Nonstationary Covariance Functions for Gaussian Process Regression

By Christopher J. Paciorek, Mark J. Schervish. 2003

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “There are many other examples of nonstationary covariance functions [3], [22], [54], [70], [118], [121], [126], [132] that have been proposed for GP regression along with closely related output warping techniques [141] that can also model certain kinds of nonstationary processes.”
Computational Phenotype Discovery Using Unsupervised Feature Learning over Noisy, Sparse, and Irregular Clinical Data (2013, neutral): “Methods exist to model this nonstationarity in Gaussian processes [46–48].”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, methodology): “Applications include the construction of nonstationary covariances (Higdon, 1998; Higdon et al., 1998; Fuentes, 2002a,b; Pciorek and Schervish, 2004) and spatiotemporal covariances (Wikle et al., 1998; Wikle, 2002, 2003).”
Spatial modelling using a new class of nonstationary covariance functions (2006, methodology): “3; Paciorek and Schervish 2004), but the MCMC computations are slow. Instead, we represent each using a basis function approximation to a stationary GP, following Kammann and Wand (2003). The vector of values of the spatial process, φ(·), at the observation locations, φ = {φ(x1), .”
Nonstationary spatial covariance functions (2005, background): “Paciorek and Schervish (2004a) discuss the use of nonstationary models for Gaussian process regression.”
Practical options for selecting data-driven or physics-based prognostics algorithms with reviews (2015, background): “Paciorek and Schervish [84] showed that the results by nonstationary covariance functions are better than those by the stationary GP, but pointed out the loss of simplicity of the algorithm, as the non-stationary GP requires more parameters.”
Dependent Gaussian Processes (2004, methodology): “The convolution approach has been used to formulate flexible nonstationary covariance functions [13, 12].”
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, unknown): “Paciorek and Schervish [2004] have generalized Gibbs’ construction to obtain non-stationary versions of arbitrary isotropic covariance functions.”
Anomaly Detection and Removal Using Non-Stationary Gaussian Processes (2015, background): “Paciorek [6] proposes a non-stationary GP kernel which guarantees continuity over region boundaries.”
MCMC Methods for MLP-network and Gaussian Process and Stuff – A documentation for Matlab Toolbox (2006, methodology): “The demonstration program demo_2input is based on the data used in Paciorek and Schervish (2004).”
Gaussian Processes for time-marked time-series data (2012, background): “While other non-parametric Gaussian Processes have been studied (Sampson and Guttorp, 1992; Nott and Dunsmuir, 2002; Schmidt and O’Hagan, 2003; Murray-Smith and Pearlmutter, 2003; Paciorek and Schervish, 2006, 2003), we consider in depth the particular case of causal GPs.”
Data-driven reduced order modeling for time-dependent problems (2019, methodology): “In such cases, we can resort to the nonstationary Gaussian process regression [31, 35].”
Gaussian process product models for nonparametric nonstationarity (2008, background): “Recently, Paciorek and Schervish (2004) extended the work of Higdon et al. (1999) to learn nonparametric variation of the covariance kernel.”
Gaussian Processes for Regression and Optimisation (2007, methodology): “We therefore describe another method for constructing non-stationary Gaussian processes, which is distinct from the nonlinear mapping approach of Gibbs [17], and the spatially variable covariance function approach described by Paciorek [52, 53].”
Bayesian Optimization over Sets (2019, background): “Moreover, because it only considers stationary kernels, GP regression is restricted to the form that cannot express non-stationary models [22].”