A PAC analysis of a Bayesian estimator

By John Shawe-Taylor, Robert C. Williamson. 1997

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, background): “Since its early beginning [32, 47], the PAC-Bayesian theory claims to provide “PAC guarantees to Bayesian algorithms” (McAllester [32]).”
PAC-Bayes-Bernstein Inequality for Martingales and its Application to Multiarmed Bandits (2011, unknown): “Keywords: PAC-Bayesian Analysis, Bernstein’s Inequality, Martingales, Multiarmed Bandits, Model Order Selection, Exploration-Exploitation Trade-off”
PAC-Bayesian Inequalities for Martingales (2011, unknown): “Donsker–Varadhan’s variational formula for relative entropy laid the basis for PAC-Bayesian analysis in statistical learning theory [9]–[12], where PAC is an abbreviation for the probably approximately correct learning model introduced by Valiant [13].”
Appendix for “Learning Overlapping Representations for the Estimation of Individualized Treatment Effects” (2020, methodology): “We ﬁrst introduce Gibbs model and Bayesian model in PAC-Bayesian theory [12,15].”
Some PAC-Bayesian Theorems (1998, methodology): “The PAC-Bayesian learning theorems presented here are related to a recent theorem by Shawe-Taylor and Williamson (1997) .”
Bayesian fractional posteriors (2016, methodology): “As a second contribution, we develop oracle inequalities for the fractional posterior based on a new PAC-Bayes inequality [11, 12, 16, 27, 44, 51] in a fully general Bayesian model.”
Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates (2019, methodology): “We make repeated use of generalized notions of priors and posteriors, which arise in the PAC-Bayes literature ([7, 20, 30], etc.”
On the properties of variational approximations of Gibbs posteriors (2015, methodology): “We will follow in this paper the PAC (Probably Approximatively Correct)-Bayesian approach, which originates from machine learning [Shawe-Taylor and Williamson, 1997, McAllester, 1998, Catoni, 2004]; see Catoni [2007] for an exhaustive study, and Jiang and Tanner [2008], Yang [2004], Zhang [2006],…”
PAC-Bayesian Stochastic Model Selection (2003, methodology): “A PAC-Bayesian approach to machine learning attempts to combine the advantages of both PAC and Bayesian approaches ( Shawe-Taylor & Williamson, 1997; McAllester, 1998).”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, background): “Shawe-Taylor and Williamson [177] present a PAC analysis of a Bayesian estimator.”
PAC-Bayesian Analysis of Co-clustering and Beyond (2010, methodology): “and build upon preceding works on PAC analysis of Bayesian learning models (Shawe-Taylor et al., 1998; Shawe-Taylor and Williamson, 1997).”