PAC-bayes bounds for supervised classification

We present in this contribution a synthesis of Seeger's (PAC-Bayesian generalization error bounds for Gaussian process classification, 2002) and our own (Catoni, PAC-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning, 2007) approach of PAC-Bayes inequalities for 0-1 loss functions. We apply it to supervised classification, and more specifically to the proof of new margin bounds for support vector machines, in the spirit of the bounds established by Langford and Shawe-Taylor (Advances in Neural Information Processing Systems, 2002) and McAllester (Learning Theory and Kernel Machines, COLT 2003).