Modifying cartesian product to allow for >2D input arrays

[ckrapu]

Currently, using the implementation of MarginalKron for structured Gaussian processes is limited by an inability to initialize the GP for input arrays for the Kronecker product which have more than 1 dimension. For example, creating a Kronecker GP with a 2D spatial covariance kernel added to a 1D temporal covariance kernel is not possible while adding a 1D spatial to a 1D temporal kernel is possible. This issue limits the utility of the Kronecker GP from being used in arguably its most suitable use case (independent space/time covariance kernels). To recreate this issue, see this gist.

The main change to the function cartesian is to first create a cartesian product of integer vectors, and then use these to index into the input arrays instead.

[ckrapu]

I didn't run the tests locally here - I'll edit and fix as appropriate so that it passes.

[bwengals]

I checked out the branch and tried the gist, it works great.

arguably its most suitable use case

Definitely agree.

Maybe a test of the new functionality with a 2D X input could be added, or existing test modified?

[ckrapu]

Thanks for taking a look at this! I just added a new test which covers the usage of a 2D input as well as a 1D length-1 input.

[bwengals]

I would think that assert_array_equal is sufficient here (no almost). I noticed the other test_cartesian does this so they should both be fixed

[ckrapu]

Good point - those assertions have been changed.

[michaelosthege]

LGTM

From your example gist my understanding is that the function you changed plays a role for the kron_Xs in the marginal likelihood?

[michaelosthege]

Ah sorry one more thing: Please add a line to the release notes.

[ckrapu]

Thanks for adding the release note!

LGTM

From your example gist my understanding is that the function you changed plays a role for the kron_Xs in the marginal likelihood?

Yes, it turns out that most of the functionality in the marginal likelihood bit was working fine - the only change was in how the input coordinates are preprocessed via pm.math.cartesian from a short array of per-axis grid coordinates to a tall array of points.