance on how to implement unit tests for this new method. Other unit tests for the BetaGeo model seem to compare the output results of similar methods with the ones given by the lifetimes library. However, there is no corresponding functionality for the new proposed method.

Related Issue

• Closes #
• Related to Include probability of 0 purchases in time range (T, T+t] #1093

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

Modules affected

• MMM
• CLV

Type of change

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

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📚 Documentation preview 📚: https://pymc-marketing--1094.org.readthedocs.build/en/1094/

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juanitorduz commented on 2024-10-19T09:20:24Z
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Can you please remove this from the notebook?

DylanZammit commented on 2024-10-19T09:25:43Z
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Removed

[juanitorduz]

I might require guidance on how to implement unit tests for this new method.

Absolutely! Some ideas for this new method are:

• Test that the method does not fail by simply calling it on a fitted model as in

  pymc-marketing/tests/clv/models/test_beta_geo.py

  Line 260 in e46f690

  def test_expected_num_purchases(self):

• Predict this on a user (or set of users) where this probability should be very high (close to one) and very low (close to zero)

[DylanZammit]

Removed

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[DylanZammit]

I might require guidance on how to implement unit tests for this new method.

Absolutely! Some ideas for this new method are:

• Test that the method does not fail by simply calling it on a fitted model as in

  pymc-marketing/tests/clv/models/test_beta_geo.py

  Line 260 in e46f690

  def test_expected_num_purchases(self):

• Predict this on a user (or set of users) where this probability should be very high (close to one) and very low (close to zero)

Thank you! I will try to work on this between today and tomorrow.

I have removed the redundant cell-block in the notebook and made reference to Equation 34 which I based the method off in the docstring of the new method. Appreciate the help and feedback, please let me know if there are any other suggested changes and I will review accordingly.

[DylanZammit]

@juanitorduz @ColtAllen

Following unit tests added:

• assertion on expected output layout
• frequent customers with large t should have probability of no purchases close to 0
• infrequent customers with small t should have probability of no purchases close to 1
• If t = 0, then the probability of no purchases should be 1

All tests passed.

[ColtAllen]

Thanks for creating this PR @DylanZammit. I noticed the expression in the research note includes the model likelihood function, but it seems here you've simplified things and removed terms that would otherwise cancel out. If results are valid this will be a more performant solution, well done.

Aside from renaming the function and a few minor details in the notebook and docstrings, I don't have any major remarks.

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ColtAllen commented on 2024-10-21T12:55:05Z
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Suppress this warning so that it does not appear in the documentation

ColtAllen commented on 2024-10-24T10:45:40Z
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Re-running the cell should clear it.

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ColtAllen commented on 2024-10-21T12:55:05Z
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See PR review notes about renaming this method. If you're curious how this method is demonstrated with ParetoNBDModel:

https://www.pymc-marketing.io/en/stable/notebooks/clv/pareto_nbd.html#probability-of-n-purchases-over-time-t

[juanitorduz]

@DylanZammit I think this one is very close to the finish line. I think there are a couple of open comments from Colt, and then we are good to go. Please let us know if you need support :)

[ColtAllen]

Re-running the cell should clear it.

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[ColtAllen]

@DylanZammit I think this one is very close to the finish line. I think there are a couple of open comments from Colt, and then we are good to go. Please let us know if you need support :)

I saw two typos in the notebook ("ot keep" and "deposits" instead of "spending"), but ReviewNB isn't allowing me to post any more comments for some reason. I'm also curious about that DIV/0 warning with the MAP fit, and noticed an older version of pytensor in the watermark.

[DylanZammit]

Made all suggested changes:

• typos
• pytensor version (reinstalled the conda environment using the same command conda env create -f environment.yml)
• remove docstring reference of special case when y=0
• re-ran the cell that gave a warning (which removes the warning).

I have still not investigated the DIV/0 error, however, I suspect it is due to numerical issues. Please let me know if you have any further suggestions.

[ColtAllen]

I have still not investigated the DIV/0 error, however, I suspect it is due to numerical issues. Please let me know if you have any further suggestions.

I'm not able to re-create the error on my 2023 M2 Macbook with identical pymc and pytensor versions; maybe it's a C++ compiler difference between your OS and mine. Anywho, if you add this cell to the top of the notebook and run it, then delete it before pushing, it'll hide all the warnings:

import warnings 
  
# Set warnings to be ignored 
warnings.filterwarnings('ignore')

[codecov]

Codecov Report

Attention: Patch coverage is 96.00000% with 1 line in your changes missing coverage. Please review.

Project coverage is 95.61%. Comparing base (e8a4e3b) to head (e3751a7).
Report is 121 commits behind head on main.

Files with missing lines	Patch %	Lines
pymc_marketing/clv/models/beta_geo.py	96.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1094   +/-   ##
=======================================
  Coverage   95.61%   95.61%           
=======================================
  Files          39       39           
  Lines        4039     4063   +24     
=======================================
+ Hits         3862     3885   +23     
- Misses        177      178    +1     

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[ColtAllen]

Good work on the notebook and augmenting existing research with a more performant function derivation! If you ever want to link your PDF to the docstring references feel free to open another PR.