PAC-Bayes bounds for stable algorithms with instance-dependent priors
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.06827
- arXiv:
- arXiv:1806.06827
- Bibcode:
- 2018arXiv180606827R
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Machine Learning
- E-Print:
- 16 pages, discussion of theory and experiments in the main body, detailed proofs and experimental details in the appendices