Rpart and bagging - how is it done?
I would like to thank Brian Ripley and Torsten Hothorn for their quick and
thoughtful responses.
I rerun the example given by Professor Ripley by just starting R and
sourcing the code below and I got slightly different results. Then I ran
it again setting the random seed before the sample command and I got
identical results a few times. However, I found the example below that
seems to be a reproducible on my system (Win200 Pro, CoreDuo Xeon about a
year old). I get the same results in 2.6.2 (patched March 4) and 2.7.0
(version of February 28). Both were compiled from the tarballs in Cygwin
and up-to-date Rtools with no errors. I just ran "make fullcheck" on 2.6.2
and it passes with no problems (just usual stuff - network conectivity
fails due to our firewall and slight numercial differences in a few cases.
The results from the rpart test are attached included at the bottom of this
post.
set.seed(123)
library(rpart)
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)
Here is what I get:
rpart(Kyphosis ~ Age + Number + Start, data=kyphosis[ind,], xval=0)
n= 81
node), split, n, loss, yval, (yprob)
* denotes terminal node
1) root 81 14 absent (0.8271605 0.1728395) *
rpart(Kyphosis ~ Age + Number + Start, data=kyphosis,
+ weights=tabulate(ind, nbins=81), xval=0)
n= 81
node), split, n, loss, yval, (yprob)
* denotes terminal node
1) root 81 14 absent (0.8271605 0.1728395)
2) Start>=8.5 62 6 absent (0.9062500 0.0937500)
4) Start>=14.5 29 0 absent (1.0000000 0.0000000) *
5) Start< 14.5 33 6 absent (0.8000000 0.2000000)
10) Age< 55 12 0 absent (1.0000000 0.0000000) *
11) Age>=55 21 6 absent (0.6000000 0.4000000)
22) Age>=111 14 2 absent (0.8000000 0.2000000) *
23) Age< 111 7 1 present (0.2000000 0.8000000) *
3) Start< 8.5 19 8 absent (0.5294118 0.4705882) *
The trees are dramatically different (the first one is just a root). The
predictions are of course different (the first model predicts all cases as
absent) but the total number of misclassified observations differs by only
1 (17 vs. 16).
Can anyone reproduce this, or is something wrong with my system?
Thanks again,
Andy
PS. rpart version is 3.1-39
rpart results from "make fullcheck"
-------- Testing package rpart --------
Massaging examples into 'rpart-Ex.R' ...
Running examples in 'rpart-Ex.R' ...
Running specific tests
Running `surv_test.R'
Running `testall.R'
Comparing `testall.Rout' to `testall.Rout.save' ...127c127
< g2 < 22.77 to the right, improve=6.8130, (6 missing)
---
g2 < 22.76 to the right, improve=6.8130, (6 missing)
159c159 < g2 < 22.77 to the right, improve=4.8340, (6 missing) ---
g2 < 22.76 to the right, improve=4.8340, (6 missing)
193c193 < grade < 3.5 to the left, agree=0.772, adj=0.188, (0 split) ---
grade < 3.5 to the left, agree=0.772, adj=0.187, (0 split)
199c199 < g2 < 13.47 to the left, improve=3.55300, (0 missing) ---
g2 < 13.48 to the left, improve=3.55300, (0 missing)
241c241 < 1) root 146 53.420 5.893e-18 ---
1) root 146 53.420 -4.563e-17
275c275 < mean=5.893e-18, MSE=0.3659 ---
mean=-4.563e-17, MSE=0.3659
346c346 < g2 < 13.47 to the left, improve=4.238e-02, (3 missing) ---
g2 < 13.48 to the left, improve=4.238e-02, (3 missing)
375c375 < g2 < 17.91 to the right, improve=0.1271000, (1 missing) ---
g2 < 17.92 to the right, improve=0.1271000, (1 missing)
515c515 < g2 < 13.47 to the left, improve=1.94600, (3 missing) ---
g2 < 13.48 to the left, improve=1.94600, (3 missing)
555c555 < g2 < 17.91 to the right, improve=3.122000, (1 missing) ---
g2 < 17.92 to the right, improve=3.122000, (1 missing)
647c647 < life < 70.25 to the right, improve=0.25230, (0 missing) ---
life < 70.26 to the right, improve=0.25230, (0 missing)
OK Running `usersplits.R' Comparing `usersplits.Rout' to `usersplits.Rout.save' ...174c174 < Timing ratio = 3.2 ---
Timing ratio = 5.9
OK
__________________________________
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
Prof Brian Ripley
<ripley at stats.ox.
ac.uk> To
apjaworski at mmm.com
03/07/2008 03:11 cc
AM Torsten.Hothorn at R-project.org
R-help at R-project.org
Subject
Re: [R] Rpart and bagging - how is
it done?
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 ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide
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and provide commented, minimal, self-contained, reproducible code.
-- 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