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PACBayes bounds for the risk of the majority vote and the variance of the Gibbs classifier
 In Neural Information Processing Systems (NIPS
, 2006
"... We propose new PACBayes bounds for the risk of the weighted majority vote that depend on the mean and variance of the error of its associated Gibbs classifier. We show that these bounds can be smaller than the risk of the Gibbs classifier and can be arbitrarily close to zero even if the risk of the ..."
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Cited by 17 (3 self)
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We propose new PACBayes bounds for the risk of the weighted majority vote that depend on the mean and variance of the error of its associated Gibbs classifier. We show that these bounds can be smaller than the risk of the Gibbs classifier and can be arbitrarily close to zero even if the risk
From PACBayes Bounds to Quadratic Programs for Majority Votes
"... We propose to construct a weighted majority vote on a set of basis functions by minimizing a risk bound (called the Cbound) that depends on the first two moments of the margin of the Qconvex combination realized on the data. This bound minimization algorithm turns out to be a quadratic program tha ..."
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Cited by 16 (6 self)
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We propose to construct a weighted majority vote on a set of basis functions by minimizing a risk bound (called the Cbound) that depends on the first two moments of the margin of the Qconvex combination realized on the data. This bound minimization algorithm turns out to be a quadratic program
PACBayes risk bounds for samplecompressed Gibbs classifiers
 Proceedings of the 22nth International Conference on Machine Learning (ICML 2005
, 2005
"... We extend the PACBayes theorem to the samplecompression setting where each classifier is represented by two independent sources of information: a compression set which consists of a small subset of the training data, and a message string of the additional information needed to obtain a classifier. ..."
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Cited by 5 (4 self)
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. The new bound is obtained by using a prior over a dataindependent set of objects where each object gives a classifier only when the training data is provided. The new PACBayes theorem states that a Gibbs classifier defined on a posterior over samplecompressed classifiers can have a smaller risk bound
A pacbayes risk bound for general loss functions
 Advances in Neural Information Processing Systems 19
, 2007
"... We provide a PACBayesian bound for the expected loss of convex combinations of classifiers under a wide class of loss functions (which includes the exponential loss and the logistic loss). Our numerical experiments with Adaboost indicate that the proposed upper bound, computed on the training set, ..."
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Cited by 5 (1 self)
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of research, known as the “PACBayes theorem”, provides a tight upper bound on the risk of a stochastic classifier (defined on the posterior Q) called the Gibbs classifier. In the context of binary classification, the Qweighted majority vote classifier (related to this stochastic
From PACBayes bounds to KL regularization
 Advances in Neural Information Processing Systems 22
, 2009
"... We show that convex KLregularized objective functions are obtained from a PACBayes risk bound when using convex loss functions for the stochastic Gibbs classifier that upperbound the standard zeroone loss used for the weighted majority vote. By restricting ourselves to a class of posteriors, tha ..."
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Cited by 9 (3 self)
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We show that convex KLregularized objective functions are obtained from a PACBayes risk bound when using convex loss functions for the stochastic Gibbs classifier that upperbound the standard zeroone loss used for the weighted majority vote. By restricting ourselves to a class of posteriors
PACBayes Risk Bounds for Stochastic Averages and Majority Votes of SampleCompressed Classifiers
, 2007
"... We propose a PACBayes theorem for the samplecompression setting where each classifier is described by a compression subset of the training data and a message string of additional information. This setting, which is the appropriate one to describe many learning algorithms, strictly generalizes the ..."
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Cited by 13 (1 self)
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We propose a PACBayes theorem for the samplecompression setting where each classifier is described by a compression subset of the training data and a message string of additional information. This setting, which is the appropriate one to describe many learning algorithms, strictly generalizes
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
A PACBayes Sample Compression Approach to Kernel Methods
"... We propose a PACBayes sample compression approach to kernel methods that can accommodate any bounded similarity function and show that the support vector machine (SVM) classifier is a particular case of a more general class of datadependent classifiers known as majority votes of samplecompressed c ..."
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Cited by 1 (0 self)
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We propose a PACBayes sample compression approach to kernel methods that can accommodate any bounded similarity function and show that the support vector machine (SVM) classifier is a particular case of a more general class of datadependent classifiers known as majority votes of samplecompressed
Additive Logistic Regression: a Statistical View of Boosting
 Annals of Statistics
, 1998
"... Boosting (Freund & Schapire 1996, Schapire & Singer 1998) is one of the most important recent developments in classification methodology. The performance of many classification algorithms can often be dramatically improved by sequentially applying them to reweighted versions of the input dat ..."
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Cited by 1719 (25 self)
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data, and taking a weighted majority vote of the sequence of classifiers thereby produced. We show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles, namely additive modeling and maximum likelihood. For the twoclass problem, boosting can
Results 1  10
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