Add Multiple types of trend in MMM

[thipokKub]

Current trend implementation only support linear trend. It would be nice to add more variation to this

• Other simple trend regression such as
  • Linear
  • Logarithmic
  • Exponential
  • Power
  • Polynomial
• From MBrouns/timeseers, he showed how to implement prophet-like trend using piece-wise linear trend from Lapacian prior (see his presentation video)
• Orbit/KTR use spline regression to model time-varying coefficient. It might be possible to model trend like this too (see implementation Add uber/orbit like model in pymc example #250)
• From MMM Example Notebook: Time Varying Coefficients #43, it is mentioned that hierarchical gaussian process can be used (I haven't looked into this yet). But I haven't found a working example yet

[juanitorduz]

Thanks! In principle, you could add these trends as "control features". From the notebook:

df["trend"] = (np.linspace(start=0.0, stop=50, num=n) + 10) ** (1 / 4) - 1

[thipokKub]

Hello! Thanks for the reply

To use df['trend'] as a control feature, we have to transform it beforehand (not learnable). It might be more desirable to learn it from data

It will be nicer if the model can let other trend mode to be select. Something like

DelayedSaturatedMMM(..., trend_mode="power", trend_kargs={...})

What do you think?

Also I think I have implemented Hierarchical Gaussian Process. But I'm not sure it is correct as the performance is not consistent. But at least I think it should be possible to add (normal) gaussian process as an option

[wd60622]

Hi @thipokKub,

The TVP implementation now used has a hierarchical option or could be extended pretty easily I believe. We the #632 change, there are now some smaller media components that can be used for custom models. There are still some missing abstractions but I am working toward highlighting them a bit in #748 to start addressing #711. I will be addressing #679
soon. I also have an issue to create smaller wrapper around the current TVP (#751)

If you have any thoughts, let us know!