Local and global sparse Gaussian process approximations

By Edward Snelson, Zoubin Ghahramani. International Conference on Artificial Intelligence and Statistics, 2007

308 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f7d96ad32e3d2476b1e6bbc40381b21a5301b4da

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Citations in the corpus

Local Gaussian Process Regression for Real Time Online Model Learning (2008, methodology): “This results in an approach inspired by [6,8] using many local GPs in order to obtain a signiﬁcant reduction of the computational cost during both prediction and learning step allowing the application to online learning.”
Incremental Variational Sparse Gaussian Process Regression (2016, background): “� This general maximum likelihood scheme for ﬁnding the inducing points is adopted with variations in [23, 26, 8, 2].”
Simultaneous quantification of epistemic and aleatory uncertainty in GMPEs using Gaussian process regression (2014, methodology): “An overview of different sparse approximation of the covariance matrix can be found in Quiñonero-Candela and Rasmussen (2005) and Snelson and Ghahramani (2007).”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, background): “In the fully independent training conditional (FITC) approximation or the fully independent conditional (FIC) approximation (Snelson and Ghahramani, 2006, 2007), a factorization across the data points is assumed.”
Robot Learning by Demonstration with local Gaussian process regression (2010, background): “The other group contains (ii) local GP approximations or mixture of experts (ME) [11], [14], [20], where the input space is divided into smaller subspaces and only points ”near” the test point are considered in prediction.”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, methodology): “3.7 Multi-resolution approximation (MRA; Katzfuss, 2017) The MRA can be viewed as an iterative extension of the FSA-block, in which the domain D is iteratively partitioned into J subregions, and we select r i variables in each of the resulting subregions, such that S i ⊂ D i .”
Fast Direct Methods for Gaussian Processes (2014, methodology): “Index Terms—Covariance function, Gaussian process, hierarchical off-diagonal low-rank, direct solver, fast multipole method, Bayesian analysis, likelihood, evidence F”
Gaussian Processes for Big Data (2013, unknown): “One approach is to partition the data set into separate groups [e.g. Snelson and Ghahramani, 2007, Urtasun and Darrell, 2008].”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, background): “Recently, attempts have been made to improve the model capability through, for example, the interdomain strategy [39], hierarchical structure [40], and hybrid of global & local approximations or neural networks (NNs) [34], [41], [42], showcasing the state-of-the-art performance [34], [43].”
Learning to Control in Operational Space (2008, methodology): “…these methods cannot be used for online, real-time training for an interesting robot system however, specialized approaches such as local Gaussian process regression (NguyenTuong 2007 Snelson and Ghahramani 2007) can be used in order to bring these function approximators into this new domain.”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, background): “Both of them rely on a set of inducing points, also referred to as inducing variables [36], [37] and basis vectors [38], whose number is usually”
Model Learning with Local Gaussian Process Regression (2009, background): “In contrast to SGP, the ME approach divides the whole input space in smaller subspaces employing a gating network which activates responsible Gaussian process experts [21, 22].”
Parametric Gaussian process regression for big data (2017, background): “sian process to a dataset of size N, exact inference has computational complexity O(N3) with storage demands of O(N2). In recent years, we have been witnessing tremendous amount of efforts (see e.g., [10, 11]) toreducethesecomplexities. SucheffortsgenerallyleadtoacomputationalcomplexityofO(NM2) and ”