Higher dimensional outputs

[jbrea]

This came up on discourse.

[chris-nemeth]

How difficult would it be to extend the package to multi-dimensional output? I haven't looked at this before, but my first guess would be that other packages that do this are probably vectorising the output matrix.

[maximerischard]

I don't think it's that trivial. One needs to specify the covariance between the different outputs. It's also not good to assume that all of the outputs are observed at each location (imagine for example looking at measurements of different pollutants, if they are not obtained from the same sensors). Alvarez 2012 seems to be a decent introduction to the things that need to be thought about.

Alvarez, Mauricio A., Lorenzo Rosasco, and Neil D. Lawrence. "Kernels for vector-valued functions: A review." Foundations and Trends® in Machine Learning 4, no. 3 (2012): 195-266.