Introduction to Gaussian Processes

By Iain Murray. 2008

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Deep Kernel Learning (2015, methodology): “By contrast, Gaussian processes with popular kernel functions were used typically as simple smoothing devices.”
Manifold Gaussian Processes for regression (2014, methodology): “According to MacKay (1998), a function deﬁned as in Equation (10) is a valid covariance function and, therefore, the mGP is a valid GP.”
Entropy Search for Information-Efficient Global Optimization (2011, background): “…exponential kernel which induces a measure that puts nonzero mass on only smooth functions of characteristic length-scale S and signal variance s 2 (MacKay, 1998b), and the rational quadratic kernel (Mat´ern, 1960; Rasmussen and Williams, 2006) which induces a belief over smooth functions whose…”
Gaussian Process Kernels for Pattern Discovery and Extrapolation (2013, background): “Such simple smoothing devices are not a realistic replacement for neural networks, which were envisaged as intelligent agents that could discover hidden features in data 2 via adaptive basis functions (MacKay, 1998).”
Gaussian Process Regression Networks (2011, background): “…been great interest in extending Gaussian process (GP) regression to account for input dependent noise variances (Goldberg et al., 1998; Kersting et al., 2007; Adams and Stegle, 2008; Turner and Sahani, 2008; Turner, 2010; Wilson and Ghahramani, 2010a,b; L´azaro-Gredilla and Titsias, 2011).”
Computational Phenotype Discovery Using Unsupervised Feature Learning over Noisy, Sparse, and Irregular Clinical Data (2013, background): “…process regression assumes that at any time t , the posterior density is Gaussian, or where is the posterior mean value, is the posterior variance, K is a matrix with elements K ij ~ C ( t oi , t oj ) , k is a vector with elements k i ~ C ( t oi , t ) , and k ~ C ( t , t ) is a scalar [44,45].”
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control (2017, methodology): “The GP is trained via the standard procedure of evidence maximisation [21, 39].”
Gaussian processes for time-series modelling (2013, background): “Note that a valid covariance function under any arbitrary (smooth) map remains a valid covariance function [1,8].”
Variable Noise and Dimensionality Reduction for Sparse Gaussian processes (2006, methodology): “For our experiments later on we will use the standard stationary squared exponential covariance with ‘automatic relevance de-termination’ (ARD) hyperparameters [MacKay, 1998]: where θ = { c, b } and b = ( b 1 , . . . , b D ).”
Gaussian Process Covariance Kernels for Pattern Discovery and Extrapolation (2013, background): “Such simple smoothing devices are not a realistic replacement for neural networks, which were envisaged as intelligent agents that could discover hidden features in data2 via adaptive basis functions (MacKay, 1998).”
Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology (2014, background): “The exponentiated quadratic covariance can be shown [MacKay, 1998] to be the similarity between inputs after they are projected into a feature space by an infinite number of centered radial basis functions.”
Variational Gaussian Process Dynamical Systems (2011, methodology): “Then, we can optimise the 2( Q × N ) parameters ( λ q , ¯ µ q ) and obtain the original parameters using (15).”
Distributed learning and cooperative control for multi-agent systems (2009, methodology): “Other popular nonparametric approaches are Gaussian processes [23] [24] and kriging models [25].”
Generalizing Surrogate-Assisted Evolutionary Computation (2010, methodology): “The GP surrogate model [55] assumes the presence of an unknown true modeling function f (x) and an additive noise term v to account for anomalies in the observed data.”
Learning Scalable Deep Kernels with Recurrent Structure (2016, background): “Input embedding is well-known in the Gaussian process literature (e.g. MacKay, 1998; Hinton and Salakhutdinov, 2008).”
A non‐stationary covariance‐based Kriging method for metamodelling in engineering design (2007, methodology): “In our work, the MLE method is used to estimate the hyperparameters = { 2 ; )} for the non-stationary covariance.”
Hierarchical Gaussian process latent variable models (2007, methodology): “As the motion is broadly periodic, we made use of a periodic kernel (MacKay, 1998) for the regressive dynamics in each latent space (see pg.”