Multi-output GPQR
=================

:math:`y = f(X)` where the dimension of :math:`y` is greater than 1.

Default quantile regression with 1-D :math:`y` is already multi-task, as it models multiple quantiles levels.
Multi-output quantile regression expands this, modeling multiple quantiles of multiple outputs at the same time.

Placing prior mean is difficult for direct GPQR because latents GPs are mixed to form different outputs.
On the other hand, center-gap GPQR more easily supports placing prior means because central quantiles can be decorrelated from each other.

It is, of course, possible to correlate central quantiles with each other or even further, with gap quantiles.
This can be done by using different LMC variational strategies.
The disadvantage is that placing prior mean becomes difficult again.

.. toctree::
   :maxdepth: 1

   mtgpqr.ipynb
   mtgpqr_cg.ipynb
   mtgpqr_cg_correlated_centrals.ipynb