Solved by KFrank in post #3 
              
              
                Hello Zhenhua! 

Let me tell you how I understand your question. 
I don’t see the use case you describe as being a multi-label, 
multi-class problem.  I guess I would call it something like 
“multiple multi-class.” 
That is (and to make things simpler, let me speak of just y_1 
and y_2), let’s say y…