I have a multi-output regression problem with $d_x$ input features and $d_y$ outputs. The outputs have a complex, non-linear correlation structure.
I'd like to use random forests to do the regression. As far as I can tell, random forests for regression only work with a single output, so I would have to train $d_y$ random forests - one for each output. This ignores their correlations.
Is there an extension to random forests that takes output correlations into account? Maybe something like Gaussian process regression for multi-task learning.