Decision tree functions are discontinuous functions of the predictors. Have continuous decision trees with smooth transitions been studied? For example, a decision tree in two variables

f(x1,x2) = c1 if x1 <  t1 and x2 <  t2
           c2 if x1 <  t1 and x2 >= t2
           c3 if x1 >= t1 and x2 <  t3
           c4 if x1 >= t1 and x2 >= t3

could be replaced by

    f(x1,x2) = c1*lg(t1-x1)*lg(t2-x2) + c2*lg(t1-x1)*lg(x2-t2) + 
               c3*lg(x1-t1)*lg(t3-x2) + c4*lg(x1-t1)*lg(x2-t3)

where lg is the logistic function.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.