"The regression trees returned by the operators W-M5P and W-REPTree"

nicugeorgian

Hello,

in the text version of the regression trees returned by W-M5P and W-REPTree: how should one read a tree branch (leaf) of the following form:

 attribute = RU,PK,TW,TR,IT <= 0.5 : : LM5 (798/81.241%) 

Does

 attribute = RU,PK,TW,TR,IT <= 0.5 

mean that attribute is not among the values RU,PK,TW,TR,IT?

LM5 is defined below the tree, and I assume it represents the value predicted (forecasted) for that leaf, correct? 

What do the numbers 798 and 81.241% represent?

It seems to me that, in my example, attribute is treated as numerical although it's categorical (nominal). Is there a way to specify before the regression trees are run?

Many thanks for any idea!

Cheers,
Geo

IngoRM

Hi,

mean that attribute  is not among the values RU,PK,TW,TR,IT?

Yes. As far as I remember this is the way how it is represented. You can get the idea if you look at the graph view.

What do the numbers 798 and 81.241% represent?

The first number is the number of training instances falling into this leaf and the second number is the root mean squared error of the linear model on these training examples divided by the global absolute deviation.

It seems to me that, in my example, attribute is treated as numerical although it's categorical (nominal). Is there a way to specify before the regression trees are run?

As far as I know the nominal attributes are internally all converted into binary attributes which are then handled as numerical (hence the split value 0.5). I don't think that you can change this behavior since it one of the basic idea of the M5 algorithm.

Cheers,
Ingo

nicugeorgian

Hi Ingo,

thanks for the explanations.

mierswa wrote:
the second number is the root mean squared error of the linear model on these training examples divided by the global absolute deviation.

What do you exactly mean by

the global absolute deviation

? Do you mean the global average absolute deviation defined as

the average of all the absolute differences between every element of the whole sample (not only the instances falling into that leaf) and the mean of the whole sample set?

Is there a document where I can see the exact definitions of the numbers in the tree's leaves?

Thanks in advance!

Cheers,
Geo

IngoRM

Hello,

the average of all the absolute differences between every element of the whole  sample (not only the instances falling into that leaf) and the mean of the whole  sample set?

Yes.

Is there a document where I can see the exact definitions of the numbers in the tree's leaves?

I took the information from the Weka source code and as far as I know there is no document describing this.

Cheers,
Ingo

BAMBAMBAM

Further questions on "text view" and "graph view" when viewing (tree) models :

This is the output (RapidMiner version 4.4)

W-REPTree
REPTree
============
Intensity < 0.98 : 0.23 (240/0.48) [144/0.49]
Intensity >= 0.98 : -0.07 (1754/0.47) [853/0.48]
Size of the tree : 3


or to simplify, for each leaf we have

Condition : A (B/C) [D/E]

I'm guessing that:

A is the label or predicted class
B is the number of training samples found at this leaf and used to calculate the statistics
C is the RMSE (root mean squared error) when 'A' is used as the prediction for the B samples,  divided by the global absolute deviation

... but I don't know what D or E are...

Any help would be appreciated.
Thanks!

land

Hi,
I'm sorry, but I'm completely unfamiliar with the weka learners. Unlike Ingo I don't even have the source code to take a deeper look into. Did you search on the Weka Mailing list for informations about that?

Greetings,
  Sebastian

radone

The code is the following in the case of numeric values:

0410:                        buffer.append(" : "
0411:                                + Utils.doubleToString(classMean, 2));
0412:                        double avgError = 0;
0413:                        if (m_Distribution[1] > 0) {
0414:                            avgError = m_Distribution[0] / m_Distribution[1];
0415:                        }
0416:                        buffer
0417:                                .append(" ("
0418:                                        + Utils.doubleToString(
0419:                                                m_Distribution[1], 2) + "/"
0420:                                        + Utils.doubleToString(avgError, 2)
0421:                                        + ")");
0422:                        avgError = 0;
0423:                        if (m_HoldOutDist[0] > 0) {
0424:                            avgError = m_HoldOutError / m_HoldOutDist[0];
0425:                        }
0426:                        buffer
0427:                                .append(" ["
0428:                                        + Utils.doubleToString(
0429:                                                m_HoldOutDist[0], 2) + "/"
0430:                                        + Utils.doubleToString(avgError, 2)
0431:                                        + "]");

and the following in the case of nominal values:

0440:                        return " : "
0441:                                + m_Info.classAttribute().value(maxIndex)
0442:                                + " ("
0443:                                + Utils.doubleToString(Utils
0444:                                        .sum(m_Distribution), 2)
0445:                                + "/"
0446:                                + Utils
0447:                                        .doubleToString(
0448:                                                (Utils.sum(m_Distribution) - m_Distribution[maxIndex]),
0449:                                                2)
0450:                                + ")"
0451:                                + " ["
0452:                                + Utils.doubleToString(
0453:                                        Utils.sum(m_HoldOutDist), 2)
0454:                                + "/"
0455:                                + Utils
0456:                                        .doubleToString(
0457:                                                (Utils.sum(m_HoldOutDist) - m_HoldOutDist[maxIndex]),
0458:                                                2) + "]";

I would be honest if anyone can understand the code.