Bayesian Classification With Gaussian Processes

By Christopher K. I. Williams, David Barber. 1998

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Citations in the corpus

Kernel Adaptive Metropolis-Hastings (2013, methodology): “In the first experiment, we illustrate usefulness of the MCMC Kameleon sampler in the context of Bayesian classification with GPs (Williams & Barber, 1998).”
GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning (2021, methodology): “Some classic non-augmentation based methods include the Laplace approximation (Williams & Barber, 1998), expectation-propagation (Minka, 2001), and the least square approach (Rifkin & Klautau, 2004).”
Deep Neural Networks as Gaussian Processes (2017, methodology): “Future work may involve evaluating the NNGP on a cross entropy loss using the approach in (Williams & Barber, 1998; Rasmussen & Williams, 2006).”
Efficient multiple hyperparameter learning for log-linear models (2007, methodology): “This integration can be performed using a hybrid Monte Carlo strategy [27, 38].”
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, unknown): “In the coming sections, we describe two analytic approximations which both approximate the non-Gaussian joint posterior with a Gaussian one: the first is the straightforward Laplace approximation method [Williams and Barber, 1998], and the second is the more sophisticated expectation propagation (EP”
Assessing Approximate Inference for Binary Gaussian Process Classification (2005, methodology): “…chain Monte Carlo (MCMC) sampling, some of these in conjunction with generalisation bounds, online learning schemes and sparse approximations (e.g. Neal, 1998; Williams and Barber, 1998; Gibbs and MacKay, 2000; Opper and Wi ther, 2000; Csató and Opper, 2002; Seeger, 2002; Lawrence et al., 2003).”
Gaussian Processes for Ordinal Regression (2005, background): “Gaussian processes (O’Hagan, 1978; Neal, 1997) have provided a promising non-parametric Bayesian approach to metric regression (Williams and Rasmussen, 1996) and classiﬂcation problems (Williams and Barber, 1998).”
Dependent Gaussian Processes (2004, background): “Because of this they have been suggested as replacements for supervised neural networks in non-linear regression [8, 18], extended to handle classification tasks [11, 17, 6], and used in a variety of other ways (e.g. [16, 14]).”
Gaussian processes:iterative sparse approximations (2002, methodology): “For classification more approximations are needed, and the Laplace approximation for GPs [Williams and Barber 1998] was implemented leading to iterative solutions to the MAP approximation to the posterior.”
Exponential Families for Conditional Random Fields (2004, methodology): “For Φ(x, y) = ey × Φ(x) (where ey is an element of the canonical basis) we obtain the kernel proposed in [Williams and Barber, 1998].”
On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation (2010, background): “…where the problem of over-ﬁtting in both learning and model selection is greatest, the preferred approach would be to eliminate model selection altogether and opt for a fully Bayesian approach, where the hyper-parameters are integrated out rather than optimised (e.g., Williams and Barber, 1998).”
Pattern Recognition and Machine Learning (2006, unknown): “In this sense, it is analogous to the choice of a restrictive form f covariance matrix (for example, a diagonal matrix) in a multivariate Gaussian distribution.”
Bayesian Gaussian Process Classification with the EM-EP Algorithm (2006, methodology): “The Expectation Propagation (EP) algorithm is an approximate Bayesian inference method [12].”
Scalable Gaussian Process Regression Using Deep Neural Networks (2015, background): “The resulting model, Marginalized NN mixture (mixMNN1), performs better than FITC at almost the same computational cost on several low-dimensional datasets.”