Use SoftPlusHSGP in multidimensional HSGP

[wd60622]

Description

This might still differ from the other implementation where the HSGP intercept has a baseline which is then multiplied by HSGP:

pymc-marketing/pymc_marketing/mmm/mmm.py

Lines 482 to 498 in 89c9e97

	baseline_intercept = self.model_config["intercept"].create_variable(
	"baseline_intercept"
	)
	intercept_latent_process = create_time_varying_gp_multiplier(
	name="intercept",
	dims="date",
	time_index=time_index,
	time_index_mid=self._time_index_mid,
	time_resolution=self._time_resolution,
	hsgp_kwargs=self.model_config["intercept_tvp_config"],
	)
	intercept = pm.Deterministic(
	name="intercept",
	var=baseline_intercept * intercept_latent_process,
	dims="date",
	)

Another alternative is to build that part into the HSGP model itself. However, the mmm would require another prior for the intercept. Which I think is good to keep separate. We can always wrap that logic into a separate function like in MuEffect

pymc-marketing/pymc_marketing/mmm/multidimensional.py

Lines 58 to 68 in 89c9e97

	class MuEffect(Protocol):
	"""Protocol for arbitrary additive mu effect."""
	def create_data(self, mmm: MMM) -> None:
	"""Create the required data in the model."""
	def create_effect(self, mmm: MMM) -> pt.TensorVariable:
	"""Create the additive effect in the model."""
	def set_data(self, mmm: MMM, model: pm.Model, X: xr.Dataset) -> None:
	"""Set the data for new predictions."""

Thoughts?

Related Issue

• Closes #
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass. Feel free to comment pre-commit.ci autofix to auto-fix.
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks) using numpydoc format.
• If you are a pro: each commit corresponds to a relevant logical change

---

📚 Documentation preview 📚: https://pymc-marketing--1510.org.readthedocs.build/en/1510/

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.75%. Comparing base (26e80c0) to head (b9bbcd4).
Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1510   +/-   ##
=======================================
  Coverage   92.74%   92.75%           
=======================================
  Files          52       52           
  Lines        6120     6126    +6     
=======================================
+ Hits         5676     5682    +6     
  Misses        444      444           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[juanitorduz]

@wd60622 can you please explain the motivation behind the softplus transform? 🙏

[wd60622]

• Aligns the default hsgp with other MMM class
• remove negative channel contributions with time varying media = True

[juanitorduz]

Thanks @wd60622 ! Would you mind running the time-varying parameter notebooks affected by this change just to control the expected result? 🙏

[wd60622]

Is there a multidimensional mmm notebook already? This is just the new class

[juanitorduz]

Right, but in theory you could reproduce the results of the MMM basic class with this object right? The intention is not to update the docs but maybe have some experiments on the effect of this parametrization. I think you can just share some plots or experiments 9for the sake of illustrating the benefits) :) Just for future reference. It is not a blocker, but more to have a bit more intuition WDYT?

[wd60622]

Sure. I can update
However, there is still slight difference in the intercept which I noted. Should that be consolidated?

Thoughts @cetagostini

[wd60622]

I will make sure that the baseline is in. I think without it might be too inflexible.

[wd60622]

This is an adapted version of the other MMM intercept:

import pandas as pd
import pymc as pm

import matplotlib.pyplot as plt

from pymc_marketing.mmm import SoftPlusHSGP

n_dates = 52 * 2

dates = pd.date_range("2025-01-01", periods=n_dates, freq="W-MON")

X = (dates - dates[0]).days.values

hsgp = SoftPlusHSGP.parameterize_from_data(X, ls_lower=10, ls_upper=25, dims="date")

coords = {"date": dates}
with pm.Model(coords=coords) as model:
    name = "intercept"
    intercept_baseline = pm.Gamma(f"{name}_baseline", mu=3, sigma=1)
    intercept_moving = hsgp.create_variable(f"{name}_multiplier")

    intercept = pm.Deterministic(
        name,
        intercept_baseline * intercept_moving,
        dims=hsgp.dims,
    )

    idata = pm.sample_prior_predictive()


prior = idata.prior

from pymc_marketing.plot import plot_curve

prior["intercept"].pipe(plot_curve, {"date"})
plt.show()

Results in:

Note

Without the baseline, the intercept is just centered around 1.

[juanitorduz]

Thanks for the example @wd60622 !

[wd60622]

Realizing that the current implementation does that have baseline and multiplier concept

pymc-marketing/pymc_marketing/mmm/multidimensional.py

Lines 1030 to 1044 in b9bbcd4

	baseline_intercept = self.model_config["intercept"].create_variable(
	"baseline_intercept"
	)
	intercept_latent_process = SoftPlusHSGP.parameterize_from_data(
	X=time_index, # this is
	dims=("date", *self.dims),
	**self.model_config["intercept_tvp_config"],
	).create_variable("intercept_latent_process")
	intercept = pm.Deterministic(
	name="intercept_contribution",
	var=baseline_intercept[None, ...] * intercept_latent_process,
	dims=("date", *self.dims),
	)

So merging this now!