Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond

By Christopher K. I. Williams. 1999

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Citations in the corpus

Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, neutral): “See e.g. (Williams, 1998; Neal, 1994; MacKay, 2003) for details.”
The kernel recursive least-squares algorithm (2004, methodology): “Our method is most closely related to a sparsication method used By Csat o and Opper [6, 7] in the context of learning with Gaussian Processes [13, 42 ].”
Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis (2002, methodology): “24 is equivalent with the gaussian process (GP) formulation (Gibbs, 1997; Neal, 1997; Rasmussen, 1996; Sollich, 2000; Williams, 1998; Williams & Barber, 1998) for regression.”
Optimized Cutting Plane Algorithm for Large-Scale Risk Minimization (2009, background): “Keywords: risk minimization, linear support vector machine, multi-class classification, binary classification, large-scale learning, parallelization”
The generalized LASSO (2004, methodology): “SPARSE BAYESIAN KERNEL REGRESSION Applying a Bayesian method to the regression problem requires us to specify a set of probabilistic models of the data, see, e.g., [20].”
Learning to learn with the informative vector machine (2004, background): “Copyright 2004 by the authors. cluding maximum likelihood estimation and hierarchical Bayesian learning (Williams, 1998).”
Sparse Bayesian Learning and the Relevance Vector Machine (2001, methodology): “This is a Gaussian process model (Rasmussen, 1996; MacKay, 1998; Williams, 1999): i.”
Kernels and Regularization on Graphs (2003, background): “, in Gaussian Process estimation, where K is the covariance matrix of a stochastic process [Williams, 1999].”
Transformations of Gaussian Process Priors (2004, methodology): “In the continuous case output = ∫ Ω system× inputdΩ, m(t) = ∫ K(t, x) y(x) dx (1) which could represent a nonlinear mapping fromx to m.”
Accelerating evolutionary algorithms with Gaussian process fitness function models (2005, methodology): “Since the ratios of upper to lower bounds are very large, we operate with the log of the hyperparameter values, as proposed by Williams [25].”
Learning Gaussian processes from multiple tasks (2005, unknown): “The exposition here follows (Williams, 1998).”
Learning with Kernels: support vector machines, regularization, optimization, and beyond (2001, unknown): “The Kernel Trick — Summary • any algorithm that only depends on dot products can benefit from the kernel trick • this way, we can apply linear methods to vectorial as well as non-vectorial data • think of the kernel as a nonlinear similarity measure • examples of common kernels: Polynomial k(x, x′) ”
Adaptive Sparseness for Supervised Learning (2003, methodology): “Well known discriminative approaches include linear and generalized linear models, k-nearest neighbor classifiers, tree classifiers [9], feed-forward neural networks [6], support vector machines (SVM), and other kernel-based methods [4], [7], [ 10 ].”
Advances in Large Margin Classifiers (2000, background): “The similarity is most obvious in regression, where the Support Vector solution is the maximum a posteriori estimate of the corre- sponding Bayesian inference scheme (Williams, 1998).”