Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)
Alexandre Lacasse, François Laviolette, Mario Marchand, Pascal Germain, Nicolas Usunier
We propose new PAC-Bayes bounds for the risk of the weighted majority vote that depend on the mean and variance of the error of its associated Gibbs classiﬁer. We show that these bounds can be smaller than the risk of the Gibbs classiﬁer and can be arbitrarily close to zero even if the risk of the Gibbs classiﬁer is close to 1/2. Moreover, we show that these bounds can be uniformly estimated on the training data for all possible posteriors Q. Moreover, they can be improved by using a large sample of unlabelled data.