PAC-Bayes bounds for stable algorithms with instance-dependent priors
This provides improved theoretical guarantees for practitioners using stable algorithms like SVMs, though it is an incremental extension of PAC-Bayes theory.
The paper tackles the problem of obtaining tighter risk estimates for stable learning algorithms by combining PAC-Bayes bounds with hypothesis stability, using data-dependent Gaussian priors. The result includes a new bound for SVM classifiers that evaluates to non-trivial values, outperforming previous stability-based bounds in experiments.
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.