| J. Langford, M. Seeger, and N. Megiddo. An improved predictive accuracy bound for averaging classifiers. In Proceedings of the Eighth International Conference on Machine Learning, 2001. |
....the training set in the MED solution. 3. 10.3 PAC Bayes Bounds An alternative to VC dimension arguments for generalization includes PAC bounds (probably approximately correct, Valiant 1984) Recent contributions in terms of a PAC Bayesian model selection criteria by McAllester [125] and Langford [116] have given theoretical generalization arguments that directly motivate the MED approach (MED was actually developed prior to the generalization results) Essentially PAC Bayesian approaches allow the combination of a Bayesian integration of prior domain knowledge with PAC generalization ....
....the generalization results) Essentially PAC Bayesian approaches allow the combination of a Bayesian integration of prior domain knowledge with PAC generalization guarantees without forcing the PAC framework to assume the truthfulness of the prior. We loosely adapt and state the main results of [116] here but further details are available from the original work as well as [125] Effectively, the generalization guarantees are for model averaging where a stochastic model selection criterion is given in favor of a deterministic one. MED is a model averaging framework in that a distribution over ....
J. Langford, M. Seeger, and N. Megiddo. An improved predictive accuracy bound for averaging classifiers. In Proceedings of the Eighth International Conference on Machine Learning, 2001.
....bound for the so called Gibbs algorithm, which selects a hypothesis at random from based on the posterior distribution #(h S) Essentially, this result provides a bound on the average error E h#QL(h) rather than a bound on the error of the averaged hypothesis. Later, Langford et al. [6] extended this result to a mixture of classifiers using a margin based loss function. A more general result can also be obtained using the covering number approach described in [14] Finally, Herbrich and Graepel [4] showed that under certain conditions the bounds for the Gibbs classifier can be ....
J. Langford, M. Seeger, and N. Megiddo. An improved predictive accuracy bound for averaging classifiers. In Proceeding of the Eighteenth International Conference on Machine Learning, pages 290--297, 2001.
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John Langford, Matthias Seeger, and Nimrod Megiddo, An Improved Predictive Accuracy Bound for Averaging Classiers ICML2001.
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John Langford, Matthias Seeger, and Nimrod Megiddo, \An Improved Predictive Accuracy Bound for Averaging Classi ers" ICML2001.
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J. Langford, M. Seeger, and N. Megiddo. An improved predictive accuracy bound for averaging classifiers. In Proceedings of the Eighth International Conference on Machine Learning, 2001.
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