[R] Rpart and bagging - how is it done?

[Prof Brian Ripley]

I believe that the procedure you describe at the end (resampling the 
cases) is the original interpretation of bagging, and that using weighting 
is equivalent when a procedure uses case weights.

If you are getting different results when replicating cases and when using 
weights then rpart is not using its weights strictly as case weights and 
it would be preferable to replicate cases.  But I am getting identical 
predictions by the two routes:

ind <- sample(1:81, replace=TRUE)
rpart(Kyphosis ~ Age + Number + Start, data=kyphosis[ind,], xval=0)
rpart(Kyphosis ~ Age + Number + Start, data=kyphosis,
       weights=tabulate(ind, nbins=81), xval=0)

My memory is that rpart uses unweighted numbers for its control params 
(unlike tree) and hence is not strictly using case weights.  I believe you 
can avoid that by setting the control params to their minimum and relying 
on pruning.

BTW, it is inaccurate to call these trees 'non-pruned' -- the default
setting of cp is still (potentially) doing quite a lot of pruning.

Torsten Hothorn can explain why he chose to do what he did.  There's a 
small (but only small) computational advantage in using case weights, but 
the tricky issue for me is how precisely tree growth is stopped, and I 
don't think that rpart at its default settings is mimicing what Breiman 
was doing (he would have been growing much larger trees).


On Thu, 6 Mar 2008, apjaworski at mmm.com wrote:

>
> Hi there.
>
> I was wondering if somebody knows how to perform a bagging procedure on a
> classification tree without running the classifier with weights.
>
> Let me first explain why I need this and then give some details of what I
> have found out so far.
>
> I am thinking about implementing the bagging procedure in Matlab.  Matlab
> has a simple classification tree function (in their Statistics toolbox) but
> it does not accept weights.  A modification of the Matlab procedure to
> accommodate weights would be very complicated.
>
> The rpart function in R accepts weights.  This seems to allow for a rather
> simple implementation of bagging.  In fact Everitt and Hothorn in chapter 8
> of "A Handbook of Statistical Analyses Using R" describe such a procedure.
> The procedure consists in generating several samples with replacement from
> the original data set.  This data set has N rows.  The implementation
> described in the book first fits a non-pruned tree to the original data
> set.  Then it generates several (say, 25) multinomial samples of size N
> with probabilities 1/N.  Then, each sample is used in turn as the weight
> vector to update the original tree fit.  Finally, all the updated trees are
> combined to produce "consensus" class predictions.
>
> Now, a typical realization of a multinomial sample consists of small
> integers and several 0's.  I thought that the way that weighting worked was
> this:  the observations with weights equal to 0 are omitted and the
> observations with weights > 1 are essentially replicated according to the
> weight.  So I thought that instead of running the rpart procedure with
> weights, say, starting with (1, 0, 2, 0, 1, ... etc.)  I could simply
> generate a sample data set by retaining row 1, omitting row 2, replicating
> row 3 twice, omitting row 4, retaining row 5, etc.  However, this does not
> seem to work as I expected.  Instead of getting identical trees (from
> running weighted rpart on the original data set and running rpart on the
> sample data set described above with no weighting) I get trees that are
> completely different (different threshold values and different order of
> variables entering the splits).  Moreover,  the predictions from these
> trees can be different so the misclassification rates usually differ.
>
> This finally brings me to my question - is there a way to mimic the
> workings of the weighting in rpart by, for example, modification of the
> data set or, perhaps, some other means.
>
> Thanks in advance for your time,
>
> Andy
>
> __________________________________
> Andy Jaworski
> 518-1-01
> Process Laboratory
> 3M Corporate Research Laboratory
> -----
> E-mail: apjaworski at mmm.com
> Tel:  (651) 733-6092
> Fax:  (651) 736-3122
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595