# On the Insufficiency of the Large Margins Theory in Explaining the Performance of Ensemble Methods

## TL;DR

This paper challenges the large margins theory by demonstrating that improving margin distribution does not necessarily enhance ensemble classifier performance, indicating the theory's insufficiency in explaining ensemble success.

## Contribution

The paper provides evidence that the large margins theory is not sufficient to explain the performance of ensemble methods, highlighting the need for alternative explanations.

## Key findings

- Improving margin distribution does not always lead to better test performance.
- Large margins are not the sole factor in ensemble generalization.
- The theory's limitations are demonstrated through specific examples.

## Abstract

Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that AdaBoost is especially effective at increasing the margins of the training data. Schapire et al. (1998) also developed an upper bound on the generalization error of any ensemble based on the margins of the training data, from which it was concluded that larger margins should lead to lower generalization error, everything else being equal (sometimes referred to as the ``large margins theory''). Tighter bounds have been derived and have reinforced the large margins theory hypothesis. For instance, Wang et al. (2011) suggest that specific margin instances, such as the equilibrium margin, can better summarize the margins distribution. These results have led many researchers to consider direct optimization of the margins to improve ensemble generalization error with mixed results. We show that the large margins theory is not sufficient for explaining the performance of voting classifiers. We do this by illustrating how it is possible to improve upon the margin distribution of an ensemble solution, while keeping the complexity fixed, yet not improve the test set performance.