Approximations for Binary Gaussian Process Classification

By Hannes Nickisch, Carl E. Rasmussen. 2008

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Citations in the corpus

A deterministic and computable Bernstein-von Mises theorem (2019, background): “Indeed, as the number of datapoints grows, sampling methods struggle computationally since the calculation of one additional sample requires a pass through the whole dataset (but see Bardenet et al. [2014], Chen et al.”
Scalable Variational Gaussian Process Classification (2014, methodology): “The Laplace approximation is known to be relatively ineﬀective for classiﬁcation [Nickisch and Rasmussen, 2008], so it is no surprise that this variational approximation should be ineﬀective.”
Expectation propagation for neural networks with sparsity-promoting priors (2013, background): “Keywords: expectation propagation, neural network, multilayer perceptron, linear model, sparse prior, automatic relevance determination”
Gaussian Kullback-Leibler approximate inference (2013, methodology): “The G-KL bound has been noted before, empirically in the case of binary classification (Nickisch and Rasmussen, 2008) and analytically for the special case of symmetric potentials (Seeger, 2009), to be tighter than the local bound.”
A Scalable Hierarchical Gaussian Process Classifier (2019, methodology): “For a review and comparison of the approximation methods for nonconjugacy of GP two-class classification, the interested reader can refer to [8].”
Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models (2019, methodology): “We assume that the class labels are independent according to a Bernoulli likelihood with probability σ(y) [25].”
Cold-start Active Learning with Robust Ordinal Matrix Factorization (2014, methodology): “We compare our model for heteroskedastic ordinal matrix factorization (HOMF) against the following methods: i) the homoskedastic model with an ordinal likelihood in Paquet et al. (2012) (Paquet); ii) a method for robust Bayesian matrix factorization (RBMF) based on a Gaussian likelihood which includ”
Non-conjugate Variational Message Passing for Multinomial and Binary Regression (2011, result): “We also demonstrate, in agreement with [19] and [14], that for univariate expectations such as required for logistic regression, carefully designed quadrature methods can be effective.”
Learning manipulation skills from a single demonstration (2018, background): “Therefore, the GP models a discriminative function g ( θ ) which deﬁnes a class probability via the sigmoid function, Since this likelihood is non-Gaussian the exact posterior over g is not a Gaussian process—one instead uses a Laplace approximation (Nickisch and Rasmussen 2008).”
Pseudo-Marginal Bayesian Inference for Gaussian Processes (2013, background): “…the Laplace Approximation (LA) [13], Expectation Propagation (EP) [14], Variational Bayes [15], Integrated Nested Laplace Approxima-tions [16], and mean ﬁeld approximations [17]; see [18], [19] for extensive assessments of the relative merits of different approximation schemes for GP classiﬁcation.”
Safe Exploration for Active Learning with Gaussian Processes (2015, methodology): “To solve this problem, we use the efficient and accurate Laplace approximation to calculate an approximate Gaussian posterior q (g | c,X ) similar to Nickisch and Rasmussen (2008). The approximate posterior distribution forms the basis for the subsequent prediction of class affiliations for test poi”
Scalable Gaussian Process Regression Using Deep Neural Networks (2015, background): “Gaussian Processes (GPs) are widely used in regression [Rasmussen and Williams, 2006; Seeger, 2004] and classification [Nickisch and Rasmussen, 2008; Naish-Guzman and Holden, 2007] for their flexibility and competitive learnability.”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, methodology): “To this end, the binary GP classiﬁcation (GPC) model [227] with y ∈ { 0 , 1 is usually formulated as f ∼ GP (0 , k ) , p ( y f ) = Bernoulli( π ( f )) , (36) where π ( .”
Variational Heteroscedastic Gaussian Process Regression (2011, methodology): “In this work, we introduce a novel variational inference method for HGP regression that is based on variational Bayes and the Gaussian approximation (Opper & Archambeau, 2009; Nickisch & Rasmussen, 2008; Honkela et al., 2011).”
A Unifying Framework for Sparse Gaussian Process Approximation using Power Expectation Propagation (2016, background): “The main approaches of this sort can be characterised in terms of two parallel frameworks that are described in the following sections.”
MCMC for Variationally Sparse Gaussian Processes (2015, methodology): “Computation may be reduced somewhat by considering variational methods, approximating the posterior using some fixed family of distributions [13, 14, 15, 16, 1, 17], though many covariance matrix inversions are generally required.”