's are real-valued weights depending on the accuracy of h

The success of boosted classifiers is most often attributed to improvements in margins.

We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. (2021) for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the ``margins theory'' proposed by Schapire et al. (1998) for the generalisation of ensemble classifiers.

Ensemble learning is a powerful machine learning tool; it enables us to transform weak learners; hypothesis classes that are barely better than guessing, into learners with state-of-the-art performance. In essence, ensemble methods take a set of base classifiers, weigh those classifiers according to performance on the training set and retrieve the final prediction by aggregating according to those weights. An important historical example is AdaBoost (Freund and Schapire [1997]), a type of voting classifier, which builds the ensemble classifier sequentially; new base classifiers are added to the ensemble to correct the mistakes of the current ensemble. AdaBoost was the first efficient and practical implementation of a boosting algorithm, and hence the relevance of ensemble learners is often attributed to AdaBoost. Much theoretical research has been done to explain the impressive practical performance of AdaBoost and other ensemble methods.

's are real-valued weights depending on the accuracy of h