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  1. Random Forests (RFs) is a competitive data modeling/mining method.

  2. An RF model has one output -- the output/prediction variable.

  3. The naive approach to modeling multiple outputs with RFs would be to construct an RF for each output variable. So we have N independent models, and where there is correlation between output variables we will have redundant/duplicate model structure. This could be very wasteful, indeed. Also as a general rule more model variables implies a more overfit model (less generalisation). Not sure if this applies here but it probably does.

In principle we could have an RF with multiple outputs. The prediction variable is now a vector (n-tuple). The decision nodes in each decision tree are now splitting the set of target/prediction vectors based on a threshold vector, I figure this threshold is taken to be a plane in the n-dimensional space and that therefore we can determine which side of the threshold vector each of the target vectors is on.

The optimal prediction value for each side of the decision split is the mean (centroid) calculated for the vectors on each side.

Finding the optimal split point when working with single variables is trivial and computationally fast/efficient. For an n-tuple we cannot find the optimal split (or at least it becomes computationally infeasible as N increases), but we may be able to find a near optimal split using a Monte Carlo type method (or some hybrid of Monte Carlo and local gradient traversal).

Would this actually work? That is, would it just map the training pairs without generalising? Does this technique already exist under a different name?

You might also want to consider how this relates to neural nets such as Restricted Boltzmann Machines (RBMs) and Deep Belief Networks.

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  • $\begingroup$ Googling "multilabel random forest" shows this has been even done in a few distinct ways; anyway, I have been playing with this many-binary-rfs approach in musical information retrieval and it was doing pretty well. $\endgroup$ – user88 May 23 '12 at 10:59
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    $\begingroup$ I would suggest you this article. They do something very close to what you described. $\endgroup$ – Dmitry Laptev Jun 5 '12 at 12:33
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    $\begingroup$ This already exists in the party package and some other packages (R language). $\endgroup$ – Jase Jan 30 '14 at 10:26
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Multiple output decision trees (and hence, random forests) have been developed and published. Pierre Guertz distributes a package for this (download). See also Segal & Xiao, Multivariate random forests, WIREs Data Mining Knowl Discov 2011 1 80–87, DOI: 10.1002/widm.12 I believe the latest version of Scikit-learn also supports this. A good review of the state of the art can be found in the thesis by Henrik Linusson entitled "MULTI-OUTPUT RANDOM FORESTS". The simplest method for making the split choices at each node is to randomly choose ONE of the output variables and then follow the usual random forest approach for choosing a split. Other methods based on a weighted sum of the mutual information score with respect to each input feature and output variable have been developed, but they are quite expensive compared to the randomized approach.

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As stated here:

All classifiers in scikit-learn do multiclass classification out-of-the-box.

And that includes Random Forest.

Also the page: http://scikit-learn.org/stable/modules/tree.html#tree-multioutput has a lot of references on that topic.

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    $\begingroup$ To be clear; the question relates to multi-output regression. $\endgroup$ – redcalx Apr 12 '17 at 11:42
  • $\begingroup$ Sorry for the delay in my reply but it looks like scikit-learn offers multioutput regression as well, for instance: scikit-learn.org/stable/auto_examples/tree/… And in any case, there is a strategy that consists of fitting one regressor per target. This is a simple strategy for extending regressors that do not natively support multi-target regression: scikit-learn.org/stable/modules/generated/… HTH $\endgroup$ – 0asa Jul 9 '18 at 15:17

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