Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations

By Matthias W. Seeger. 2003

218 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, neutral): “However, despite the amount of work dedicated to this statistical learning theory—many authors improved the initial results [9, 29, 33, 43, 48] and/or generalized them for various machine learning setups [4, 14, 20, 28, 38, 44, 45, 46]—it is mostly used as a frequentist method.”
A PAC-Bayesian bound for Lifelong Learning (2013, methodology): “For more details, see (Langford, 2005; Seeger, 2003; Catoni, 2007).”
Scalable Variational Gaussian Process Classification (2014, methodology): “We note that our bound is similar to that proposed by Chai [2012] for multinomial probit regression, and also by [Seeger, 2003] for a subset-of-data approach: we propose scalability of our method through stochastic optimization of the variational parameters and inducing input positions.”
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) (2015, methodology): “Inducing point methods (Snelson and Ghahramani, 2006; Hensman et al., 2013; Quiñonero-Candela and Rasmussen, 2005; Seeger, 2005; Smola and Bartlett, 2001; Silverman, 1985) have been introduced to scale up Gaussian processes to larger datasizes.”
Asymmetric Transfer Learning with Deep Gaussian Processes (2015, background): “Furthermore, unlike non-probabilistic discriminative models, they take into account the variance of the predicted data points, which is known to boost up prediction performance (Seeger, 2003).”
Semiparametric latent factor models (2005, methodology): “In particular, we make use of the informative vector machine (IVM) framework for Gaussian processes [8, 11].”
Approximate Gaussian Integration using Expectation Propagation (2011, background): “re p(x) could be arbitrary. The exponential families are exible parametric families of distributions which contain many familiar families such as the Gaussian, Dirichlet, Poisson, etc. (Bishop, 2006; Seeger, 2003). Reusing the notation from Seeger (2003), an exponential family is dened by specifying”
Variable Noise and Dimensionality Reduction for Sparse Gaussian processes (2006, methodology): “There have been many methods proposed in recent years to address this problem, and bring the scaling down to O ( M 2 N ) where M N [Tresp, 2000, Smola and Bartlett, 2001, Williams and Seeger, 2001, Csat´o, 2002a,b, Lawrence et al., 2003, Seeger et al., 2003, Seeger, 2003, Qui˜nonero Candela, 2004].”
Assessing Approximate Inference for Binary Gaussian Process Classification (2005, background): “In the context of sparse EP approximations Seeger (2003) proposed alower bound on the marginal likelihood.”
Variational Learning of Inducing Variables in Sparse Gaussian Processes (2009, methodology): “A related objective function used in (Seeger et al., 2003) corresponds to the projected process approximation (PP).”
Approximations for Binary Gaussian Process Classification (2008, methodology): “This bound has been used in the context of sparse approximations (Seeger, 2003). ln Z = ln P (y|X, θ) = ln Z P (y|f) P (f|X, θ) df = ln Z Q (f|θ) P (y|f) P (f|X, θ) Q (f|θ) df Jensen ≥ Z Q (f|θ) ln P (y|f) P (f|X, θ) Q (f|θ) df =: ln Z B .”
Approximation Methods for Gaussian Process Regression (2007, methodology): “For methods that select X u from the training data, one typically interleaves optimization of the hyperparameters with with selection of X u , as proposed for example by Seeger et al. (2003).”
Gaussian Processes for Regression and Optimisation (2007, background): “Additionally, Seeger provides recent reviews [63, 64, 65] and relates Gaussian processes for machine learning to other kernel machine methods.”
PAC-Bayesian Bounds based on the Rényi Divergence (2016, background): “Our new proof also eases forthcoming “customizations” of the proof to obtain novel bounds.”