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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).

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    $\begingroup$ 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 $X$). $\endgroup$ – Momo Mar 14 '14 at 9:26
  • $\begingroup$ 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? $\endgroup$ – Daniel Mar 14 '14 at 10:35

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