Multi MMM does not work with time_varying_intercept_ and custom priors

[juanitorduz]

I was trying to run the example notebook from #1521 with

model_config = {
    "intercept": Prior("Normal", mu=0.5, sigma=0.2, dims="geo"),
    "gamma_control": Prior("Normal", mu=0, sigma=0.03, dims="control"),
    "gamma_fourier": Prior("Laplace", mu=0, b=0.2, dims=("geo", "fourier_mode")),
    'intercept_tvp_config': HSGPKwargs(m=200, L=None, eta_lam=1, ls_mu=5, ls_sigma=5),
    "likelihood": Prior(
        "TruncatedNormal",
        lower=0,
        sigma=Prior("HalfNormal", sigma=Prior("HalfNormal", sigma=1)),
        dims=("date", "geo"),
    ),
}

and I get the error at build time

File ~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1109, in MMM.build_model(self, X, y, **kwargs)
   [1104](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1104) if self.time_varying_intercept:
   [1105](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1105)     baseline_intercept = self.model_config["intercept"].create_variable(
   [1106](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1106)         "baseline_intercept"
   [1107](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1107)     )
-> [1109](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1109)     intercept_latent_process = SoftPlusHSGP.parameterize_from_data(
   [1110](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1110)         X=time_index,  # this is
   [1111](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1111)         dims=("date", *self.dims),
   [1112](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1112)         **self.model_config["intercept_tvp_config"],
   [1113](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1113)     ).create_variable("intercept_latent_process")
   [1115](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1115)     intercept = pm.Deterministic(
   [1116](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1116)         name="intercept_contribution",
   [1117](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1117)         var=baseline_intercept[None, ...] * intercept_latent_process,
   [1118](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1118)         dims=("date", *self.dims),
   [1119](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1119)     )
   [1120](https://file+.vscode-resource.vscode-cdn.net/Users/juanitorduz/Documents/pymc-marketing/docs/source/notebooks/mmm/~/Documents/pymc-marketing/pymc_marketing/mmm/multidimensional.py:1120) else:

TypeError: pymc_marketing.mmm.hsgp.HSGP.parameterize_from_data() argument after ** must be a mapping, not HSGPKwargs

I think the issue is we are not not expecting HSGPKwargs anywhere as the default config has 'intercept_tvp_config': {'ls_lower': 0.3, 'ls_upper': 2.0},, which is passed to

pymc-marketing/pymc_marketing/mmm/multidimensional.py

Lines 1109 to 1113 in 06d1a34

	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")

However, we are parsing the model_config at the init stage:

pymc-marketing/pymc_marketing/mmm/multidimensional.py

Lines 297 to 300 in 06d1a34

	model_config = parse_model_config(
	model_config, # type: ignore
	hsgp_kwargs_fields=["intercept_tvp_config", "media_tvp_config"],
	)

[juanitorduz]

@williambdean Regarding the design, how do you view the integration between SoftPlusHSGP (and other HSGP) and HSGPKwargs?

[williambdean]

It might not accept that at the moment. Are we expecting to use the HSGPKwargs in the new MMMM class? CC: @cetagostini

I think the HSGPKwargs should be removed completely and work toward just passing a HSGP class itself (HSGP, SoftPlusHSGP, HSGPPeriodic). See #1432. But not there yet.

This would allow for the different parameter requirements for the classes to be handled within the class itself. It is more flexible with the cost that it becomes a bit more verbose to pass.

Maybe we can explore a different interface that makes use of the mu_effects

mmm = MMM(..., # no hsgp information here)
hsgp = HSGP.parameterize_from_data(...)
mmm.add_intercept(hsgp)

Bit of a chicken or egg for both of these solutions since the HSGP requires data (register_data method) would be called within the MMM class.

What are your thoughts?

[juanitorduz]

I agree with removing the HSHPKwargs! Please let me know if you want some support or if there is any way I could help!

[gdeleva]

Thank you for this great library.

I understand that we cannot define a custom prior, but would the default prior be a time varying intercept equal across all geographical regions?