saving with media transformation config

[wd60622]

MMM with adstock and saturation configurations can potentially not be saved correctly since the additional kwargs are not saved off.

Having these classes serializable and taking advantage of them in save and load methods would be a good idea.

For instance, a model that would not be able to be loaded correctly would be:

from pymc_marketing.mmm import MMM, GeometricAdstock, LogisticSaturation

mmm = MMM(
    ..., 
    adstock=GeometricAdstock(l_max=4, normalize=False, mode="Before"), 
    saturation=LogisticSaturation(),
    ..., 
)

This is because both the normalize and mode are not saved off.

This would involve reconstructing the adstock and saturation upon loading here:

pymc-marketing/pymc_marketing/mmm/delayed_saturated_mmm.py

Lines 637 to 659 in 2be2664

	model = cls(
	date_column=json.loads(idata.attrs["date_column"]),
	control_columns=json.loads(idata.attrs["control_columns"]),
	# Media Transformations
	channel_columns=json.loads(idata.attrs["channel_columns"]),
	adstock_max_lag=json.loads(idata.attrs["adstock_max_lag"]),
	adstock=json.loads(idata.attrs.get("adstock", "geometric")),
	saturation=json.loads(idata.attrs.get("saturation", "logistic")),
	adstock_first=json.loads(idata.attrs.get("adstock_first", True)),
	# Seasonality
	yearly_seasonality=json.loads(idata.attrs["yearly_seasonality"]),
	# TVP
	time_varying_intercept=json.loads(
	idata.attrs.get("time_varying_intercept", False)
	),
	time_varying_media=json.loads(
	idata.attrs.get("time_varying_media", False)
	),
	# Configurations
	validate_data=json.loads(idata.attrs["validate_data"]),
	model_config=model_config,
	sampler_config=json.loads(idata.attrs["sampler_config"]),
	)

[wd60622]

Think that this is rather important but the version of the model will likely have to be updated. Making the previous version not able to be reloaded.
Have any thoughts on this @juanitorduz ?

[wd60622]

There might be a benefit of having a to_json and from_json on the classes directly

[juanitorduz]

Yes! Even though we "break" some model versions, we should fix this so that we can recover the complete (and consistent!) model.