Student T-Process Regression with Student T-Process Likelihood

[sunshineinsandiego]

Hi - I was looking at the documentation for the TPRegression as well as the paper off of which the implementation is based. A few questions if I may:

• Multi-target TPRs are possible per the docs: "Multiple independent outputs are allowed using columns of Y." So am I correct in interpreting this as targets are modeled as statistically independent T-distributions? In which case the covariance matrix should be diagonal?
• The kernels used in the paper are sums of squared exponential and delta (first experiment in paper) and a Matern and delta (second experiment in paper). The default in GPy.TPR is rbf, but am I correct in assuming that we can select any kernel as an input into GPy.TPR and the inverse wishart prior is used over whichever kernel we use as input?
• Finally, if I'm interested in prediction intervals on multi-target regression outputs, I see that the confidence interval / density intervals are only implemented for single dimensions. This makes sense because there's as of yet no consensus for C.I. estimations in multi-output densities. That said, I should be able to approximate the prediction intervals using the diagonals of the covariance matrix, correct?

Thanks much for your thoughts!