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If I have a regression problem where I try to estimate the value of $y$ as function of $x_1 \dots x_d$: $$ y = f(x_1,\dots,x_d) $$

using a Boosted Regression Tree or a Random Forest Regression, is it possible to estimate the probability distribution of the output value (instead of only an estimate of $y$) :

$$ p(y\ |\ x_1,\dots,x_d) $$

from the distribution of the outputs of the individual nodes ? (i.e. for fixed $x_1,\dots,x_d$ I'm interested in having a probability distribution for $y$ from which one then could obtain the mode, mean and also the width which is an indication of 'how well' this value is predicted).

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Yes, see, for example:

Meinshausen, Nicolai. "Quantile regression forests." The Journal of Machine Learning Research 7 (2006): 983-999.

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    $\begingroup$ Welcome to the site, @AJC. Would you mind expanding on your answer a little? EG, it would help readers if you could give readers a couple sentence overview of the paper & the answer contained therein. $\endgroup$ Mar 16, 2013 at 21:38

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