# Probablistic counterpart for decision trees

We know if Gaussian Mixture Model is a probablistic counterpart of k-means algorithm. Is there a probablistic counterpart for decision-trees?

UPDATE: I know that branching in DT can be probablistic. But what I meant, is the way we create separated regions in the input space by each branching (as apposed to soft clustering of the input space).

• Please explain more what you aim at in this question. Decision trees are probabilistic (they estimate some function of the conditional distribution of $Y$ given $X$). – Momo Mar 14 '14 at 9:26
• Yes, correct. Branching can be probablistic. But what I meant, is the way we create separated regions in the input space by each branching (as apposed to soft clustering of the input space). Does this make sense? – Daniel Mar 14 '14 at 10:35