PAC Bayes and Margins

By J. Langford, John Shawe-Taylor. 2003

82 citations recorded by the source corpus.

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Citations in the corpus

A PAC-Bayesian bound for Lifelong Learning (2013, methodology): “For each task we use 2% of the data (approximately 20 images) available for collie class and the same amount of images from the another task, such that data between different tasks does not overlap.”
PAC-bayes bounds with data dependent priors (2012, background): “The tightest bounds for practical applications appear to be the PAC-Bayes bound (McAllester, 1999; Langford and Shawe-Taylor, 2002; Catoni, 2007) and in particular the form given in Seeger (2002), Langford (2005) and Germain et al. (2009).”
PAC-Bayesian Collective Stability (2014, methodology): “PAC-Bayesian analysis was introduced by McAllester (1999) and later refined by a number of authors (e.g., Langford and Shawe-Taylor, 2002; Seeger, 2002; Ambroladze et al., 2006; Germain et al., 2009).”
Multitask Sparsity via Maximum Entropy Discrimination (2011, methodology): “This may involve exploiting PAC-Bayesian model selectionmethods or online mistake bound methods (McAllester, 1999; Langford and Shawe-Taylor, 2002; Long and Wu, 2004) which have already given generalization arguments for the single-task MED approach.”
On Bayesian bounds (2006, background): “For example, dimension independent margin bounds can be derived by choosing the prior and posterior to be shifted versions of an identity covariance Gaussian distribution (Langford & Shawe-Taylor, 2002; McAllester, 2003b; Langford, 2005).”
Semi-supervised learning using randomized mincuts (2004, methodology): “mincuts, and also how this approach compares with the semi-supervised learning schemes of Zhu et al. (2003) and Joachims (2003).”
Chromatic PAC-Bayes Bounds for Non-IID Data (2009, background): “general Pac-Bayes bound of Germain et al. (2009) to be non degenerate). Likewise, it would be interesting to see how the possibly more accurate Pac-Bayes bound for large margin classiﬁers proposed by Langford and Shawe-taylor (2002), which should translate to the case of bipartite ranking as well, p”
Robust Forward Algorithms via PAC-Bayes and Laplace Distributions (2014, methodology): “Support vector machines [6] were analyzed using PACBayes bounds in a few contexts [23, 16].”
A Note on the PAC Bayesian Theorem (2004, methodology): “We will use this Theorem in form of the following inequalities p 2 n n e n < n! < p 2 n n e n e 1 12n : (8)”
Simplified PAC-Bayesian Margin Bounds (2003, methodology): “Here, building on the work of Langford and Shawe-Taylor [11], we use a PAC-Bayesian argument to show that with probability at least 1− δ over the choice of the sample S we have the following simultaneously for all w with ||w|| = 1 and where ln (x) abbreviates max(0, ln x).”
Tighter PAC-Bayes bounds through distribution-dependent priors (2013, methodology): “Here the stochastic predictive classifier is drawn from a Gaussian posterior centred at an SVM solution (as in Langford and Shawe-taylor, 2002) and the main result, Theorem 6, is developed by use of a distribution dependent prior.”
Stability and Generalization in Structured Prediction (2016, methodology): “PAC-Bayesian analysis is often accredited to McAllester (1998, 1999), and has been refined by a number of authors (e.g., Herbrich and Graepel, 2001; Langford and Shawe-Taylor, 2002; Seeger, 2002; Ambroladze et al., 2006; Catoni, 2007; Germain et al., 2009; Lever et al., 2010; Seldin et al., 2012).”
Human Action Segmentation and Recognition Using Discriminative Semi-Markov Models (2011, background): “2 of [14], to deal with structured output.”
Sparse multinomial logistic regression: fast algorithms and generalization bounds (2005, methodology): “While our derivation is similar to these results (especially [20]), we specifically focus on bounds for our own SMLR algorithm, both to analyze its generalization performance and to justify our choice of a Laplacian prior.”
Lifelong Learning with Non-i.i.d. Tasks (2015, background): “The empirical error of the Gibbs classifiers in the case of 0/1-loss and Gaussian distributions is given by the following expression (we again approximate the expectation by the value at θ) [20, 21]:”
Bayesian Counterfactual Risk Minimization (2018, methodology): “We have presented a PAC-Bayesian analysis of counterfactual risk minimization, for learning Bayesian policies from logged bandit feedback.”