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I'm wondering if there are any implementations of random forests that allow one to provide error terms for the inputs.

An error term could be based on a per-variable basis, or on a per-sample/variable basis.

If an error term was specified on a per variable basis, we would let the random forest algorithm know that "this variable $A$ has a sampling error of $\pm 5\%$, whereas this variable $B$ has a sampling error of $\pm 10\%$".

If an error term was specified on a per sample/variable basis, we would specify the error terms on all individual samples. We would let the random forest know that "for sample 1, variable $A$ has a sampling error of $\pm 5\%$, and variable B has a sampling error of $\pm 8\%$, whereas sample 2, variable $A$ has a sampling error of $\pm 6\%$ and variable $B$ has a sampling error of $\pm 12\%$".

I am particularly interested in implementations in R, C++, C# or Python.

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  • $\begingroup$ @Glen_b Thanks for the edit, it looks much cleaner now. $\endgroup$ – Contango Sep 7 '14 at 11:00
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You may replace each training example ($x$, $\sigma(x)$, y) with a set of training examples (or just one training example) distributed as $N(x, \sigma(x))\rho(x)$, where $\rho(x)$ is the prior distribution of $x$.

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  • $\begingroup$ Brilliant answer. I'm wondering if its possible to deal with variables that might have some known correlation? I'm assuming that you would randomly generate the first variable $A$ then generate the second variable $B$ assuming the correlation? $\endgroup$ – Contango Sep 7 '14 at 11:03
  • $\begingroup$ Just specify the multivariate normal mean vector and covariance matrix and then draw training example vectors from that distribution. $\endgroup$ – Sycorax says Reinstate Monica Sep 7 '14 at 14:48

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