

![0_image_0.png](0_image_0.png)

Table It is worth mentioning a method that averages Pi x  for each i over all level   models yielding P i x and then predicts class I for which P i x P i x for all i / I . According to b this method produces an error rate almost identical to that of majority Breiman vote

## 3.4  Why Does Stacked Generalization Work Best With M' Generated From Mlr?

We have shown that stacked generalization works best when output class probabilities rather than class predictions  are used with the MLR algorithm  rather than C
IB
NB In retrospect this is not surprising and can be explained intuitively as follows The level model should provide a simple way of combining all the evidence available This evidence includes not just the predictions  but the confidence of each level   model in its predictions  A linear combination is the simplest way of pooling the level   models confidence  and MLR provides just that The alternative methods of NB C     and IB  ea have shortcomings  A Bayesian ap proach could form the basis for a suitable alternative way of pooling the level - models confi dence  but the independence assumption central to Naive Bayes hampers its performance in some datasets because the evidence provided by the individual level    models is certainly not independent C builds trees that can model interaction amongst attributes particularly when the tree is large   but this is not desirable for combining confidences  Nearest neigh bor methods do not really give a way of combining confidences  also  the similarity  metric employed could misleadingly assume that two different sets of confidence levels are similar Table summarizes the results in Table by comparing M with M ′ for ea level generalizer  across all datasets  C     is clearly better off with a label based representation because discretizing continuous valued attributes creates intra attribute interaction in ad dition to interactions between different attributes  The evidence from Table   is that NB
is indifferent to the use of labels or confidences the normal distribution assumption that it embodies in the latter case could be another reason why it is unsuitable for combining confidence measures  Both MLR and IB  handle continuous valued attributes better than label based ones  since this is the domain in which they are designed to work

## Summary

We summarize our findings in this section as follows
- None of the four learning algorithms used to obtain model M perform satisfactorily