Majority Votes

par/by François Laviolette
Département d'Informatique
Université Laval

In supervised learning, what can we say about democracy? Is it possible for a majority vote to be almost always correct, even if it is only composed of weak voters? It is a fact that many learning algorithms are doing so. Indeed, the popular Support Vector Machine (SVM) can be seen as a majority vote of weak learners. Nearest neighbor, Bagging, Boosting algorithms are other important examples. However, there are other situations where the majority vote can be twice as bad as the average of its voters. Until now, very few theoretical results exist for explaining whether or not a majority vote beats the average value of its voters or not. We will here present a new bound on the majority vote classifier that depend on this average value and also on the variance of the error of its associated Gibbs classifier. Moreover, we will show how this bound can be uniformly estimated on the training data for all possible weighting of the voters. Finally, we will show how the accuracy of this estimation can be improved by using a large sample of unlabeled data. The presentation is a summary of a NIPS-06 paper that can be found at: