  PAC-Bayes bounds have been proposed to get risk estimates based on a training
sample. In this paper the PAC-Bayes approach is combined with stability of the
hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting
is used with a Gaussian prior centered at the expected output. Thus a novelty
of our paper is using priors defined in terms of the data-generating
distribution. Our main result estimates the risk of the randomized algorithm in
terms of the hypothesis stability coefficients. We also provide a new bound for
the SVM classifier, which is compared to other known bounds experimentally.
Ours appears to be the first stability-based bound that evaluates to
non-trivial values.
