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PAC-Bayes bounds for stable algorithms with instance-dependent priors

Rivasplata, O; Szepesvari, C; Shawe-Taylor, J; Parrado-Hernandez, E; Shiliang, S; (2019) PAC-Bayes bounds for stable algorithms with instance-dependent priors. In: Bengio, Samy and Wallach, Hanna M. and Larochelle, Hugo and Grauman, Kristen and Cesa-Bianchi, Nicolò, (eds.) Proceedings of the 32nd International Conference on Neural Information Processing Systems - NIPS'18. (pp. pp. 9234-9244). ACM: Montréal, Canada. (In press). Green open access

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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 uniform hypothesis stability-based bound that evaluates to non-trivial values.

Type: Proceedings paper
Title: PAC-Bayes bounds for stable algorithms with instance-dependent priors
Event: 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), 2 - 8 December 2018, Montreal, Canada.
Location: Montreal, Canada
Dates: 02 December 2018 - 08 December 2018
Open access status: An open access version is available from UCL Discovery
Publisher version: https://dl.acm.org/citation.cfm?id=3327595
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/10067406
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