Regression and Classification Using Gaussian Process Priors

By James O. Berger, A. P. Dawid. 2009

436 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c2f80c32e5b922a634991ea89bcf31eee2f82a4e

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

Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences (2018, background): “RKHSs defined as powers of that RKHS; therefore GPs and RKHSs are still deeply connected in terms of the induced hypothesis spaces, and the difference such as the one mentioned by Neal [1998] should not warrant strong conceptual separation between the two frameworks.”
Handbook of Markov Chain Monte Carlo (2011, unknown): “This may not be a good strategy in general, but I have found it useful for Gaussian process models (Neal, 1998; Rasmussen and Williams, 2006), for which computation time scales as the cube of the number of data points, so that even a small reduction in the number of points produces a useful speedup.”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, methodology): “Finally we mention that in [42] the algorithm with γ = 0 is mentioned, although the derivation does not use the SPDE motivation that we develop here, and the concept of a nonparametric limit is not used to motivate the construction.”
A Bayesian nonparametric approach to marginal structural models for point treatments and a continuous or survival outcome. (2017, methodology): “Some of these forms are described in Neal (1998).”
Bayesian Semiparametric Modelling in Quantile Regression (2009, methodology): “Here, we work with data discussed in Royston & Altman (1994), and used also by Yu & Moyeed (2001) to illustrate quantile regression analysis based on an asymmetric Laplace error distribution with fixed scale parameter equal to 1 (thus, a special case of model M0).”
Picture: A probabilistic programming language for scene perception (2015, background): “Elliptical Slice Proposals: To adaptively propose changes to a large set of latent variables at once, our inference library supports elliptical slice moves with or without adaptive step sizes (see Figure 2 for an example) [4, 33].”
MCMC algorithms for Subset Simulation (2015, methodology): “It is noted that this proposal distribution has been used for sampling Gaussian process prior models (e.g. Neal 1998).”
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors (2020, methodology): “We use data from Neal (1998).”
Quasi-site-specific multivariate probability distribution model for sparse, incomplete, and three-dimensional spatially varying soil data (2021, methodology): “This method is termed GPR-MUSIC-X in this paper, because it is based on a variant of the Gaussian process regression (GPR) (e.g. Neal 1998; Rasmussen and Williams 2016; Yoshida, Tomizawa, and Otake 2021).”
Gaussian Processes in Machine Learning (2003, unknown): “One can resort to approximations, such as the Laplace approximation [3], or approximations based on projecting the non-Gaussian posterior onto the closest Gaussian (in a KL sense) [4] or sampling techniques [5].”
Uncertainty in prior elicitations: a nonparametric approach (2007, methodology): “Gaussian process priors for functions have been proposed in various different settings, including regression (O’Hagan, 1978; Neal, 1999), classification (Neal, 1999) and numerical analysis (O’Hagan, 1992).”
Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models (2019, methodology): “We adopt a fully Bayesian treatment and prescribe prior distributions over these parameters, which we will specify later [24].”
Practical options for selecting data-driven or physics-based prognostics algorithms with reviews (2015, background): “Neal [89] considered the scale parameters as distributions rather than deterministic values, and An and Choi [88] found that the result with distributions outperforms the one by deterministic values.”
Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters (2011, methodology): “The details of the integrations and the formulas involved in performing the sensitivity analysis can be found in Oakley and O’Hagan (2004). 5 Morris et al. (2008) show a practical application of Gaussian process emulation for sensitivity analysis using a radiative transfer model.”
Deep Generative Vision as Approximate Bayesian Computation (2014, unknown): “We can now formulate the image interpretation task as approximately sampling the posterior distribution of scene elements Si given observations (ID): π(S|ID) ≈ π (S|ID), where π (S|ID) = ∫ π (S, IR|ID)dIR ∝ π(S)g(IR|Θ ∗ S)IA ,ID (IR)∫ A ,ID×S π(S)g(IR|Θ ∗ S)dS (1)”
Robust Multi-Class Gaussian Process Classification (2011, background): “Robust Multi-Class Gaussian Process Classification Consider n training instances in the form of a collection of feature vectors X = {x1, . . . , xn} with associated labels y = {y1, . . . , yn}, where yi ∈ C = {1, . . . , l}.”