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In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework.
Asymptotic evaluation of certain markov process expectations for large time
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Experiments with a new boosting algorithm
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Multi-class support vector machines
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Improved boosting algorithms using confidence-rated predictions
Schapire, R. E. and Singer, Y. (1999) · 1999
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BoosTexter: A boosting-based system for text categorization
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An improved predictive accuracy bound for averaging classifiers
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On the algorithmic implementation of multiclass kernel-based vector machines
Crammer, K. and Singer, Y. (2002) · 2002
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PAC-bayes & margins
Langford, J. and Shawe-Taylor, J. (2002) · 2002
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Completely bounded maps and operator algebras
Paulsen, V. (2002) · 2002
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PAC-bayesian generalization error bounds for gaussian process classification
Seeger, M. (2002) · 2002
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Simplified PAC-bayesian margin bounds
McAllester, D. A. (2003) · 2003
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4. gibbs estimators
Catoni, O. (2004) · 2004
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Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data
Lee, Y., Lin, Y., and Wahba, G. (2004) · 2004
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PAC-bayesian supervised classification: The thermodynamics of statistical learning
Catoni, O. (2007) · 2007
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PAC-bayes bounds for the risk of the majority vote and the variance of the Gibbs classifier
Lacasse, A., Laviolette, F., Marchand, M., Germain, P., and Usunier, N. (2007) · 2007
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A new approach to collaborative filtering: Operator estimation with spectral regularization
Abernethy, J., Bach, F., Evgeniou, T., and Vert, J.-P. (2009) · 2009
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Multi-class adaboost
Zhu, J., Zou, H., Rosset, S., and Hastie, T. (2009) · 2009
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From PAC-Bayes Bounds to Quadratic Programs for Majority Votes
Laviolette, F., Marchand, M., and Roy, J.-F. (2011) · 2011
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Tutorial on practical prediction theory for classification
Langford, J. (2005) · 2005
Cited alongside, same era.
PAC-bayesian model averaging
McAllester, D. A. (1999a)
Cited in the paper.
Some PAC-bayesian theorems
McAllester, D. A. (1999b)
Cited in the paper.
Mukherjee, I. and Schapire, R. E. (2011) · 2011
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User-friendly tail bounds for sums of random matrices
Tropp, J. A. (2011) · 2011
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