Gaussian Processes for Classification: Mean-Field Algorithms

By Manfred Opper, Ole Winther. 2000

277 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Expectation Propagation for approximate Bayesian inference (2001, methodology): “Figure 3 (b) plots cost vs. error for EP versus three other algorithms for estimating the Bayes point: the billiard al gorithm of Herbrich et al. (1999), the TAP algorithm of Opper & Winther (2000) , and the mean-field (MF) algo rithm of Opper & Winther (2000).”
Assessing Approximate Inference for Binary Gaussian Process Classification (2005, methodology): “Keywords: Gaussian process priors, probabilistic classification, Laplace’s approximation, expectation propagation, marginal likelihood, evidence, MCMC”
Bayesian Inference and Optimal Design in the Sparse Linear Model (2007, methodology): “In this Section, we show how to apply the recently proposed Expectation Propagation (EP) method [8, 11] to this problem, circumventing some caveats we have not seen being addressed before.”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “the adaptive TAP method of Opper and Winther [179, 180].”
Gaussian processes:iterative sparse approximations (2002, methodology): “6% as test errors [Ripley 1996; Opper and Winther 2000].”
Semiparametric latent factor models (2005, background): “This setup allows for conditional dependencies among the coordinates of _ to be expressed via { and the latent v variables.”
Fast Sparse Gaussian Process Methods: The Informative Vector Machine (2002, background): “The special case of ADF(4) for GP models has been proposed in [5].”
Cross-Validation Optimization for Large Scale Structured Classification Kernel Methods (2008, methodology): “(2004) propose an interesting approach of approximating leave-one-out (LOO) CV using expectation propagation (EP) (see also (Opper and Winther, 2000)) and use a sparse approximation for efficiency, but they deal with a single-process model only (C = 1), and it is not clear how to implement EP effici”
Bayesian Gaussian Process Classification with the EM-EP Algorithm (2006, unknown): “Ç”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, background): “…if the observation model is Gaussian (see, e.g., Shao, 1993; Orr, 1996; Peruggia, 1997; Sundararajan and Keerthi, 2001) or approximated efficiently with expectation propagation (Opper and Winther, 2000; Rasmussen and Williams, 2006) or Laplace approximation (Held, Schrödle and Rue, 2010).”
Approximate Gaussian Integration using Expectation Propagation (2011, methodology): “Here we develop an analytic approximation to F ( A ) using Expectation Propagation (EP) (Minka, 2001a,b, 2005; Opper and Winther, 2001, 2000) as an approximate integration method.”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “, n}) is the cavity TAP method of [139], and Theorem 3.”
Approximations for Binary Gaussian Process Classification (2008, methodology): “A faster “naïve” variant updating only n parameters has also been proposed (Opper and Winther, 2000) but it does not lead to the same fixed point.”
Expectation Consistent Approximate Inference (2005, methodology): “Our framework of approximation will be restricted to problems, where both parts fq and fr can be considered as tractable relative to some suitable g, and the intractability processes (Opper and Winther, 2000)–Minka introduced his EP framework and showed the equivalence of the fixed points of the two”
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, unknown): “Compare this with the exact mean, given by Opper and Winther [2000] as”