From: <apjaworski_at_mmm.com>

Date: Fri, 07 Mar 2008 11:00:39 -0600

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

> 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
*

*> https://stat.ethz.ch/mailman/listinfo/r-help
*

*> PLEASE do read the posting guide
*

http://www.R-project.org/posting-guide.html

> and provide commented, minimal, self-contained, reproducible code.

>

Date: Fri, 07 Mar 2008 11:00:39 -0600

I would like to thank Brian Ripley and Torsten Hothorn for their quick and
thoughtful responses.

weights=tabulate(ind, nbins=81), xval=0)

> rpart(Kyphosis ~ Age + Number + Start, data=kyphosis[ind,], xval=0)

n= 81

node), split, n, loss, yval, (yprob)

- denotes terminal node
- root 81 14 absent (0.8271605 0.1728395) *

> rpart(Kyphosis ~ Age + Number + Start, data=kyphosis,

+ weights=tabulate(ind, nbins=81), xval=0) n= 81

- root 81 14 absent (0.8271605 0.1728395) *

node), split, n, loss, yval, (yprob)

- denotes terminal node
- root 81 14 absent (0.8271605 0.1728395)
- Start>=8.5 62 6 absent (0.9062500 0.0937500)
- Start>=14.5 29 0 absent (1.0000000 0.0000000) *
- Start< 14.5 33 6 absent (0.8000000 0.2000000)
- Age< 55 12 0 absent (1.0000000 0.0000000) *
- Age>=55 21 6 absent (0.6000000 0.4000000)
- Age>=111 14 2 absent (0.8000000 0.2000000) *
- Age< 111 7 1 present (0.2000000 0.8000000) *
- 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

>

> Let me first explain why I need this and then give some details of what I

>

> I am thinking about implementing the bagging procedure in Matlab. Matlab

but

> it does not accept weights. A modification of the Matlab procedure to

>

> 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

are

> combined to produce "consensus" class predictions.

>

> Now, a typical realization of a multinomial sample consists of small

was

> this: the observations with weights equal to 0 are omitted and the

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

>

> This finally brings me to my question - is there a way to mimic the

>

> Thanks in advance for your time,

>

>

> __________________________________

>> R-help@r-project.org mailing list

> ______________________________________________

http://www.R-project.org/posting-guide.html

> 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 ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Fri 07 Mar 2008 - 17:08:49 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Mon 10 Mar 2008 - 16:30:22 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*