Suppose, i have a dataset $X$ and two binary labels $y_{1}$ and $y_{2}$. The classes are very inbalanced - 3% of true in $y_{1}$  and 2% in $y_{2}$ And there are no pairs of (0,1), so, if the  $y_{1} = 0$, then  $y_{2}=0$.I have a choise between:Associating the labels with each other, so it's a 3-class classification problemBuild a model for  $y_{1}$ scoring, then joining to $X$ and making scoring of  $y_{2}$, using $X$ and  $y_{1}$.So the first idea is formalised as :$$ y_{f} = y_{1} \bullet y_{2}; \,\,\,\, y_{f} = \{(1,1),(0,0),(1,0) \}; \,\,\, y_{f} = \Phi_{f}(X)$$And the second road my be formalised like this:$$ y_{1} = \Phi_{1}(X); \,\,\, \, \, X=X\cup y_{1};  \,\,\,\, y_{2}=\Phi_{2}(X) $$ Taking into account all condition, what is the possible theoretical background of projecting the best algorithm?  I'am trying to give estimates to an error, which is :bias + variance + noise. E.g.:For both: $\Phi_{f}$ and $\Phi_{2}$, which are RandomForests, bias and noise will be the same, variance will be higher for  $\Phi_{f}$(just intuition till now). Can somebody point me the right way?
Theoretical background for model arhitecture choosing
predictive modeling;prediction;error handling