Non-scalar ls in HSGP / HSGPPeriodic

[wd60622]

I would like to be able to use vector (including hierarchical) ls for these two classes.

It would look like this:

from pymc_marketing.prior import Prior
from pymc_marketing.mmm import HSGP

ls = Prior("HalfNormal", dims="channel")
hsgp = HSGP(ls=ls, ..., dims=("date", "channel"))

The dims would have to be handled here:

pymc-marketing/pymc_marketing/mmm/hsgp.py

Lines 720 to 730 in 181b348

	cov_func = eta**2 * cov_funcs[self.cov_func.lower()](input_dim=1, ls=ls)
	gp = pm.gp.HSGP(
	m=[self.m],
	L=[self.L],
	cov_func=cov_func,
	drop_first=self.drop_first,
	)
	phi, sqrt_psd = gp.prior_linearized(
	self.X[:, None] - self.X_mid,
	)

[wd60622]

Have you done this logic @bwengals ?
I tried and see that that the shapes out of prior_linearized need a bit of handling

[juanitorduz]

This would be great! I think we would need to make sure the spectral density expressions vecorize over ls?

Actually, it seems the spectral density functions do handle vector length scales:

https://github.com/pymc-devs/pymc/blob/5d51953df0168fce4029675575f7002db71e4347/pymc/gp/cov.py#L574-L587

[wd60622]

This would be great! I think we would need to make sure the spectral density expressions vecorize over ls?

Actually, it seems the spectral density functions do handle vector length scales:

https://github.com/pymc-devs/pymc/blob/5d51953df0168fce4029675575f7002db71e4347/pymc/gp/cov.py#L574-L587

Yes, think we just need the dims to broadcast correctly. But i tried out and there needs a little thought behind the following operations with psd, etc

[bwengals]

@juanitorduz they do handle vector lengthscales, but in terms of input dimension. For example, a spatial GP with a different lengthscale for the x and the y directions. It'd be really nice if they could handle both input dimension and the case below (vectorized, multi-dimensional inputs), but I had no idea how to do that.

There are examples here of using a vector of lengthscales for the case where you have multiple GPs each with a different lengthscale that you're implementing in a vectorized way. I'm purposefully saying they're multiple GP's because if the lengthscales are different then the kernels are different, and that's what differentiates one GP from another. I'd bet for most hierarchical GPs they'd share the same lengthscale parameter.

Which of these two cases are you trying to implement?

[juanitorduz]

Thanks @bwengals for the clarification. I think for MMMs you are right, all lengths scales would be similar. I think the main ingredients are in the HSGP advanced example you shared (which should be a similar strategy as in https://www.pymc-labs.com/blog-posts/modelling-changes-marketing-effectiveness-over-time/ I believe)